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2f14ed70c4
Using surface volume for injection rather than reservoir volume. Chase change in class TransportModelCompressiblePolymer and function computeInjectedProduced(). Also changed interface to computeInjectedProduced() to take state rather than individual state variables.
1694 lines
61 KiB
C++
1694 lines
61 KiB
C++
/*
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Copyright 2012 SINTEF ICT, Applied Mathematics.
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This file is part of the Open Porous Media project (OPM).
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OPM is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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OPM is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with OPM. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include <opm/polymer/TransportModelCompressiblePolymer.hpp>
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#include <opm/core/fluid/BlackoilPropertiesInterface.hpp>
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#include <opm/core/grid.h>
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#include <opm/core/transport/reorder/reordersequence.h>
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#include <opm/core/utility/RootFinders.hpp>
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#include <opm/core/utility/miscUtilities.hpp>
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#include <opm/core/utility/miscUtilitiesBlackoil.hpp>
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#include <opm/core/pressure/tpfa/trans_tpfa.h>
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#include <cmath>
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#include <list>
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#include <opm/core/utility/ErrorMacros.hpp>
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// Choose error policy for scalar solves here.
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typedef Opm::RegulaFalsi<Opm::WarnAndContinueOnError> RootFinder;
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class Opm::TransportModelCompressiblePolymer::ResidualEquation
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{
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public:
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GradientMethod gradient_method;
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int cell;
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double s0;
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double c0;
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double cmax0;
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double influx; // B_i sum_j b_j min(v_ij, 0)*f(s_j) - B_i q_w
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double influx_polymer;
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double outflux; // sum_j max(v_ij, 0) - B_i q
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double porevolume0;
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double porevolume;
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double porosity0;
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double porosity;
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double B_cell0;
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double B_cell;
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double dtpv; // dt/pv(i)
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double dps;
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double rhor;
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double ads0;
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TransportModelCompressiblePolymer& tm;
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ResidualEquation(TransportModelCompressiblePolymer& tmodel, int cell_index);
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void computeResidual(const double* x, double* res) const;
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void computeResidual(const double* x, double* res, double& mc, double& ff) const;
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double computeResidualS(const double* x) const;
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double computeResidualC(const double* x) const;
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void computeGradientResS(const double* x, double* res, double* gradient) const;
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void computeGradientResC(const double* x, double* res, double* gradient) const;
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void computeJacobiRes(const double* x, double* dres_s_dsdc, double* dres_c_dsdc) const;
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bool solveNewtonStepSC(const double*, const double*, double*) const;
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bool solveNewtonStepC(const double* , const double*, double*) const;
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private:
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void computeResAndJacobi(const double* x, const bool if_res_s, const bool if_res_c,
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const bool if_dres_s_dsdc, const bool if_dres_c_dsdc,
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double* res, double* dres_s_dsdc,
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double* dres_c_dsdc, double& mc, double& ff) const;
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};
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class Opm::TransportModelCompressiblePolymer::ResidualCGrav {
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public:
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const TransportModelCompressiblePolymer& tm;
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const int cell;
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const double s0;
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const double c0;
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const double cmax0;
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const double porevolume;
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const double porosity;
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const double dtpv; // dt/pv(i)
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const double dps;
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const double rhor;
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double c_ads0;
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double gf[2];
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int nbcell[2];
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mutable double last_s;
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ResidualCGrav(const TransportModelCompressiblePolymer& tmodel,
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const std::vector<int>& cells,
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const int pos,
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const double* gravflux);
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double operator()(double c) const;
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double computeGravResidualS(double s, double c) const;
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double computeGravResidualC(double s, double c) const;
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double lastSaturation() const;
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};
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class Opm::TransportModelCompressiblePolymer::ResidualSGrav {
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public:
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const ResidualCGrav& res_c_eq_;
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double c;
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ResidualSGrav(const ResidualCGrav& res_c_eq, const double c_init = 0.0);
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double operator()(double s) const;
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};
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namespace
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{
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bool check_interval(const double* xmin, const double* xmax, double* x);
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double norm(double* res)
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{
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return std::max(std::abs(res[0]), std::abs(res[1]));
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}
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// Define a piecewise linear curve along which we will look for zero of the "s" or "r" residual.
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// The curve starts at "x", goes along the direction "direction" until it hits the boundary of the box of
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// admissible values for "s" and "x" (which is given by "[x_min[0], x_max[0]]x[x_min[1], x_max[1]]").
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// Then it joins in a straight line the point "end_point".
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class CurveInSCPlane{
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public:
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CurveInSCPlane();
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void setup(const double* x, const double* direction,
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const double* end_point, const double* x_min,
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const double* x_max, const double tol,
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double& t_max_out, double& t_out_out);
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void computeXOfT(double*, const double) const;
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private:
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double direction_[2];
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double end_point_[2];
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double x_max_[2];
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double x_min_[2];
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double t_out_;
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double t_max_; // t_max = t_out + 1
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double x_out_[2];
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double x_[2];
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};
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}
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namespace Opm
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{
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TransportModelCompressiblePolymer::TransportModelCompressiblePolymer(const UnstructuredGrid& grid,
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const BlackoilPropertiesInterface& props,
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const PolymerProperties& polyprops,
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const RockCompressibility& rock_comp,
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const SingleCellMethod method,
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const double tol,
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const int maxit)
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: grid_(grid),
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props_(props),
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polyprops_(polyprops),
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rock_comp_(rock_comp),
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darcyflux_(0),
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porevolume0_(0),
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porevolume_(0),
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source_(0),
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polymer_inflow_c_(0),
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dt_(0.0),
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tol_(tol),
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maxit_(maxit),
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method_(method),
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adhoc_safety_(1.1),
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concentration_(0),
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cmax_(0),
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fractionalflow_(grid.number_of_cells, -1.0),
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mc_(grid.number_of_cells, -1.0),
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gravity_(0),
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mob_(2*grid.number_of_cells, -1.0),
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ia_upw_(grid.number_of_cells + 1, -1),
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ja_upw_(grid.number_of_faces, -1),
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ia_downw_(grid.number_of_cells + 1, -1),
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ja_downw_(grid.number_of_faces, -1)
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{
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const int np = props.numPhases();
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const int num_cells = grid.number_of_cells;
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if (props.numPhases() != 2) {
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THROW("Property object must have 2 phases");
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}
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visc_.resize(np*num_cells);
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A_.resize(np*np*num_cells);
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A0_.resize(np*np*num_cells);
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smin_.resize(np*num_cells);
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smax_.resize(np*num_cells);
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allcells_.resize(num_cells);
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for (int i = 0; i < num_cells; ++i) {
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allcells_[i] = i;
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}
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props.satRange(num_cells, &allcells_[0], &smin_[0], &smax_[0]);
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}
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void TransportModelCompressiblePolymer::setPreferredMethod(SingleCellMethod method)
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{
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method_ = method;
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}
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void TransportModelCompressiblePolymer::solve(const double* darcyflux,
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const std::vector<double>& initial_pressure,
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const std::vector<double>& pressure,
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const double* porevolume0,
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const double* porevolume,
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const double* source,
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const double* polymer_inflow_c,
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const double dt,
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std::vector<double>& saturation,
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std::vector<double>& surfacevol,
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std::vector<double>& concentration,
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std::vector<double>& cmax)
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{
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darcyflux_ = darcyflux;
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porevolume0_ = porevolume0;
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porevolume_ = porevolume;
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source_ = source;
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dt_ = dt;
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polymer_inflow_c_ = polymer_inflow_c;
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toWaterSat(saturation, saturation_);
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concentration_ = &concentration[0];
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cmax_ = &cmax[0];
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#if PROFILING
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res_counts.clear();
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#endif
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props_.viscosity(grid_.number_of_cells, &pressure[0], NULL, &allcells_[0], &visc_[0], NULL);
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props_.matrix(grid_.number_of_cells, &initial_pressure[0], NULL, &allcells_[0], &A0_[0], NULL);
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props_.matrix(grid_.number_of_cells, &pressure[0], NULL, &allcells_[0], &A_[0], NULL);
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// Check immiscibility requirement (only done for first cell).
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if (A_[1] != 0.0 || A_[2] != 0.0) {
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THROW("TransportCompressibleModelCompressibleTwophase requires a property object without miscibility.");
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}
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std::vector<int> seq(grid_.number_of_cells);
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std::vector<int> comp(grid_.number_of_cells + 1);
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int ncomp;
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compute_sequence_graph(&grid_, darcyflux_,
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&seq[0], &comp[0], &ncomp,
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&ia_upw_[0], &ja_upw_[0]);
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const int nf = grid_.number_of_faces;
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std::vector<double> neg_darcyflux(nf);
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std::transform(darcyflux, darcyflux + nf, neg_darcyflux.begin(), std::negate<double>());
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compute_sequence_graph(&grid_, &neg_darcyflux[0],
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&seq[0], &comp[0], &ncomp,
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&ia_downw_[0], &ja_downw_[0]);
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reorderAndTransport(grid_, darcyflux);
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toBothSat(saturation_, saturation);
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// Compute surface volume as a postprocessing step from saturation and A_
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computeSurfacevol(grid_.number_of_cells, props_.numPhases(), &A_[0], &saturation[0], &surfacevol[0]);
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}
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// Residual for saturation equation, single-cell implicit Euler transport
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//
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// r(s) = s - s0 + dt/pv*( influx + outflux*f(s) )
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//
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// where influx is water influx, outflux is total outflux.
