opm-simulators/opm/polymer/TransportModelPolymer.cpp

946 lines
30 KiB
C++

/*
Copyright 2012 SINTEF ICT, Applied Mathematics.
This file is part of the Open Porous Media project (OPM).
OPM is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
OPM is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with OPM. If not, see <http://www.gnu.org/licenses/>.
*/
#include <opm/polymer/TransportModelPolymer.hpp>
#include <opm/core/fluid/IncompPropertiesInterface.hpp>
#include <opm/core/grid.h>
#include <opm/core/utility/RootFinders.hpp>
#include <cmath>
namespace
{
double norm(double* res)
{
return std::max(std::abs(res[0]), std::abs(res[1]));
}
}
namespace Opm
{
TransportModelPolymer::TransportModelPolymer(const UnstructuredGrid& grid,
const double* porosity,
const double* porevolume,
const IncompPropertiesInterface& props,
const PolymerProperties& polyprops,
const SingleCellMethod method,
const double tol,
const int maxit)
: grid_(grid),
porosity_(porosity),
porevolume_(porevolume),
props_(props),
polyprops_(polyprops),
tol_(tol),
maxit_(maxit),
darcyflux_(0),
source_(0),
dt_(0.0),
inflow_c_(0.0),
saturation_(0),
concentration_(0),
cmax_(0),
fractionalflow_(grid.number_of_cells, -1.0),
mc_(grid.number_of_cells, -1.0),
method_(method)
{
if (props.numPhases() != 2) {
THROW("Property object must have 2 phases");
}
visc_ = props.viscosity();
// Set up smin_ and smax_
int num_cells = props.numCells();
smin_.resize(props.numPhases()*num_cells);
smax_.resize(props.numPhases()*num_cells);
std::vector<int> cells(num_cells);
for (int i = 0; i < num_cells; ++i) {
cells[i] = i;
}
props.satRange(props.numCells(), &cells[0], &smin_[0], &smax_[0]);
}
void TransportModelPolymer::solve(const double* darcyflux,
const double* source,
const double dt,
const double inflow_c,
double* saturation,
double* concentration,
double* cmax)
{
darcyflux_ = darcyflux;
source_ = source;
dt_ = dt;
inflow_c_ = inflow_c;
saturation_ = saturation;
concentration_ = concentration;
cmax_ = cmax;
reorderAndTransport(grid_, darcyflux);
}
// Residual for saturation equation, single-cell implicit Euler transport
//
// r(s) = s - s0 + dt/pv*( influx + outflux*f(s) )
//
// where influx is water influx, outflux is total outflux.
// Influxes are negative, outfluxes positive.
struct TransportModelPolymer::ResidualS
{
const TransportModelPolymer& tm_;
const int cell_;
const double s0_;
const double influx_; // sum_j min(v_ij, 0)*f(s_j)
const double outflux_; // sum_j max(v_ij, 0)
const double dtpv_; // dt/pv(i)
const double c_;
explicit ResidualS(const TransportModelPolymer& tmodel,
const int cell,
const double s0,
const double influx,
const double outflux,
const double dtpv,
const double c)
: tm_(tmodel),
cell_(cell),
s0_(s0),
influx_(influx),
outflux_(outflux),
dtpv_(dtpv),
c_(c)
{
}
double operator()(double s) const
{
return s - s0_ + dtpv_*(outflux_*tm_.fracFlow(s, c_, cell_) + influx_);
}
};
// Residual for concentration equation, single-cell implicit Euler transport
//
// \TODO doc me
// where ...
// Influxes are negative, outfluxes positive.
struct TransportModelPolymer::ResidualC
{
int cell;
double s0;
double c0;
double cmax0;
double influx; // sum_j min(v_ij, 0)*f(s_j)
double influx_polymer; // sum_j min(v_ij, 0)*f(s_j)*mc(c_j)
double outflux; // sum_j max(v_ij, 0)
double porosity;
double dtpv; // dt/pv(i)
mutable double s; // Mutable in order to change it with every operator() call to be the last computed s value.
const TransportModelPolymer& tm;
explicit ResidualC(const TransportModelPolymer& tmodel, int cell_index)
: tm(tmodel)
{
cell = cell_index;
s0 = tm.saturation_[cell];
c0 = tm.concentration_[cell];
cmax0 = tm.cmax_[cell];
double dflux = -tm.source_[cell];
bool src_is_inflow = dflux < 0.0;
influx = src_is_inflow ? dflux : 0.0;
influx_polymer = src_is_inflow ? dflux*tm.computeMc(tm.inflow_c_) : 0.0;
outflux = !src_is_inflow ? dflux : 0.0;
dtpv = tm.dt_/tm.porevolume_[cell];
porosity = tm.porosity_[cell];
s = -1e100;
for (int i = tm.grid_.cell_facepos[cell]; i < tm.grid_.cell_facepos[cell+1]; ++i) {
int f = tm.grid_.cell_faces[i];
double flux;
int other;
// Compute cell flux
if (cell == tm.grid_.face_cells[2*f]) {
flux = tm.darcyflux_[f];
other = tm.grid_.face_cells[2*f+1];
} else {
flux =-tm.darcyflux_[f];
other = tm.grid_.face_cells[2*f];
}
// Add flux to influx or outflux, if interior.
if (other != -1) {
if (flux < 0.0) {
influx += flux*tm.fractionalflow_[other];
influx_polymer += flux*tm.fractionalflow_[other]*tm.mc_[other];
} else {
outflux += flux;
}
}
}
}
void computeBothResiduals(const double s_arg, const double c_arg, double& res_s, double& res_c, double& mc, double& ff) const
{
double dps = tm.polyprops_.deadPoreVol();
ff = tm.fracFlow(s_arg, c_arg, cell);
mc = tm.computeMc(c_arg);
double rhor = tm.polyprops_.rockDensity();
double ads0 = tm.polyprops_.adsorbtion(std::max(c0, cmax0));
double ads = tm.polyprops_.adsorbtion(std::max(c_arg, cmax0));
res_s = s_arg - s0 + dtpv*(outflux*ff + influx);
res_c = (s_arg - dps)*c_arg - (s0 - dps)*c0
+ rhor*((1.0 - porosity)/porosity)*(ads - ads0)
+ dtpv*(outflux*ff*mc + influx_polymer);
}
double operator()(double c) const
{
double dps = tm.polyprops_.deadPoreVol();
ResidualS res_s(tm, cell, s0, influx, outflux, dtpv, c);
int iters_used;
// Solve for s first.
s = modifiedRegulaFalsi(res_s, std::max(tm.smin_[2*cell], dps), tm.smax_[2*cell],
tm.maxit_, tm.tol_, iters_used);
double ff = tm.fracFlow(s, c, cell);
double mc = tm.computeMc(c);
double rhor = tm.polyprops_.rockDensity();
double ads0 = tm.polyprops_.adsorbtion(std::max(c0, cmax0));
double ads = tm.polyprops_.adsorbtion(std::max(c, cmax0));
double res = (s - dps)*c - (s0 - dps)*c0
+ rhor*((1.0 - porosity)/porosity)*(ads - ads0)
+ dtpv*(outflux*ff*mc + influx_polymer);
#ifdef EXTRA_DEBUG_OUTPUT
std::cout << "c = " << c << " s = " << s << " c-residual = " << res << std::endl;
#endif
return res;
}
double lastSaturation() const
{
return s;
}
};
// Residual for s and c. Includes method to compute the gradient.