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// Influxes are negative, outfluxes positive.
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struct TransportModelCompressiblePolymer::ResidualS
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{
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TransportModelCompressiblePolymer::ResidualEquation& res_eq_;
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const double c_;
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explicit ResidualS(TransportModelCompressiblePolymer::ResidualEquation& res_eq,
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const double c)
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: res_eq_(res_eq),
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c_(c)
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{
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}
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double operator()(double s) const
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{
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double x[2];
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x[0] = s;
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x[1] = c_;
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return res_eq_.computeResidualS(x);
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}
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};
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// Residual for concentration equation, single-cell implicit Euler transport
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//
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// \TODO doc me
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// where ...
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// Influxes are negative, outfluxes positive.
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struct TransportModelCompressiblePolymer::ResidualC
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{
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mutable double s; // Mutable in order to change it with every operator() call to be the last computed s value.
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TransportModelCompressiblePolymer::ResidualEquation& res_eq_;
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explicit ResidualC(TransportModelCompressiblePolymer::ResidualEquation& res_eq)
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: res_eq_(res_eq)
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{}
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void computeBothResiduals(const double s_arg, const double c_arg, double& res_s, double& res_c, double& mc, double& ff) const
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{
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double x[2];
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double res[2];
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x[0] = s_arg;
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x[1] = c_arg;
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res_eq_.computeResidual(x, res, mc, ff);
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res_s = res[0];
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res_c = res[1];
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}
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double operator()(double c) const
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{
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ResidualS res_s(res_eq_, c);
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int iters_used;
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// Solve for s first.
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// s = modifiedRegulaFalsi(res_s, std::max(tm.smin_[2*cell], dps), tm.smax_[2*cell],
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// tm.maxit_, tm.tol_, iters_used);
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s = RootFinder::solve(res_s, res_eq_.s0, 0.0, 1.0,
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res_eq_.tm.maxit_, res_eq_.tm.tol_, iters_used);
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double x[2];
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x[0] = s;
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x[1] = c;
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double res = res_eq_.computeResidualC(x);
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#ifdef EXTRA_DEBUG_OUTPUT
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std::cout << "c = " << c << " s = " << s << " c-residual = " << res << std::endl;
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#endif
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return res;
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}
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double lastSaturation() const
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{
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return s;
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}
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};
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// ResidualEquation gathers parameters to construct the residual, computes its
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// value and the values of its derivatives.
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TransportModelCompressiblePolymer::ResidualEquation::ResidualEquation(TransportModelCompressiblePolymer& tmodel, int cell_index)
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: tm(tmodel)
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{
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gradient_method = Analytic;
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cell = cell_index;
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const int np = tm.props_.numPhases();
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s0 = tm.saturation_[cell];
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c0 = tm.concentration_[cell];
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cmax0 = tm.cmax_[cell];
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double src_flux = -tm.source_[cell];
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bool src_is_inflow = src_flux < 0.0;
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B_cell0 = 1.0/tm.A0_[np*np*cell + 0];
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B_cell = 1.0/tm.A_[np*np*cell + 0];
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influx = src_is_inflow ? B_cell*src_flux : 0.0;
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outflux = !src_is_inflow ? src_flux : 0.0;
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porevolume0 = tm.porevolume0_[cell];
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porevolume = tm.porevolume_[cell];
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const double vol_cell = tm.grid_.cell_volumes[cell];
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porosity0 = porevolume0/vol_cell;
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porosity = porevolume/vol_cell;
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dtpv = tm.dt_/porevolume;
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dps = tm.polyprops_.deadPoreVol();
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rhor = tm.polyprops_.rockDensity();
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tm.polyprops_.adsorption(c0, cmax0, ads0);
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double mc;
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tm.computeMc(tm.polymer_inflow_c_[cell_index], mc);
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influx_polymer = src_is_inflow ? src_flux*mc : 0.0;
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for (int i = tm.grid_.cell_facepos[cell]; i < tm.grid_.cell_facepos[cell+1]; ++i) {
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int f = tm.grid_.cell_faces[i];
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double flux;
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int other;
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// Compute cell flux
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if (cell == tm.grid_.face_cells[2*f]) {
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flux = tm.darcyflux_[f];
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other = tm.grid_.face_cells[2*f+1];
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} else {
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flux =-tm.darcyflux_[f];
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other = tm.grid_.face_cells[2*f];
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}
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// Add flux to influx or outflux, if interior.
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if (other != -1) {
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if (flux < 0.0) {
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const double b_face =tm.A_[np*np*other+ 0];
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influx += B_cell*b_face*flux*tm.fractionalflow_[other];
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influx_polymer += flux*tm.fractionalflow_[other]*tm.mc_[other];
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} else {
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outflux += flux; // Because B_cell*b_face = 1 for outflow faces
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}
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}
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}
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}
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void TransportModelCompressiblePolymer::ResidualEquation::computeResidual(const double* x, double* res) const
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{
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double dres_s_dsdc[2];
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double dres_c_dsdc[2];
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double mc;
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double ff;
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computeResAndJacobi(x, true, true, false, false, res, dres_s_dsdc, dres_c_dsdc, mc, ff);
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}
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void TransportModelCompressiblePolymer::ResidualEquation::computeResidual(const double* x, double* res, double& mc, double& ff) const
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{
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double dres_s_dsdc[2];
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double dres_c_dsdc[2];
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computeResAndJacobi(x, true, true, false, false, res, dres_s_dsdc, dres_c_dsdc, mc, ff);
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}
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double TransportModelCompressiblePolymer::ResidualEquation::computeResidualS(const double* x) const
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{
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double res[2];
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double dres_s_dsdc[2];
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double dres_c_dsdc[2];
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double mc;
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double ff;
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computeResAndJacobi(x, true, false, false, false, res, dres_s_dsdc, dres_c_dsdc, mc, ff);
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return res[0];
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}
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double TransportModelCompressiblePolymer::ResidualEquation::computeResidualC(const double* x) const
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{
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double res[2];
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double dres_s_dsdc[2];
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double dres_c_dsdc[2];
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double mc;
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double ff;
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computeResAndJacobi(x, false, true, false, false, res, dres_s_dsdc, dres_c_dsdc, mc, ff);
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return res[1];
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}
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void TransportModelCompressiblePolymer::ResidualEquation::computeGradientResS(const double* x, double* res, double* gradient) const
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// If gradient_method == FinDif, use finite difference
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// If gradient_method == Analytic, use analytic expresions
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{
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double dres_c_dsdc[2];
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double mc;
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double ff;
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computeResAndJacobi(x, true, true, true, false, res, gradient, dres_c_dsdc, mc, ff);
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}
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void TransportModelCompressiblePolymer::ResidualEquation::computeGradientResC(const double* x, double* res, double* gradient) const
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// If gradient_method == FinDif, use finite difference
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// If gradient_method == Analytic, use analytic expresions
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{
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double dres_s_dsdc[2];
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double mc;
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double ff;
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computeResAndJacobi(x, true, true, false, true, res, dres_s_dsdc, gradient, mc, ff);
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}
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// Compute the Jacobian of the residual equations.
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void TransportModelCompressiblePolymer::ResidualEquation::computeJacobiRes(const double* x, double* dres_s_dsdc, double* dres_c_dsdc) const
|
|
{
|
|
double res[2];
|
|
double mc;
|
|
double ff;
|
|
computeResAndJacobi(x, false, false, true, true, res, dres_s_dsdc, dres_c_dsdc, mc, ff);
|
|
}
|
|
|
|
void TransportModelCompressiblePolymer::ResidualEquation::computeResAndJacobi(const double* x, const bool if_res_s, const bool if_res_c,
|
|
const bool if_dres_s_dsdc, const bool if_dres_c_dsdc,
|
|
double* res, double* dres_s_dsdc,
|
|
double* dres_c_dsdc, double& mc, double& ff) const
|
|
{
|
|
if ((if_dres_s_dsdc || if_dres_c_dsdc) && gradient_method == Analytic) {
|
|
double s = x[0];
|
|
double c = x[1];
|
|
double dff_dsdc[2];
|
|
double mc_dc;
|
|
double ads_dc;
|
|
double ads;
|
|
tm.fracFlowWithDer(s, c, cmax0, cell, ff, dff_dsdc);
|
|
if (if_dres_c_dsdc) {
|
|
tm.polyprops_.adsorptionWithDer(c, cmax0, ads, ads_dc);
|
|
tm.computeMcWithDer(c, mc, mc_dc);
|
|
} else {
|
|
tm.polyprops_.adsorption(c, cmax0, ads);
|
|
tm.computeMc(c, mc);
|
|
}
|
|
if (if_res_s) {
|
|
res[0] = s - B_cell/B_cell0*porosity0/porosity*s0 + dtpv*(outflux*ff + influx);
|
|
#if PROFILING
|
|
tm.res_counts.push_back(Newton_Iter(true, cell, x[0], x[1]));
|
|
#endif
|
|
}
|
|
if (if_res_c) {
|
|
// Not clear if the rock compressibility should be
|
|
// considered as a constant in the adsorption term.
|
|
res[1] = (1 - dps)*s*c - (1 - dps)*B_cell/B_cell0*porosity0/porosity*s0*c0
|
|
+ rhor*B_cell/porosity*((1.0 - porosity)*ads - (1.0 - porosity0)*ads0)
|
|
+ dtpv*(outflux*ff*mc + influx_polymer);
|
|
#if PROFILING
|
|
tm.res_counts.push_back(Newton_Iter(false, cell, x[0], x[1]));
|
|
#endif
|
|
}
|
|
if (if_dres_s_dsdc) {
|
|
dres_s_dsdc[0] = 1 + dtpv*outflux*dff_dsdc[0];
|
|
dres_s_dsdc[1] = dtpv*outflux*dff_dsdc[1];
|
|
}
|
|
if (if_dres_c_dsdc) {
|
|
dres_c_dsdc[0] = (1.0 - dps)*c + dtpv*outflux*dff_dsdc[0]*mc;
|
|
dres_c_dsdc[1] = (1 - dps)*s + rhor*B_cell/porosity*(1.0 - porosity)*ads_dc
|
|
+ dtpv*outflux*(dff_dsdc[1]*mc + ff*mc_dc);
|
|
}
|
|
|
|
} else if (if_res_c || if_res_s) {
|
|
double s = x[0];
|
|
double c = x[1];
|
|
tm.fracFlow(s, c, cmax0, cell, ff);
|
|
if (if_res_s) {
|
|
res[0] = s - B_cell/B_cell0*porosity0/porosity*s0 + dtpv*(outflux*ff + influx);
|
|
#if PROFILING
|
|
tm.res_counts.push_back(Newton_Iter(true, cell, x[0], x[1]));
|
|
#endif
|
|
}
|
|
if (if_res_c) {
|
|
tm.computeMc(c, mc);
|
|
double ads;
|
|
tm.polyprops_.adsorption(c, cmax0, ads);
|
|
res[1] = (1 - dps)*s*c - (1 - dps)*B_cell/B_cell0*porosity0/porosity*s0*c0
|
|
+ rhor*B_cell/porosity*((1.0 - porosity)*ads - (1.0 - porosity0)*ads0)
|
|
+ dtpv*(outflux*ff*mc + influx_polymer);
|
|
#if PROFILING
|
|
tm.res_counts.push_back(Newton_Iter(false, cell, x[0], x[1]));
|
|
#endif
|
|
}
|
|
}
|
|
|
|
if ((if_dres_c_dsdc || if_dres_s_dsdc) && gradient_method == FinDif) {
|
|
double epsi = 1e-8;
|
|
double res_epsi[2];
|
|
double res_0[2];
|
|
double x_epsi[2];
|
|
computeResidual(x, res_0);
|
|
if (if_dres_s_dsdc) {
|
|
x_epsi[0] = x[0] + epsi;
|
|
x_epsi[1] = x[1];
|
|
computeResidual(x_epsi, res_epsi);
|
|
dres_s_dsdc[0] = (res_epsi[0] - res_0[0])/epsi;
|
|
x_epsi[0] = x[0];
|
|
x_epsi[1] = x[1] + epsi;
|
|
computeResidual(x_epsi, res_epsi);
|
|
dres_s_dsdc[1] = (res_epsi[0] - res_0[0])/epsi;
|
|
}
|
|
if (if_dres_c_dsdc) {
|
|
x_epsi[0] = x[0] + epsi;
|
|
x_epsi[1] = x[1];
|
|
computeResidual(x_epsi, res_epsi);
|
|
dres_c_dsdc[0] = (res_epsi[1] - res_0[1])/epsi;
|
|
x_epsi[0] = x[0];
|
|
x_epsi[1] = x[1] + epsi;
|
|
computeResidual(x_epsi, res_epsi);
|
|
dres_c_dsdc[1] = (res_epsi[1] - res_0[1])/epsi;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Compute the "s" residual along the curve "curve" for a given residual equation "res_eq".
|
|
// The operator() is sent to a root solver.
|
|
class TransportModelCompressiblePolymer::ResSOnCurve
|
|
{
|
|
public:
|
|
ResSOnCurve(const TransportModelCompressiblePolymer::ResidualEquation& res_eq);
|
|
double operator()(const double t) const;
|
|
CurveInSCPlane curve;
|
|
private:
|
|
const TransportModelCompressiblePolymer::ResidualEquation& res_eq_;
|
|
};
|
|
|
|
// Compute the "c" residual along the curve "curve" for a given residual equation "res_eq".
|
|
// The operator() is sent to a root solver.
|
|
class TransportModelCompressiblePolymer::ResCOnCurve
|
|
{
|
|
public:
|
|
ResCOnCurve(const TransportModelCompressiblePolymer::ResidualEquation& res_eq);
|
|
double operator()(const double t) const;
|
|
CurveInSCPlane curve;
|
|
private:
|
|
const TransportModelCompressiblePolymer::ResidualEquation& res_eq_;
|
|
};
|
|
|
|
TransportModelCompressiblePolymer::ResSOnCurve::ResSOnCurve(const TransportModelCompressiblePolymer::ResidualEquation& res_eq)
|
|
: res_eq_(res_eq)
|
|
{
|
|
}
|
|
|
|
double TransportModelCompressiblePolymer::ResSOnCurve::operator()(const double t) const
|
|
{
|
|
double x_of_t[2];
|
|
double x_c[2];
|
|
curve.computeXOfT(x_of_t, t);
|
|
res_eq_.tm.scToc(x_of_t, x_c);
|
|
return res_eq_.computeResidualS(x_c);
|
|
}
|
|
|
|
TransportModelCompressiblePolymer::ResCOnCurve::ResCOnCurve(const TransportModelCompressiblePolymer::ResidualEquation& res_eq)
|
|
: res_eq_(res_eq)
|
|
{
|
|
}
|
|
|
|
double TransportModelCompressiblePolymer::ResCOnCurve::operator()(const double t) const
|
|
{
|
|
double x_of_t[2];
|
|
double x_c[2];
|
|
curve.computeXOfT(x_of_t, t);
|
|
res_eq_.tm.scToc(x_of_t, x_c);
|
|
return res_eq_.computeResidualC(x_c);
|
|
}
|
|
|
|
|
|
|
|
void TransportModelCompressiblePolymer::solveSingleCell(const int cell)
|
|
{
|
|
switch (method_) {
|
|
case Bracketing:
|
|
solveSingleCellBracketing(cell);
|
|
break;
|
|
case Newton:
|
|
solveSingleCellNewton(cell);
|
|
break;
|
|
case Gradient:
|
|
solveSingleCellGradient(cell);
|
|
break;
|
|
case NewtonSimpleSC:
|
|
solveSingleCellNewtonSimple(cell,true);
|
|
break;
|
|
case NewtonSimpleC:
|
|
solveSingleCellNewtonSimple(cell,false);
|
|
break;
|
|
default:
|
|
THROW("Unknown method " << method_);
|
|
}
|
|
}
|
|
|
|
|
|
void TransportModelCompressiblePolymer::solveSingleCellBracketing(int cell)
|
|
{
|
|
|
|
ResidualEquation res_eq(*this, cell);
|
|
ResidualC res(res_eq);
|
|
const double a = 0.0;
|
|
const double b = polyprops_.cMax()*adhoc_safety_; // Add 10% to account for possible non-monotonicity of hyperbolic system.
|
|
int iters_used;
|
|
|
|
// Check if current state is an acceptable solution.
|
|
double res_sc[2];
|
|
double mc, ff;
|
|
res.computeBothResiduals(saturation_[cell], concentration_[cell], res_sc[0], res_sc[1], mc, ff);
|
|
if (norm(res_sc) < tol_) {
|
|
fractionalflow_[cell] = ff;
|
|
mc_[cell] = mc;
|
|
return;
|
|
}
|
|
|
|
concentration_[cell] = RootFinder::solve(res, a, b, maxit_, tol_, iters_used);
|
|
cmax_[cell] = std::max(cmax_[cell], concentration_[cell]);
|
|
saturation_[cell] = res.lastSaturation();
|
|
fracFlow(saturation_[cell], concentration_[cell], cmax_[cell], cell,
|
|
fractionalflow_[cell]);
|
|
computeMc(concentration_[cell], mc_[cell]);
|
|
}
|
|
|
|
|
|
|
|
// Newton method, where we first try a Newton step. Then, if it does not work well, we look for
|
|
// the zero of either the residual in s or the residual in c along a specified piecewise linear
|
|
// curve. In these cases, we can use a robust 1d solver.
|
|
void TransportModelCompressiblePolymer::solveSingleCellGradient(int cell)
|
|
{
|
|
int iters_used_falsi = 0;
|
|
const int max_iters_split = maxit_;
|
|
int iters_used_split = 0;
|
|
|
|
// Check if current state is an acceptable solution.