// Compute residual in s (or c) for a given piecewise linear curve (with only one node) in the s-c
// plane. The method operator() is used by a 1d root solver.
struct TransportModelPolymer::Residual
{
int cell;
double s0;
double c0;
double cmax0;
double influx; // sum_j min(v_ij, 0)*f(s_j)
double influx_polymer; // sum_j min(v_ij, 0)*f(s_j)*mc(c_j)
double outflux; // sum_j max(v_ij, 0)
double porosity;
double dtpv; // dt/pv(i)
double direction[2];
double end_point[2];
double x_max[2];
double x_min[2];
double t_out;
double t_max; // t_max = t_out + 1
double x_out[2];
double x[2];
bool if_res_s;
const TransportModelPolymer& tm;
Residual(const TransportModelPolymer& tmodel, int cell_index)
: tm(tmodel)
{
cell = cell_index;
s0 = tm.saturation_[cell];
c0 = tm.concentration_[cell];
cmax0 = tm.cmax_[cell];
double dflux = -tm.source_[cell];
bool src_is_inflow = dflux < 0.0;
influx = src_is_inflow ? dflux : 0.0;
influx_polymer = src_is_inflow ? dflux*tm.computeMc(tm.inflow_c_) : 0.0;
outflux = !src_is_inflow ? dflux : 0.0;
dtpv = tm.dt_/tm.porevolume_[cell];
porosity = tm.porosity_[cell];
for (int i = tm.grid_.cell_facepos[cell]; i < tm.grid_.cell_facepos[cell+1]; ++i) {
int f = tm.grid_.cell_faces[i];
double flux;
int other;
// Compute cell flux
if (cell == tm.grid_.face_cells[2*f]) {
flux = tm.darcyflux_[f];
other = tm.grid_.face_cells[2*f+1];
} else {
flux =-tm.darcyflux_[f];
other = tm.grid_.face_cells[2*f];
}
// Add flux to influx or outflux, if interior.
if (other != -1) {
if (flux < 0.0) {
influx += flux*tm.fractionalflow_[other];
influx_polymer += flux*tm.fractionalflow_[other]*tm.mc_[other];
} else {
outflux += flux;
}
}
}
}
void computeResidual(const double* x, double* res) const
{
double s = x[0];
double c = x[1];
double ff = tm.fracFlow(s, c, cell);
double mc = tm.computeMc(c);
double dps = tm.polyprops_.deadPoreVol();
double rhor = tm.polyprops_.rockDensity();
double ads0 = tm.polyprops_.adsorbtion(std::max(c0, cmax0));
double ads = tm.polyprops_.adsorbtion(std::max(c, cmax0));
res[0] = s - s0 + dtpv*(outflux*ff + influx);
res[1] = (s - dps)*c - (s0 - dps)*c0
+ rhor*((1.0 - porosity)/porosity)*(ads - ads0)
+ dtpv*(outflux*ff*mc + influx_polymer);
}
void computeResidual(const double* x, double* res, double& mc, double& ff) const
{
double s = x[0];
double c = x[1];
ff = tm.fracFlow(s, c, cell);
mc = tm.computeMc(c);
double dps = tm.polyprops_.deadPoreVol();
double rhor = tm.polyprops_.rockDensity();
double ads0 = tm.polyprops_.adsorbtion(std::max(c0, cmax0));
double ads = tm.polyprops_.adsorbtion(std::max(c, cmax0));
res[0] = s - s0 + dtpv*(outflux*ff + influx);
res[1] = (s - dps)*c - (s0 - dps)*c0
+ rhor*((1.0 - porosity)/porosity)*(ads - ads0)
+ dtpv*(outflux*ff*mc + influx_polymer);
}
bool solveNewtonStep(const double* x, double* x_new, const int& gradient_method) {
// If gradient_method == 1, use finite difference
// If gradient_method == 2, use analytic expresions
double res[2];
double res_s_ds_dc[2];
double res_c_ds_dc[2];
if (gradient_method == 1) {
double epsi = 1e-8;
double res_epsi[2];
double x_epsi[2];
computeResidual(x, res);
x_epsi[0] = x[0] + epsi;