|
|
ResidualEquation res_eq(*this, cell);
|
|
double x[2] = {saturation_[cell], saturation_[cell]*concentration_[cell]};
|
|
double res[2];
|
|
double mc;
|
|
double ff;
|
|
double x_c[2];
|
|
scToc(x, x_c);
|
|
res_eq.computeResidual(x_c, res, mc, ff);
|
|
if (norm(res) <= tol_) {
|
|
cmax_[cell] = std::max(cmax_[cell], concentration_[cell]);
|
|
fractionalflow_[cell] = ff;
|
|
mc_[cell] = mc;
|
|
return;
|
|
}
|
|
|
|
double x_min[2] = { 0.0, 0.0 };
|
|
double x_max[2] = { 1.0, polyprops_.cMax()*adhoc_safety_ };
|
|
double x_min_res_s[2] = { x_min[0], x_min[1] };
|
|
double x_max_res_s[2] = { x_max[0], x_min[0] };
|
|
double x_min_res_sc[2] = { x_min[0], x_min[1] };
|
|
double x_max_res_sc[2] = { x_max[0], x_max[1] };
|
|
double t;
|
|
double t_max;
|
|
double t_out;
|
|
double direction[2];
|
|
double end_point[2];
|
|
double gradient[2];
|
|
ResSOnCurve res_s_on_curve(res_eq);
|
|
ResCOnCurve res_c_on_curve(res_eq);
|
|
bool if_res_s;
|
|
|
|
while ((norm(res) > tol_) && (iters_used_split < max_iters_split)) {
|
|
if (std::abs(res[0]) < std::abs(res[1])) {
|
|
if (res[0] < -tol_) {
|
|
direction[0] = x_max_res_s[0] - x[0];
|
|
direction[1] = x_max_res_s[1] - x[1];
|
|
if_res_s = true;
|
|
} else if (res[0] > tol_) {
|
|
direction[0] = x_min_res_s[0] - x[0];
|
|
direction[1] = x_min_res_s[1] - x[1];
|
|
if_res_s = true;
|
|
} else {
|
|
scToc(x, x_c);
|
|
res_eq.computeGradientResS(x_c, res, gradient);
|
|
// dResS/d(s_) = dResS/ds - c/s*dResS/ds
|
|
// dResS/d(sc_) = -1/s*dResS/dc
|
|
if (x[0] > 1e-2*tol_) {
|
|
// With s,c variables, we should have
|
|
// direction[0] = -gradient[1];
|
|
// direction[1] = gradient[0];
|
|
// With s, sc variables, we get:
|
|
scToc(x, x_c);
|
|
direction[0] = 1.0/x[0]*gradient[1];
|
|
direction[1] = gradient[0] - x_c[1]/x[0]*gradient[1];
|
|
} else {
|
|
// acceptable approximation for nonlinear relative permeability.
|
|
direction[0] = 0.0;
|
|
direction[1] = gradient[0];
|
|
}
|
|
if_res_s = false;
|
|
}
|
|
} else {
|
|
if (res[1] < -tol_) {
|
|
direction[0] = x_max_res_sc[0] - x[0];
|
|
direction[1] = x_max_res_sc[1] - x[1];
|
|
if_res_s = false;
|
|
} else if (res[1] > tol_) {
|
|
direction[0] = x_min_res_sc[0] - x[0];
|
|
direction[1] = x_min_res_sc[1] - x[1];
|
|
if_res_s = false;
|
|
} else {
|
|
res_eq.computeGradientResC(x, res, gradient);
|
|
// dResC/d(s_) = dResC/ds - c/s*dResC/ds
|
|
// dResC/d(sc_) = -1/s*dResC/dc
|
|
if (x[0] > 1e-2*tol_) {
|
|
// With s,c variables, we should have
|
|
// direction[0] = -gradient[1];
|
|
// direction[1] = gradient[0];
|
|
// With s, sc variables, we get:
|
|
scToc(x, x_c);
|
|
direction[0] = 1.0/x[0]*gradient[1];
|
|
direction[1] = gradient[0] - x_c[1]/x[0]*gradient[1];
|
|
} else {
|
|
// We take 1.0/s*gradient[1]: wrong for linear permeability,
|
|
// acceptable for nonlinear relative permeability.
|
|
direction[0] = 1.0 - res_eq.dps;
|
|
direction[1] = gradient[0];
|
|
}
|
|
if_res_s = true;
|
|
}
|
|
}
|
|
if (if_res_s) {
|
|
if (res[0] < 0) {
|
|
end_point[0] = x_max_res_s[0];
|
|
end_point[1] = x_max_res_s[1];
|
|
res_s_on_curve.curve.setup(x, direction, end_point, x_min, x_max, tol_, t_max, t_out);
|
|
if (res_s_on_curve(t_out) >= 0) {
|
|
t_max = t_out;
|
|
}
|
|
} else {
|
|
end_point[0] = x_min_res_s[0];
|
|
end_point[1] = x_min_res_s[1];
|
|
res_s_on_curve.curve.setup(x, direction, end_point, x_min, x_max, tol_, t_max, t_out);
|
|
if (res_s_on_curve(t_out) <= 0) {
|
|
t_max = t_out;
|
|
}
|
|
}
|
|
// Note: In some experiments modifiedRegularFalsi does not yield a result under the given tolerance.
|
|
t = RootFinder::solve(res_s_on_curve, 0., t_max, maxit_, tol_, iters_used_falsi);
|
|
res_s_on_curve.curve.computeXOfT(x, t);
|
|
} else {
|
|
if (res[1] < 0) {
|
|
end_point[0] = x_max_res_sc[0];
|
|
end_point[1] = x_max_res_sc[1];
|
|
res_c_on_curve.curve.setup(x, direction, end_point, x_min, x_max, tol_, t_max, t_out);
|
|
if (res_c_on_curve(t_out) >= 0) {
|
|
t_max = t_out;
|
|
}
|
|
} else {
|
|
end_point[0] = x_min_res_sc[0];
|
|
end_point[1] = x_min_res_sc[1];
|
|
res_c_on_curve.curve.setup(x, direction, end_point, x_min, x_max, tol_, t_max, t_out);
|
|
if (res_c_on_curve(t_out) <= 0) {
|
|
t_max = t_out;
|
|
}
|
|
}
|
|
t = RootFinder::solve(res_c_on_curve, 0., t_max, maxit_, tol_, iters_used_falsi);
|
|
res_c_on_curve.curve.computeXOfT(x, t);
|
|
|
|
}
|
|
scToc(x, x_c);
|
|
res_eq.computeResidual(x_c, res, mc, ff);
|
|
iters_used_split += 1;
|
|
}
|
|
|
|
|
|
|
|
if ((iters_used_split >= max_iters_split) && (norm(res) > tol_)) {
|
|
MESSAGE("Newton for single cell did not work in cell number " << cell);
|
|
solveSingleCellBracketing(cell);
|
|
} else {
|
|
scToc(x, x_c);
|
|
concentration_[cell] = x_c[1];
|
|
cmax_[cell] = std::max(cmax_[cell], concentration_[cell]);
|
|
saturation_[cell] = x[0];
|
|
fractionalflow_[cell] = ff;
|
|
mc_[cell] = mc;
|
|
}
|
|
}
|
|
|
|
void TransportModelCompressiblePolymer::solveSingleCellNewton(int cell)
|
|
{
|
|
const int max_iters_split = maxit_;
|
|
int iters_used_split = 0;
|
|
|
|
// Check if current state is an acceptable solution.
|
|
ResidualEquation res_eq(*this, cell);
|
|
double x[2] = {saturation_[cell], concentration_[cell]};
|
|
double res[2];
|
|
double mc;
|
|
double ff;
|
|
res_eq.computeResidual(x, res, mc, ff);
|
|
if (norm(res) <= tol_) {
|
|
cmax_[cell] = std::max(cmax_[cell], concentration_[cell]);
|
|
fractionalflow_[cell] = ff;
|
|
mc_[cell] = mc;
|
|
return;
|
|
} else if (0.99 < x[0]) {
|
|
// x[0] = 0.5;
|
|
// x[1] = polyprops_.cMax()/2.0;
|
|
// res_eq.computeResidual(x, res, mc, ff);
|
|
}
|
|
|
|
const double x_min[2] = { 0.0, 0.0 };
|
|
const double x_max[2] = { 1.0, polyprops_.cMax()*adhoc_safety_ };
|
|
bool successfull_newton_step = true;
|
|
// initialize x_new to avoid warning
|
|
double x_new[2] = {0.0, 0.0};
|
|
double res_new[2];
|
|
ResSOnCurve res_s_on_curve(res_eq);
|
|
ResCOnCurve res_c_on_curve(res_eq);
|
|
|
|
// We switch to s-sc variable
|
|
x[1] = x[0]*x[1];
|
|
// x_c will contain the s-c variable
|
|
double x_c[2];
|
|
|
|
while ((norm(res) > tol_) &&
|
|
(iters_used_split < max_iters_split) &&
|
|
successfull_newton_step) {
|
|
double dres_s_dsdc[2];
|
|
double dres_c_dsdc[2];
|
|
scToc(x, x_c);
|
|
res_eq.computeJacobiRes(x_c, dres_s_dsdc, dres_c_dsdc);
|
|
double dFx_dx = (dres_s_dsdc[0]-x_c[1]*dres_s_dsdc[1]);
|
|
double dFx_dy;
|
|
if (x[0] < 1e-2*tol_) {
|
|
dFx_dy = 0.0;
|
|
} else {
|
|
dFx_dy = (dres_s_dsdc[1]/x[0]);
|
|
}
|
|
double dFy_dx = (dres_c_dsdc[0]-x_c[1]*dres_c_dsdc[1]);
|
|
double dFy_dy;
|
|
if (x[0] < 1e-2*tol_) {
|
|
dFy_dy = 1.0 - res_eq.dps;
|
|
} else {
|
|
dFy_dy = (dres_c_dsdc[1]/x[0]);
|
|
}
|
|
double det = dFx_dx*dFy_dy - dFy_dx*dFx_dy;
|
|
double alpha = 1.0;
|
|
int max_lin_it = 100;
|
|
int lin_it = 0;
|
|
res_new[0] = res[0]*2;
|
|
res_new[1] = res[1]*2;
|
|
while((norm(res_new)>norm(res)) && (lin_it<max_lin_it)) {
|
|
x_new[0] = x[0] - alpha*(res[0]*dFy_dy - res[1]*dFx_dy)/det;
|
|
x_new[1] = x[1] - alpha*(res[1]*dFx_dx - res[0]*dFy_dx)/det;
|
|
check_interval(x_min, x_max, x_new);
|
|
scToc(x_new, x_c);
|
|
res_eq.computeResidual(x_c, res_new, mc, ff);
|
|
alpha = alpha/2.0;
|
|
lin_it = lin_it + 1;
|
|
}
|
|
if (lin_it>=max_lin_it) {
|
|
successfull_newton_step = false;
|
|
} else {
|
|
scToc(x_new, x_c);
|
|
x[0] = x_c[0];
|
|
x[1] = x_c[1];
|
|
res[0] = res_new[0];
|
|
res[1] = res_new[1];
|
|
iters_used_split += 1;
|
|
successfull_newton_step = true;;
|
|
}
|
|
}
|
|
|
|
if ((iters_used_split >= max_iters_split) && (norm(res) > tol_)) {
|
|
MESSAGE("Newton for single cell did not work in cell number " << cell);
|
|
solveSingleCellBracketing(cell);
|
|
} else {
|
|
concentration_[cell] = x[1];
|
|
cmax_[cell] = std::max(cmax_[cell], concentration_[cell]);
|
|
saturation_[cell] = x[0];
|
|
fractionalflow_[cell] = ff;
|
|
mc_[cell] = mc;
|
|
}
|
|
}
|
|
|
|
void TransportModelCompressiblePolymer::solveSingleCellNewtonSimple(int cell,bool use_sc)
|
|
{
|
|
const int max_iters_split = maxit_;
|
|
int iters_used_split = 0;
|
|
|
|
// Check if current state is an acceptable solution.