x_epsi[1] = x[1];
computeResidual(x_epsi, res_epsi);
res_s_ds_dc[0] = (res_epsi[0] - res[0])/epsi;
x_epsi[0] = x[0];
x_epsi[1] = x[1] + epsi;
computeResidual(x_epsi, res_epsi);
res_s_ds_dc[1] = (res_epsi[0] - res[0])/epsi;
x_epsi[0] = x[0] + epsi;
x_epsi[1] = x[1];
computeResidual(x_epsi, res_epsi);
res_c_ds_dc[0] = (res_epsi[1] - res[1])/epsi;
x_epsi[0] = x[0];
x_epsi[1] = x[1] + epsi;
computeResidual(x_epsi, res_epsi);
res_c_ds_dc[1] = (res_epsi[1] - res[1])/epsi;
} else if (gradient_method == 2) {
double s = x[0];
double c = x[1];
double ff_ds_dc[2];
double ff = tm.fracFlowWithDer(s, c, cell, ff_ds_dc);
double mc_dc;
double mc = tm.computeMcWithDer(c, &mc_dc);
double dps = tm.polyprops_.deadPoreVol();
double rhor = tm.polyprops_.rockDensity();
double ads0 = tm.polyprops_.adsorbtion(std::max(c0, cmax0));
double ads;
double ads_dc;
if (c < cmax0) {
ads = tm.polyprops_.adsorbtion(cmax0);
ads_dc = 0;
} else {
ads = tm.polyprops_.adsorbtionWithDer(c, &ads_dc);
}
res[0] = s - s0 + dtpv*(outflux*ff + influx);
res[1] = (s - dps)*c - (s0 - dps)*c0
+ rhor*((1.0 - porosity)/porosity)*(ads - ads0)
+ dtpv*(outflux*ff*mc + influx_polymer);
res_s_ds_dc[0] = 1 + dtpv*outflux*ff_ds_dc[0];
res_s_ds_dc[1] = dtpv*outflux*ff_ds_dc[1];
res_c_ds_dc[0] = c + dtpv*outflux*(ff_ds_dc[0])*mc;
res_c_ds_dc[1] = s - dps + rhor*((1.0 - porosity)/porosity)*ads_dc
+ dtpv*outflux*(ff_ds_dc[1]*mc + ff*mc_dc);
}
double det = res_s_ds_dc[0]*res_c_ds_dc[1] - res_c_ds_dc[0]*res_s_ds_dc[1];
if (std::abs(det) < 1e-8) {
return false;
} else {
x_new[0] = x[0] - (res[0]*res_c_ds_dc[1] - res[1]*res_s_ds_dc[1])/det;
x_new[1] = x[1] - (res[1]*res_s_ds_dc[0] - res[0]*res_c_ds_dc[0])/det;
return true;
}
}
void computeGradient(const double* x, double* res, double* gradient, const int& gradient_method) const
// If gradient_method == 1, use finite difference
// If gradient_method == 2, use analytic expresions
{
if (gradient_method == 1) {
double epsi = 1e-8;
double res_epsi[2];
double x_epsi[2];
computeResidual(x, res);
if (if_res_s) {
x_epsi[0] = x[0] + epsi;
x_epsi[1] = x[1];
computeResidual(x_epsi, res_epsi);
gradient[0] = (res_epsi[0] - res[0])/epsi;
x_epsi[0] = x[0];
x_epsi[1] = x[1] + epsi;
computeResidual(x_epsi, res_epsi);
gradient[1] = (res_epsi[0] - res[0])/epsi;
} else {
x_epsi[0] = x[0] + epsi;
x_epsi[1] = x[1];
computeResidual(x_epsi, res_epsi);
gradient[0] = (res_epsi[1] - res[1])/epsi;
x_epsi[0] = x[0];
x_epsi[1] = x[1] + epsi;
computeResidual(x_epsi, res_epsi);
gradient[1] = (res_epsi[1] - res[1])/epsi;
}
} else if (gradient_method == 2) {
double s = x[0];
double c = x[1];
double ff_ds_dc[2];
double ff = tm.fracFlowWithDer(s, c, cell, ff_ds_dc);
double mc_dc;
double mc = tm.computeMcWithDer(c, &mc_dc);
double dps = tm.polyprops_.deadPoreVol();
double rhor = tm.polyprops_.rockDensity();
double ads0 = tm.polyprops_.adsorbtion(std::max(c0, cmax0));
double ads;
double ads_dc;
if (c < cmax0) {
ads = tm.polyprops_.adsorbtion(cmax0);
ads_dc = 0;
} else {
ads = tm.polyprops_.adsorbtionWithDer(c, &ads_dc);
}
res[0] = s - s0 + dtpv*(outflux*ff + influx);
res[1] = (s - dps)*c - (s0 - dps)*c0
+ rhor*((1.0 - porosity)/porosity)*(ads - ads0)
+ dtpv*(outflux*ff*mc + influx_polymer);
if (if_res_s) {
gradient[0] = 1 + dtpv*outflux*ff_ds_dc[0];
gradient[1] = dtpv*outflux*ff_ds_dc[1];
} else {
gradient[0] = c + dtpv*outflux*(ff_ds_dc[0])*mc;
gradient[1] = s - dps + rhor*((1.0 - porosity)/porosity)*ads_dc
+ dtpv*outflux*(ff_ds_dc[1]*mc + ff*mc_dc);
}
}
}
// setup 1d function, which is called by operator()
// For a given point x=(s,c) in the s,c plane, set up a piecewise linear curve wich starts
// from "x" with slope "direction", hits the bound of the rectangle
// [s_min,s_max]x[c_min,c_max] and continue in a straight line to "end_point". 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 setup(const double* x_arg, const double* direction_arg, const double* end_point_arg, const double* x_min_arg, const double* x_max_arg, double& t_max_out, double& t_out_out)
{
x[0] = x_arg[0];
x[1] = x_arg[1];
x_max[0] = x_max_arg[0];
x_max[1] = x_max_arg[1];
x_min[0] = x_min_arg[0];
x_min[1] = x_min_arg[1];
direction[0] = direction_arg[0];
direction[1] = direction_arg[1];
end_point[0] = end_point_arg[0];
end_point[1] = end_point_arg[1];
if ((end_point[0]-x[0])*direction[0] + (end_point[1]-x[1])*direction[1] < 0) {
direction[0] *= -1.0;
direction[1] *= -1.0;
}
if ((std::abs(direction[0]) + std::abs(direction[0])) == 0) {
direction[0] = end_point[0]-x[0];
direction[1] = end_point[1]-x[1];
}
bool t0_exists = true;
double t0;
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;
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 compute_x_of_t(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));
}
}
double operator()(const double t) const
{
double x_of_t[2];
compute_x_of_t(x_of_t, t);
double s;
double c;
s = x_of_t[0];
c = x_of_t[1];
if (if_res_s) {
return s - s0 + dtpv*(outflux*tm.fracFlow(s, c, cell) + influx);
} else {
double ff = tm.fracFlow(s, c, cell);
double mc = tm.computeMc(c);
double dps = tm.polyprops_.deadPoreVol();
double rhor = tm.polyprops_.rockDensity();
double ads0 = tm.polyprops_.adsorbtion(std::max(c0, cmax0));
double ads = tm.polyprops_.adsorbtion(std::max(c, cmax0));
return (s - dps)*c - (s0 - dps)*c0
+ rhor*((1.0 - porosity)/porosity)*(ads - ads0)
+ dtpv*(outflux*ff*mc + influx_polymer);
}
}
};
void TransportModelPolymer::solveSingleCell(const int cell)
{
switch (method_) {
case Bracketing:
solveSingleCellBracketing(cell);
break;
case Newton:
solveSingleCellNewton(cell);
break;
default:
THROW("Unknown method " << method_);
}
}
void TransportModelPolymer::solveSingleCellBracketing(int cell)
{
ResidualC res(*this, cell);
const double a = 0.0;
const double b = polyprops_.cMax();
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] = modifiedRegulaFalsi(res, a, b, maxit_, tol_, iters_used);
cmax_[cell] = std::max(cmax_[cell], concentration_[cell]);
saturation_[cell] = res.lastSaturation();
fractionalflow_[cell] = fracFlow(saturation_[cell], concentration_[cell], cell);
mc_[cell] = computeMc(concentration_[cell]);
}
// Newton method, where we compute alternatively the zeros for the residual in s and c along
// a specified piecewise linear curve. At each iteration, we use a robust 1d solver.