|
|
ResidualEquation res_eq(*this, cell);
|
|
double x[2] = {saturation_[cell], concentration_[cell]};
|
|
double res[2];
|
|
double mc;
|
|
double ff;
|
|
res_eq.computeResidual(x, res, mc, ff);
|
|
if (norm(res) <= tol_) {
|
|
cmax_[cell] = std::max(cmax_[cell], concentration_[cell]);
|
|
fractionalflow_[cell] = ff;
|
|
mc_[cell] = mc;
|
|
return;
|
|
}else{
|
|
//*
|
|
x[0] = saturation_[cell]-res[0];
|
|
if((x[0]>1) || (x[0]<0)){
|
|
x[0] = 0.5;
|
|
x[1] = x[1];
|
|
}
|
|
if(x[0]>0){
|
|
x[1] = concentration_[cell]*saturation_[cell]-res[1];
|
|
x[1] = x[1]/x[0];
|
|
if(x[1]> polyprops_.cMax()){
|
|
x[1]= polyprops_.cMax()/2.0;
|
|
}
|
|
if(x[1]<0){
|
|
x[1]=0;
|
|
}
|
|
}else{
|
|
x[1]=0;
|
|
}
|
|
//x[0]=0.5;x[1]=polyprops_.cMax()/2.0;
|
|
res_eq.computeResidual(x, res, mc, ff);
|
|
//*/
|
|
}
|
|
|
|
|
|
// double x_min[2] = { std::max(polyprops_.deadPoreVol(), smin_[2*cell]), 0.0 };
|
|
double x_min[2] = { 0.0, 0.0 };
|
|
double x_max[2] = { 1.0, polyprops_.cMax()*adhoc_safety_ };
|
|
bool successfull_newton_step = true;
|
|
double x_new[2];
|
|
double res_new[2];
|
|
ResSOnCurve res_s_on_curve(res_eq);
|
|
ResCOnCurve res_c_on_curve(res_eq);
|
|
|
|
while ((norm(res) > tol_) &&
|
|
(iters_used_split < max_iters_split) &&
|
|
successfull_newton_step) {
|
|
// We first try a Newton step
|
|
double dres_s_dsdc[2];
|
|
double dres_c_dsdc[2];
|
|
double dx=tol_;
|
|
double tmp_x[2];
|
|
if(!(x[0]>0)){
|
|
tmp_x[0]=dx;
|
|
tmp_x[1]=0;
|
|
}else{
|
|
tmp_x[0]=x[0];
|
|
tmp_x[1]=x[1];
|
|
}
|
|
res_eq.computeJacobiRes(tmp_x, dres_s_dsdc, dres_c_dsdc);
|
|
double dFx_dx,dFx_dy,dFy_dx,dFy_dy;
|
|
double det = dFx_dx*dFy_dy - dFy_dx*dFx_dy;
|
|
if(use_sc){
|
|
dFx_dx=(dres_s_dsdc[0]-tmp_x[1]*dres_s_dsdc[1]/tmp_x[0]);
|
|
dFx_dy= (dres_s_dsdc[1]/tmp_x[0]);
|
|
dFy_dx=(dres_c_dsdc[0]-tmp_x[1]*dres_c_dsdc[1]/tmp_x[0]);
|
|
dFy_dy= (dres_c_dsdc[1]/tmp_x[0]);
|
|
}else{
|
|
dFx_dx= dres_s_dsdc[0];
|
|
dFx_dy= dres_s_dsdc[1];
|
|
dFy_dx= dres_c_dsdc[0];
|
|
dFy_dy= dres_c_dsdc[1];
|
|
}
|
|
det = dFx_dx*dFy_dy - dFy_dx*dFx_dy;
|
|
if(det==0){
|
|
THROW("det is zero");
|
|
}
|
|
|
|
double alpha=1;
|
|
int max_lin_it=10;
|
|
int lin_it=0;
|
|
/*
|
|
std::cout << "Nonlinear " << iters_used_split
|
|
<< " " << norm(res_new)
|
|
<< " " << norm(res) << std::endl;*/
|
|
/*
|
|
std::cout << "x" << std::endl;
|
|
std::cout << " " << x[0] << " " << x[1] << std::endl;
|
|
std::cout << "dF" << std::endl;
|
|
std::cout << " " << dFx_dx << " " << dFx_dy << std::endl;
|
|
std::cout << " " << dFy_dx << " " << dFy_dy << std::endl;
|
|
std::cout << "dres" << std::endl;
|
|
std::cout << " " << dres_s_dsdc[0] << " " << dres_s_dsdc[1] << std::endl;
|
|
std::cout << " " << dres_c_dsdc[0] << " " << dres_c_dsdc[1] << std::endl;
|
|
std::cout << std::endl;
|
|
*/
|
|
res_new[0]=res[0]*2;
|
|
res_new[1]=res[1]*2;
|
|
double update[2]={(res[0]*dFy_dy - res[1]*dFx_dy)/det,
|
|
(res[1]*dFx_dx - res[0]*dFy_dx)/det};
|
|
while((norm(res_new)>norm(res)) && (lin_it<max_lin_it)) {
|
|
x_new[0] = x[0] - alpha*update[0];
|
|
if(use_sc){
|
|
x_new[1] = x[1]*x[0] - alpha*update[1];
|
|
x_new[1] = (x_new[0]>0) ? x_new[1]/x_new[0] : 0.0;
|
|
}else{
|
|
x_new[1] = x[1] - alpha*update[1];
|
|
}
|
|
check_interval(x_min, x_max, x_new);
|
|
res_eq.computeResidual(x_new, res_new, mc, ff);
|
|
// std::cout << " " << res_new[0] << " " << res_new[1] << std::endl;
|
|
alpha=alpha/2.0;
|
|
lin_it=lin_it+1;
|
|
// std::cout << "Linear iterations" << lin_it << " " << norm(res_new) << std::endl;
|
|
}
|
|
if (lin_it>=max_lin_it) {
|
|
successfull_newton_step = false;
|
|
} else {
|
|
x[0] = x_new[0];
|
|
x[1] = x_new[1];
|
|
res[0] = res_new[0];
|
|
res[1] = res_new[1];
|
|
iters_used_split += 1;
|
|
successfull_newton_step = true;;
|
|
}
|
|
// std::cout << "Nonlinear " << iters_used_split << " " << norm(res) << std::endl;
|
|
}
|
|
|
|
if ((iters_used_split >= max_iters_split) || (norm(res) > tol_)) {
|
|
MESSAGE("NewtonSimple for single cell did not work in cell number " << cell);
|
|
solveSingleCellBracketing(cell);
|
|
} else {
|
|
concentration_[cell] = x[1];
|
|
cmax_[cell] = std::max(cmax_[cell], concentration_[cell]);
|
|
saturation_[cell] = x[0];
|
|
fractionalflow_[cell] = ff;
|
|
mc_[cell] = mc;
|
|
}
|
|
}
|
|
|
|
|
|
|
|
void TransportModelCompressiblePolymer::solveMultiCell(const int num_cells, const int* cells)
|
|
{
|
|
double max_s_change = 0.0;
|
|
double max_c_change = 0.0;
|
|
int num_iters = 0;
|
|
// Must store state variables before we start.
|
|
std::vector<double> s0(num_cells);
|
|
std::vector<double> c0(num_cells);
|
|
std::vector<double> cmax0(num_cells);
|
|
// Must set initial fractional flows etc. before we start.
|
|
for (int i = 0; i < num_cells; ++i) {
|
|
const int cell = cells[i];
|
|
fracFlow(saturation_[cell], concentration_[cell], cmax_[cell],
|
|
cell, fractionalflow_[cell]);
|
|
computeMc(concentration_[cell], mc_[cell]);
|
|
s0[i] = saturation_[cell];
|
|
c0[i] = concentration_[cell];
|
|
cmax0[i] = cmax_[i];
|
|
}
|
|
do {
|
|
// int max_s_change_cell = -1;
|
|
// int max_c_change_cell = -1;
|
|
max_s_change = 0.0;
|
|
max_c_change = 0.0;
|
|
for (int i = 0; i < num_cells; ++i) {
|
|
const int cell = cells[i];
|
|
const double old_s = saturation_[cell];
|
|
const double old_c = concentration_[cell];
|
|
saturation_[cell] = s0[i];
|
|
concentration_[cell] = c0[i];
|
|
cmax_[cell] = cmax0[i];
|
|
solveSingleCell(cell);
|
|
// std::cout << "cell = " << cell << " delta s = " << saturation_[cell] - old_s << std::endl;
|
|
// if (max_s_change < std::fabs(saturation_[cell] - old_s)) {
|
|
// max_s_change_cell = cell;
|
|
// }
|
|
// if (max_c_change < std::fabs(concentration_[cell] - old_c)) {
|
|
// max_c_change_cell = cell;
|
|
// }
|
|
max_s_change = std::max(max_s_change, std::fabs(saturation_[cell] - old_s));
|
|
max_c_change = std::max(max_c_change, std::fabs(concentration_[cell] - old_c));
|
|
}
|
|
// std::cout << "Iter = " << num_iters << " max_s_change = " << max_s_change
|
|
// << " in cell " << max_change_cell << std::endl;
|
|
} while (((max_s_change > tol_) || (max_c_change > tol_)) && ++num_iters < maxit_);
|
|
if (max_s_change > tol_) {
|
|
THROW("In solveMultiCell(), we did not converge after "
|
|
<< num_iters << " iterations. Delta s = " << max_s_change);
|
|
}
|
|
if (max_c_change > tol_) {
|
|
THROW("In solveMultiCell(), we did not converge after "
|
|
<< num_iters << " iterations. Delta c = " << max_c_change);
|
|
}
|
|
std::cout << "Solved " << num_cells << " cell multicell problem in "
|
|
<< num_iters << " iterations." << std::endl;
|
|
}
|
|
|
|
void TransportModelCompressiblePolymer::fracFlow(double s, double c, double cmax,
|
|
int cell, double& ff) const
|
|
{
|
|
double dummy[2];
|
|
fracFlowBoth(s, c, cmax, cell, ff, dummy, false);
|
|
}
|
|
|
|
void TransportModelCompressiblePolymer::fracFlowWithDer(double s, double c, double cmax,
|
|
int cell, double& ff,
|
|
double* dff_dsdc) const
|
|
{
|
|
fracFlowBoth(s, c, cmax, cell, ff, dff_dsdc, true);
|
|
}
|
|
|
|
void TransportModelCompressiblePolymer::fracFlowBoth(double s, double c, double cmax, int cell,
|
|
double& ff, double* dff_dsdc,
|
|
bool if_with_der) const
|
|
{
|
|
double relperm[2];
|
|
double drelperm_ds[4];
|
|
double sat[2] = {s, 1 - s};
|
|
if (if_with_der) {
|
|
props_.relperm(1, sat, &cell, relperm, drelperm_ds);
|
|
} else {
|
|
props_.relperm(1, sat, &cell, relperm, 0);
|
|
}
|
|
double mob[2];
|
|
double dmob_ds[4];
|
|
double dmob_dc[2];
|
|
double dmobwat_dc;
|
|
const int np = props_.numPhases();
|
|
polyprops_.effectiveMobilitiesBoth(c, cmax, &visc_[np*cell], relperm, drelperm_ds,
|
|
mob, dmob_ds, dmobwat_dc, if_with_der);
|
|
|
|
ff = mob[0]/(mob[0] + mob[1]);
|
|
if (if_with_der) {
|
|
dmob_dc[0] = dmobwat_dc;
|
|
dmob_dc[1] = 0.;
|
|
//dff_dsdc[0] = (dmob_ds[0]*mob[1] + dmob_ds[3]*mob[0])/((mob[0] + mob[1])*(mob[0] + mob[1])); // derivative with respect to s
|
|
// at the moment the dmob_ds only have diagonal elements since the saturation is derivated out in effectiveMobilitiesBoth
|
|
dff_dsdc[0] = ((dmob_ds[0]-dmob_ds[2])*mob[1] - (dmob_ds[1]-dmob_ds[3])*mob[0])/((mob[0] + mob[1])*(mob[0] + mob[1])); // derivative with respect to s
|
|
dff_dsdc[1] = (dmob_dc[0]*mob[1] - dmob_dc[1]*mob[0])/((mob[0] + mob[1])*(mob[0] + mob[1])); // derivative with respect to c
|
|
}
|
|
}
|
|
|
|
void TransportModelCompressiblePolymer::computeMc(double c, double& mc) const
|
|
{
|
|
polyprops_.computeMc(c, mc);
|
|
}
|
|
|
|
void TransportModelCompressiblePolymer::computeMcWithDer(double c, double& mc,
|
|
double &dmc_dc) const
|
|
{
|
|
polyprops_.computeMcWithDer(c, mc, dmc_dc);
|
|
}
|
|
|
|
|
|
|
|
TransportModelCompressiblePolymer::ResidualSGrav::ResidualSGrav(const ResidualCGrav& res_c_eq,
|
|
const double c_init)
|
|
: res_c_eq_(res_c_eq),
|
|
c(c_init)
|
|
{
|
|
}
|
|
|
|
double TransportModelCompressiblePolymer::ResidualSGrav::operator()(double s) const
|
|
{
|
|
return res_c_eq_.computeGravResidualS(s, c);
|
|
}
|
|
|
|
|
|
|
|
|
|
// Residual for concentration equation for gravity segregation
|
|
//
|
|
// res_c = s*(1 - dps)*c - s0*( - dps)*c0
|
|
// + dtpv*sum_{j adj i}( mc * gravmod_ij * gf_ij ).
|
|
// \TODO doc me
|
|
// where ...
|
|
// Influxes are negative, outfluxes positive.
|
|
|
|
TransportModelCompressiblePolymer::ResidualCGrav::ResidualCGrav(const TransportModelCompressiblePolymer& tmodel,
|
|
const std::vector<int>& cells,
|
|
const int pos,
|
|
const double* gravflux) // Always oriented towards next in column. Size = colsize - 1.
|
|
: tm(tmodel),
|
|
cell(cells[pos]),
|
|
s0(tm.saturation_[cell]),
|
|
c0(tm.concentration_[cell]),
|
|
cmax0(tm.cmax0_[cell]),
|
|
porevolume(tm.porevolume_[cell]),
|
|
porosity(porevolume/tm.grid_.cell_volumes[cell]),
|
|
dtpv(tm.dt_/porevolume),
|
|
dps(tm.polyprops_.deadPoreVol()),
|
|
rhor(tm.polyprops_.rockDensity())
|
|
|
|
{
|
|
last_s = s0;
|
|
nbcell[0] = -1;
|
|
gf[0] = 0.0;
|
|
if (pos > 0) {
|
|
nbcell[0] = cells[pos - 1];
|
|
gf[0] = -gravflux[pos - 1];
|
|
}
|
|
nbcell[1] = -1;
|
|
gf[1] = 0.0;
|
|
if (pos < int(cells.size() - 1)) {
|
|
nbcell[1] = cells[pos + 1];
|
|
gf[1] = gravflux[pos];
|
|
}
|
|
|
|
tm.polyprops_.adsorption(c0, cmax0, c_ads0);
|
|
}
|
|
|
|
double TransportModelCompressiblePolymer::ResidualCGrav::operator()(double c) const
|
|
{
|
|
|
|
ResidualSGrav res_s(*this);
|
|
res_s.c = c;
|
|
int iters_used;
|
|
last_s = RootFinder::solve(res_s, last_s, 0.0, 1.0,
|
|
tm.maxit_, tm.tol_,
|
|
iters_used);
|
|
return computeGravResidualC(last_s, c);
|
|
|
|
}
|
|
|
|
double TransportModelCompressiblePolymer::ResidualCGrav::computeGravResidualS(double s, double c) const
|
|
{
|
|
|
|
double mobcell[2];
|
|
tm.mobility(s, c, cell, mobcell);
|
|
|
|
double res = s - s0;
|
|
|
|
for (int nb = 0; nb < 2; ++nb) {
|
|
if (nbcell[nb] != -1) {
|
|
double m[2];
|
|
if (gf[nb] < 0.0) {
|
|
m[0] = mobcell[0];
|
|
m[1] = tm.mob_[2*nbcell[nb] + 1];
|
|
} else {
|
|
m[0] = tm.mob_[2*nbcell[nb]];
|
|
m[1] = mobcell[1];
|
|
}
|
|
if (m[0] + m[1] > 0.0) {
|
|
res += -dtpv*gf[nb]*m[0]*m[1]/(m[0] + m[1]);
|
|
}
|
|
}
|
|
}
|
|
return res;
|
|
}
|
|
|
|
double TransportModelCompressiblePolymer::ResidualCGrav::computeGravResidualC(double s, double c) const
|
|
{
|
|
|
|
double mobcell[2];
|
|
tm.mobility(s, c, cell, mobcell);
|
|
double c_ads;
|
|
tm.polyprops_.adsorption(c, cmax0, c_ads);
|
|
|
|
double res = (1 - dps)*s*c - (1 - dps)*s0*c0
|
|
+ rhor*((1.0 - porosity)/porosity)*(c_ads - c_ads0);
|
|
for (int nb = 0; nb < 2; ++nb) {
|
|
if (nbcell[nb] != -1) {
|
|
double m[2];
|
|
double mc;
|
|
if (gf[nb] < 0.0) {
|
|
m[0] = mobcell[0];
|
|
tm.computeMc(c, mc);
|
|
m[1] = tm.mob_[2*nbcell[nb] + 1];
|
|
} else {
|
|
m[0] = tm.mob_[2*nbcell[nb]];
|
|
mc = tm.mc_[nbcell[nb]];
|
|
m[1] = mobcell[1];
|
|
}
|
|
if (m[0] + m[1] > 0.0) {
|
|
res += -dtpv*gf[nb]*mc*m[0]*m[1]/(m[0] + m[1]);
|
|
}
|
|
}
|
|
}
|
|
return res;
|
|
}
|
|
|
|
double TransportModelCompressiblePolymer::ResidualCGrav::lastSaturation() const
|
|
{
|
|
return last_s;
|
|
}
|
|
|
|
|
|
void TransportModelCompressiblePolymer::mobility(double s, double c, int cell, double* mob) const
|
|
{
|
|
double sat[2] = { s, 1.0 - s };
|
|
double relperm[2];
|
|
const int np = props_.numPhases();
|
|
props_.relperm(1, sat, &cell, relperm, 0);
|
|
polyprops_.effectiveMobilities(c, cmax0_[cell], &visc_[np*cell], relperm, mob);
|
|
}
|
|
|
|
void TransportModelCompressiblePolymer::initGravity(const double* grav)
|
|
{
|
|
// Set up transmissibilities.