void TransportModelPolymer::solveSingleCellNewton(int cell)
{
// the tolerance for 1d solver is set as a function of the residual
// The tolerance falsi_tol is improved by (reduc_factor_falsi_tol * "previous residual") at each step
double falsi_tol;
const double reduc_factor_falsi_tol = 1e-4;
const double gradient_method = 2; // method to compute derivative ( 1: finite difference, 2: formulae)
int iters_used_falsi = 0;
const int max_iters_split = 20;
int iters_used_split = 0;
// Check if current state is an acceptable solution.
Residual residual(*this, cell);
double x[2] = {saturation_[cell], concentration_[cell]};
double res[2];
double mc;
double ff;
residual.computeResidual(x, 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] = { std::max(polyprops_.deadPoreVol(), smin_[2*cell]), 0.0 };
double x_max[2] = { 1.0, polyprops_.cMax() };
double t;
double t_max;
double t_out;
double direction[2];
double end_point[2];
double gradient[2];
bool unsuccessfull_newton_step;
double x_new[2];
double res_new[2];
while ((norm(res) > tol_) && (iters_used_split < max_iters_split)) {
// We first try a Newton step
if (residual.solveNewtonStep(x, x_new, gradient_method)) {
residual.computeResidual(x_new, res_new, mc, ff);
unsuccessfull_newton_step = false;
if (norm(res_new) > norm(res) || x_new[0] < x_min[0] || x_new[1] < x_min[1] || x_new[0] > x_max[0] || x_new[1] > x_max[1]) {
unsuccessfull_newton_step = true;
} 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;
}
} else {
unsuccessfull_newton_step = true;
}
if (unsuccessfull_newton_step) {
if (std::abs(res[0]) < std::abs(res[1])) {
falsi_tol = std::max(reduc_factor_falsi_tol*std::abs(res[0]), tol_);
if (res[0] < -falsi_tol) {
direction[0] = x_max[0] - x[0];
direction[1] = x_min[1] - x[1];
residual.if_res_s = true;
} else if (res[0] > falsi_tol) {
direction[0] = x_min[0] - x[0];
direction[1] = x_max[1] - x[1];
residual.if_res_s = true;
} else {
residual.computeGradient(x, res, gradient, gradient_method);
direction[0] = -gradient[1];
direction[1] = gradient[0];
residual.if_res_s = false;
}
} else {
falsi_tol = std::max(reduc_factor_falsi_tol*std::abs(res[1]), tol_);
if (res[1] < -falsi_tol) {
direction[0] = x_max[0] - x[0];
direction[1] = x_max[1] - x[1];
residual.if_res_s = false;
} else if (res[1] > falsi_tol) {
direction[0] = x_min[0] - x[0];
direction[1] = x_min[1] - x[1];
residual.if_res_s = false;
} else {
residual.computeGradient(x, res, gradient, gradient_method);
direction[0] = -gradient[1];
direction[1] = gradient[0];
residual.if_res_s = true;
}
}
if (residual.if_res_s) {
if (res[0] < 0) {
end_point[0] = x_max[0];
end_point[1] = x_min[1];
residual.setup(x, direction, end_point, x_min, x_max, t_max, t_out);
if (residual(t_out) >= 0) {
t_max = t_out;
}
} else {
end_point[0] = x_min[0];
end_point[1] = x_max[1];
residual.setup(x, direction, end_point, x_min, x_max, t_max, t_out);
if (residual(t_out) <= 0) {
t_max = t_out;
}
}
} else {
if (res[1] < 0) {
// We update the bounding box (Here we assume that the curve res_s(s,c)=0 is
// increasing). We do it only for a significantly large res[1]
// if (res[1] < -tol ) {
// x_min[0] = x[0];
// x_min[1] = x[1];
// }
//
end_point[0] = x_max[0];
end_point[1] = x_max[1];
residual.setup(x, direction, end_point, x_min, x_max, t_max, t_out);
if (residual(t_out) >= 0) {
t_max = t_out;
}
} else {
// We update the bounding box (Here we assume that the curve res_s(s,c)=0 is increasing)
// if (res[1] > tol) {
// x_max[0] = x[0];
// x_max[1] = x[1];
// }
//
end_point[0] = x_min[0];
end_point[1] = x_min[1];
residual.setup(x, direction, end_point, x_min, x_max, t_max, t_out);
if (residual(t_out) <= 0) {
t_max = t_out;
}
}
}
t = modifiedRegulaFalsi(residual, 0., t_max, maxit_, falsi_tol, iters_used_falsi);
if (std::abs(residual(t)) > falsi_tol) {
std::cout << "modifiedRegulaFalsi did not produce result under tolerance." << std::endl;
}
residual.compute_x_of_t(x, t);
residual.computeResidual(x, 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 {
concentration_[cell] = x[1];
cmax_[cell] = std::max(cmax_[cell], concentration_[cell]);
saturation_[cell] = x[0];
fractionalflow_[cell] = ff;
mc_[cell] = mc;
}
}
void TransportModelPolymer::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];
fractionalflow_[cell] = fracFlow(saturation_[cell], concentration_[cell], cell);
mc_[cell] = computeMc(concentration_[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;
}
double TransportModelPolymer::fracFlow(double s, double c, int cell) const
{
double c_max_limit = polyprops_.cMax();
double cbar = c/c_max_limit;
double mu_w = visc_[0];
double mu_m = polyprops_.viscMult(c)*mu_w;
double mu_p = polyprops_.viscMult(polyprops_.cMax())*mu_w;
double omega = polyprops_.mixParam();
double mu_m_omega = std::pow(mu_m, omega);
double mu_w_e = mu_m_omega*std::pow(mu_w, 1.0 - omega);
double mu_p_eff = mu_m_omega*std::pow(mu_p, 1.0 - omega);
double inv_mu_w_eff = (1.0 - cbar)/mu_w_e + cbar/mu_p_eff;
double inv_visc_eff[2] = { inv_mu_w_eff, 1.0/visc_[1] };
double sat[2] = { s, 1.0 - s };
double mob[2];
props_.relperm(1, sat, &cell, mob, 0);
mob[0] *= inv_visc_eff[0];
mob[1] *= inv_visc_eff[1];
return mob[0]/(mob[0] + mob[1]);
}
double TransportModelPolymer::fracFlowWithDer(double s, double c, int cell, double* der) const
{
// We should check the dimension of der
double c_max_limit = polyprops_.cMax();
double cbar = c/c_max_limit;
double mu_w = visc_[0];
double mu_m_dc; // derivative of mu_m with respect to c
double mu_m = polyprops_.viscMultWithDer(c, &mu_m_dc)*mu_w;
mu_m_dc *= mu_w;
double mu_p = polyprops_.viscMult(polyprops_.cMax())*mu_w;