|
|
std::vector<double> htrans(grid_.cell_facepos[grid_.number_of_cells]);
|
|
const int nf = grid_.number_of_faces;
|
|
trans_.resize(nf);
|
|
gravflux_.resize(nf);
|
|
tpfa_htrans_compute(const_cast<UnstructuredGrid*>(&grid_), props_.permeability(), &htrans[0]);
|
|
tpfa_trans_compute(const_cast<UnstructuredGrid*>(&grid_), &htrans[0], &trans_[0]);
|
|
|
|
// Remember gravity vector.
|
|
gravity_ = grav;
|
|
}
|
|
|
|
void TransportModelCompressiblePolymer::initGravityDynamic()
|
|
{
|
|
// Set up gravflux_ = T_ij g [ (b_w,i rho_w,S - b_o,i rho_o,S) (z_i - z_f)
|
|
// + (b_w,j rho_w,S - b_o,j rho_o,S) (z_f - z_j) ]
|
|
// But b_w,i * rho_w,S = rho_w,i, which we compute with a call to props_.density().
|
|
// We assume that we already have stored T_ij in trans_.
|
|
// We also assume that the A_ matrices are updated from an earlier call to solve().
|
|
const int nc = grid_.number_of_cells;
|
|
const int nf = grid_.number_of_faces;
|
|
const int np = props_.numPhases();
|
|
ASSERT(np == 2);
|
|
const int dim = grid_.dimensions;
|
|
density_.resize(nc*np);
|
|
props_.density(grid_.number_of_cells, &A_[0], &density_[0]);
|
|
std::fill(gravflux_.begin(), gravflux_.end(), 0.0);
|
|
for (int f = 0; f < nf; ++f) {
|
|
const int* c = &grid_.face_cells[2*f];
|
|
const double signs[2] = { 1.0, -1.0 };
|
|
if (c[0] != -1 && c[1] != -1) {
|
|
for (int ci = 0; ci < 2; ++ci) {
|
|
double gdz = 0.0;
|
|
for (int d = 0; d < dim; ++d) {
|
|
gdz += gravity_[d]*(grid_.cell_centroids[dim*c[ci] + d] - grid_.face_centroids[dim*f + d]);
|
|
}
|
|
gravflux_[f] += signs[ci]*trans_[f]*gdz*(density_[2*c[ci]] - density_[2*c[ci] + 1]);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
void TransportModelCompressiblePolymer::solveSingleCellGravity(const std::vector<int>& cells,
|
|
const int pos,
|
|
const double* gravflux)
|
|
{
|
|
const int cell = cells[pos];
|
|
ResidualCGrav res_c(*this, cells, pos, gravflux);
|
|
|
|
// Check if current state is an acceptable solution.
|
|
double res_sc[2];
|
|
res_sc[0]=res_c.computeGravResidualS(saturation_[cell], concentration_[cell]);
|
|
res_sc[1]=res_c.computeGravResidualC(saturation_[cell], concentration_[cell]);
|
|
|
|
if (norm(res_sc) < tol_) {
|
|
return;
|
|
}
|
|
|
|
const double a = 0.0;
|
|
const double b = polyprops_.cMax()*adhoc_safety_; // Add 10% to account for possible non-monotonicity of hyperbolic system.
|
|
int iters_used;
|
|
concentration_[cell] = RootFinder::solve(res_c, concentration_[cell],
|
|
a, b, maxit_, tol_, iters_used);
|
|
saturation_[cell] = res_c.lastSaturation();
|
|
cmax_[cell] = std::max(cmax0_[cell], concentration_[cell]);
|
|
computeMc(concentration_[cell], mc_[cell]);
|
|
mobility(saturation_[cell], concentration_[cell], cell, &mob_[2*cell]);
|
|
}
|
|
|
|
int TransportModelCompressiblePolymer::solveGravityColumn(const std::vector<int>& cells)
|
|
{
|
|
// Set up column gravflux.
|
|
const int nc = cells.size();
|
|
std::vector<double> col_gravflux(nc - 1);
|
|
for (int ci = 0; ci < nc - 1; ++ci) {
|
|
const int cell = cells[ci];
|
|
const int next_cell = cells[ci + 1];
|
|
for (int j = grid_.cell_facepos[cell]; j < grid_.cell_facepos[cell+1]; ++j) {
|
|
const int face = grid_.cell_faces[j];
|
|
const int c1 = grid_.face_cells[2*face + 0];
|
|
const int c2 = grid_.face_cells[2*face + 1];
|
|
if (c1 == next_cell || c2 == next_cell) {
|
|
const double gf = gravflux_[face];
|
|
col_gravflux[ci] = (c1 == cell) ? gf : -gf;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Store initial saturation s0
|
|
s0_.resize(nc);
|
|
c0_.resize(nc);
|
|
for (int ci = 0; ci < nc; ++ci) {
|
|
s0_[ci] = saturation_[cells[ci]];
|
|
c0_[ci] = concentration_[cells[ci]];
|
|
}
|
|
|
|
// Solve single cell problems, repeating if necessary.
|
|
double max_sc_change = 0.0;
|
|
int num_iters = 0;
|
|
do {
|
|
max_sc_change = 0.0;
|
|
for (int ci = 0; ci < nc; ++ci) {
|
|
const int ci2 = nc - ci - 1;
|
|
double old_s[2] = { saturation_[cells[ci]],
|
|
saturation_[cells[ci2]] };
|
|
double old_c[2] = { concentration_[cells[ci]],
|
|
concentration_[cells[ci2]] };
|
|
saturation_[cells[ci]] = s0_[ci];
|
|
concentration_[cells[ci]] = c0_[ci];
|
|
solveSingleCellGravity(cells, ci, &col_gravflux[0]);
|
|
saturation_[cells[ci2]] = s0_[ci2];
|
|
concentration_[cells[ci2]] = c0_[ci2];
|
|
solveSingleCellGravity(cells, ci2, &col_gravflux[0]);
|
|
max_sc_change = std::max(max_sc_change, 0.25*(std::fabs(saturation_[cells[ci]] - old_s[0]) +
|
|
std::fabs(concentration_[cells[ci]] - old_c[0]) +
|
|
std::fabs(saturation_[cells[ci2]] - old_s[1]) +
|
|
std::fabs(concentration_[cells[ci2]] - old_c[1])));
|
|
}
|
|
// std::cout << "Iter = " << num_iters << " max_s_change = " << max_s_change << std::endl;
|
|
} while (max_sc_change > tol_ && ++num_iters < maxit_);
|
|
|
|
if (max_sc_change > tol_) {
|
|
THROW("In solveGravityColumn(), we did not converge after "
|
|
<< num_iters << " iterations. Delta s = " << max_sc_change);
|
|
}
|
|
return num_iters + 1;
|
|
}
|
|
|
|
|
|
void TransportModelCompressiblePolymer::solveGravity(const std::vector<std::vector<int> >& columns,
|
|
const double dt,
|
|
std::vector<double>& saturation,
|
|
std::vector<double>& surfacevol,
|
|
std::vector<double>& concentration,
|
|
std::vector<double>& cmax)
|
|
{
|
|
|
|
// Assume that solve() has already been called, so that A_ and
|
|
// porosity_ are current.
|
|
initGravityDynamic();
|
|
|
|
// initialize variables.
|
|
dt_ = dt;
|
|
toWaterSat(saturation, saturation_);
|
|
concentration_ = &concentration[0];
|
|
cmax_ = &cmax[0];
|
|
const int nc = grid_.number_of_cells;
|
|
cmax0_.resize(nc);
|
|
std::copy(cmax.begin(), cmax.end(), &cmax0_[0]);
|
|
|
|
// Initialize mobilities.
|
|
const int np = props_.numPhases();
|
|
mob_.resize(np*nc);
|
|
|
|
for (int cell = 0; cell < nc; ++cell) {
|
|
mobility(saturation_[cell], concentration_[cell], cell, &mob_[np*cell]);
|
|
}
|
|
|
|
|
|
// Solve on all columns.
|
|
int num_iters = 0;
|
|
// std::cout << "Gauss-Seidel column solver # columns: " << columns.size() << std::endl;
|
|
for (std::vector<std::vector<int> >::size_type i = 0; i < columns.size(); i++) {
|
|
// std::cout << "==== new column" << std::endl;
|
|
num_iters += solveGravityColumn(columns[i]);
|
|
}
|
|
std::cout << "Gauss-Seidel column solver average iterations: "
|
|
<< double(num_iters)/double(columns.size()) << std::endl;
|
|
|
|
toBothSat(saturation_, saturation);
|
|
// Compute surface volume as a postprocessing step from saturation and A_
|
|
computeSurfacevol(grid_.number_of_cells, props_.numPhases(), &A_[0], &saturation[0], &surfacevol[0]);
|
|
|
|
}
|
|
|
|
void TransportModelCompressiblePolymer::scToc(const double* x, double* x_c) const {
|
|
x_c[0] = x[0];
|
|
if (x[0] < 1e-2*tol_) {
|
|
x_c[1] = 0.5*polyprops_.cMax();
|
|
} else {
|
|
x_c[1] = x[1]/x[0];
|
|
}
|
|
}
|
|
|
|
bool TransportModelCompressiblePolymer::ResidualEquation::solveNewtonStepSC(const double* xx,
|
|
const double* res, double* x_new) const {
|
|
|
|
double dres_s_dsdc[2];
|
|
double dres_c_dsdc[2];
|
|
double dx=1e-8;
|
|
double x[2];
|
|
if(!(x[0]>0)){
|
|
x[0] = dx;
|
|
x[1] = 0;
|
|
} else {
|
|
x[0] = xx[0];
|
|
x[1] = xx[1];
|
|
}
|
|
computeJacobiRes(x, dres_s_dsdc, dres_c_dsdc);
|
|
|
|
double dFx_dx=(dres_s_dsdc[0]-x[1]*dres_s_dsdc[1]);
|
|
double dFx_dy= (dres_s_dsdc[1]/x[0]);
|
|
double dFy_dx=(dres_c_dsdc[0]-x[1]*dres_c_dsdc[1]);
|
|
double dFy_dy= (dres_c_dsdc[1]/x[0]);
|
|
|
|
double det = dFx_dx*dFy_dy - dFy_dx*dFx_dy;
|
|
if (std::abs(det) < 1e-8) {
|
|
return false;
|
|
} else {
|
|
x_new[0] = x[0] - (res[0]*dFy_dy - res[1]*dFx_dy)/det;
|
|
x_new[1] = x[1]*x[0] - (res[1]*dFx_dx - res[0]*dFy_dx)/det;
|
|
x_new[1] = (x_new[0]>0) ? x_new[1]/x_new[0] : 0.0;
|
|
return true;
|
|
}
|
|
}
|
|
bool TransportModelCompressiblePolymer::ResidualEquation::solveNewtonStepC(const double* xx, const double* res, double* x_new) const {
|
|
|
|
double dres_s_dsdc[2];
|
|
double dres_c_dsdc[2];
|
|
double dx=1e-8;
|
|
double x[2];
|
|
if(!(x[0]>0)){
|
|
x[0] = dx;
|
|
x[1] = 0;
|
|
} else {
|
|
x[0] = xx[0];
|
|
x[1] = xx[1];
|
|
}
|
|
computeJacobiRes(x, dres_s_dsdc, dres_c_dsdc);
|
|
double det = dres_s_dsdc[0]*dres_c_dsdc[1] - dres_c_dsdc[0]*dres_s_dsdc[1];
|
|
if (std::abs(det) < 1e-8) {
|
|
return false;
|
|
} else {
|
|
x_new[0] = x[0] - (res[0]*dres_c_dsdc[1] - res[1]*dres_s_dsdc[1])/det;
|
|
x_new[1] = x[1] - (res[1]*dres_s_dsdc[0] - res[0]*dres_c_dsdc[0])/det;
|
|
return true;
|
|
}
|
|
}
|
|
|
|
|
|
} // namespace Opm
|
|
|
|
|
|
namespace
|
|
{
|
|
bool check_interval(const double* xmin, const double* xmax, double* x) {
|
|
bool test = false;
|
|
if (x[0] < xmin[0]) {
|
|
test = true;
|
|
x[0] = xmin[0];
|
|
} else if (x[0] > xmax[0]) {
|
|
test = true;
|
|
x[0] = xmax[0];
|
|
}
|
|
if (x[1] < xmin[1]) {
|
|
test = true;
|
|
x[1] = xmin[1];
|
|
} else if (x[1] > xmax[1]) {
|
|
test = true;
|
|
x[1] = xmax[1];
|
|
}
|
|
return test;
|
|
}
|
|
|
|
|
|
CurveInSCPlane::CurveInSCPlane()
|
|
{
|
|
}
|
|
|
|
// Setup the curve (see comment above).
|
|
// The curve is parametrized by t in [0, t_max], t_out is equal to t when the curve hits the bounding
|
|
// rectangle. x_out=(s_out, c_out) denotes the values of s and c at that point.
|
|
void CurveInSCPlane::setup(const double* x, const double* direction,
|
|
const double* end_point, const double* x_min,
|
|
const double* x_max, const double tol,
|
|
double& t_max_out, double& t_out_out)
|
|
{
|
|
x_[0] = x[0];
|
|
x_[1] = x[1];
|
|
x_max_[0] = x_max[0];
|
|
x_max_[1] = x_max[1];
|
|
x_min_[0] = x_min[0];
|
|
x_min_[1] = x_min[1];
|
|
direction_[0] = direction[0];
|
|
direction_[1] = direction[1];
|
|
end_point_[0] = end_point[0];
|
|
end_point_[1] = end_point[1];
|
|
const double size_direction = std::abs(direction_[0]) + std::abs(direction_[1]);
|
|
if (size_direction < tol) {
|
|
direction_[0] = end_point_[0]-x_[0];
|
|
direction_[1] = end_point_[1]-x_[1];
|
|
} else if ((end_point_[0]-x_[0])*direction_[0] + (end_point_[1]-x_[1])*direction_[1] < 0) {
|
|
direction_[0] *= -1.0;
|
|
direction_[1] *= -1.0;
|
|
}
|
|
bool t0_exists = true;
|
|
double t0 = 0; // dummy default value (so that compiler does not complain).
|
|
if (direction_[0] > 0) {
|
|
t0 = (x_max_[0] - x_[0])/direction_[0];
|
|
} else if (direction_[0] < 0) {
|
|
t0 = (x_min_[0] - x_[0])/direction_[0];
|
|
} else {
|
|
t0_exists = false;
|
|
}
|
|
bool t1_exists = true;
|
|
double t1 = 0; // dummy default value.
|
|
if (direction_[1] > 0) {
|
|
t1 = (x_max_[1] - x_[1])/direction_[1];
|
|
} else if (direction_[1] < 0) {
|
|
t1 = (x_min_[1] - x_[1])/direction_[1];
|
|
} else {
|
|
t1_exists = false;
|
|
}
|
|
if (t0_exists) {
|
|
if (t1_exists) {
|
|
t_out_ = std::min(t0, t1);
|
|
} else {
|
|
t_out_ = t0;
|
|
}
|
|
} else if (t1_exists) {
|
|
t_out_ = t1;
|
|
} else {
|
|
THROW("Direction illegal: is a zero vector.");
|
|
}
|
|
x_out_[0] = x_[0] + t_out_*direction_[0];
|
|
x_out_[1] = x_[1] + t_out_*direction_[1];
|
|
t_max_ = t_out_ + 1;
|
|
t_max_out = t_max_;
|
|
t_out_out = t_out_;
|
|
}
|
|
|
|
|
|
// Compute x=(s,c) for a given t (t is the parameter for the piecewise linear curve)
|
|
void CurveInSCPlane::computeXOfT(double* x_of_t, const double t) const {
|
|
if (t <= t_out_) {
|
|
x_of_t[0] = x_[0] + t*direction_[0];
|
|
x_of_t[1] = x_[1] + t*direction_[1];
|
|
} else {
|
|
x_of_t[0] = 1/(t_max_-t_out_)*((t_max_ - t)*x_out_[0] + end_point_[0]*(t - t_out_));
|
|
x_of_t[1] = 1/(t_max_-t_out_)*((t_max_ - t)*x_out_[1] + end_point_[1]*(t - t_out_));
|
|
}
|
|
}
|
|
|
|
} // Anonymous namespace
|
|
|
|
|
|
/* Local Variables: */
|
|
/* c-basic-offset:4 */
|
|
/* End: */
|