double omega = polyprops_.mixParam();
double mu_w_e = std::pow(mu_m, omega)*std::pow(mu_w, 1 - omega);
double mu_w_e_dc = omega*mu_m_dc*std::pow(mu_m, omega - 1)*std::pow(mu_w, 1 - omega);
double mu_p_eff = std::pow(mu_m, omega)*std::pow(mu_p, 1 - omega);
double mu_p_eff_dc = omega*mu_m_dc*std::pow(mu_m, omega - 1)*std::pow(mu_p, 1 - omega);
double mu_w_eff = 1./((1 - cbar)/mu_w_e + cbar/mu_p_eff);
double mu_w_eff_dc = -1./c_max_limit*mu_w_eff*mu_w_eff*(1./mu_p_eff - 1./mu_w_e)
+ (1-cbar)*(mu_w_eff*mu_w_eff/(mu_w_e*mu_w_e))*mu_w_e_dc
+ cbar*(mu_w_eff*mu_w_eff/(mu_p_eff*mu_p_eff))*mu_p_eff_dc;
double visc_eff[2] = { mu_w_eff, visc_[1] };
double sat[2] = { s, 1.0 - s };
double mob[2];
double mob_ds[2];
double mob_dc[2];
double perm[2];
double perm_ds[4];
props_.relperm(1, sat, &cell, perm, perm_ds);
mob[0] = perm[0]/visc_eff[0];
mob[1] = perm[1]/visc_eff[1];
mob_ds[0] = perm_ds[0]/visc_eff[0];
mob_ds[1] = perm_ds[1]/visc_eff[1];
mob_dc[0] = - perm[0]*mu_w_eff_dc/(mu_w_eff*mu_w_eff);
mob_dc[1] = 0.;
der[0] = (mob_ds[0]*mob[1] - mob_ds[1]*mob[0])/((mob[0] + mob[1])*(mob[0] + mob[1]));
der[1] = (mob_dc[0]*mob[1] - mob_dc[1]*mob[0])/((mob[0] + mob[1])*(mob[0] + mob[1]));
return mob[0]/(mob[0] + mob[1]);
}
double TransportModelPolymer::computeMc(double c) const
{
double c_max_limit = polyprops_.cMax();
double cbar = c/c_max_limit;
double mu_w = visc_[0];
double mu_m = polyprops_.viscMult(c)*mu_w;
double mu_p = polyprops_.viscMult(polyprops_.cMax())*mu_w;
double omega = polyprops_.mixParam();
double mu_m_omega = std::pow(mu_m, omega);
double mu_w_e = mu_m_omega*std::pow(mu_w, 1.0 - omega);
double mu_p_eff = mu_m_omega*std::pow(mu_p, 1.0 - omega);
double inv_mu_w_eff = (1.0 - cbar)/mu_w_e + cbar/mu_p_eff;
return c/(inv_mu_w_eff*mu_p_eff);
}
double TransportModelPolymer::computeMcWithDer(double c, double* der) const
{
double c_max_limit = polyprops_.cMax();
double cbar = c/c_max_limit;
double mu_w = visc_[0];
double mu_m_dc; // derivative of mu_m with respect to c
double mu_m = polyprops_.viscMultWithDer(c, &mu_m_dc)*mu_w;
mu_m_dc *= mu_w;
double mu_p = polyprops_.viscMult(polyprops_.cMax())*mu_w;
double omega = polyprops_.mixParam();
double mu_m_omega = std::pow(mu_m, omega);
double mu_m_omega_minus1 = std::pow(mu_m, omega-1);
double mu_w_omega = std::pow(mu_w, 1.0 - omega);
double mu_w_e = mu_m_omega*mu_w_omega;
double mu_w_e_dc = omega*mu_m_dc*mu_m_omega_minus1*mu_w_omega;
double mu_p_omega = std::pow(mu_p, 1.0 - omega);
double mu_p_eff = mu_m_omega*mu_p_omega;
double mu_p_eff_dc = omega*mu_m_dc*mu_m_omega_minus1*mu_p_omega;
double mu_w_eff = 1./((1 - cbar)/mu_w_e + cbar/mu_p_eff);
double inv_mu_w_eff_dc = -mu_w_e_dc/(mu_w_e*mu_w_e)*(1. - cbar) - mu_p_eff_dc/(mu_p_eff*mu_p_eff)*cbar + (1./mu_p_eff - 1./mu_w_e);
double mu_w_eff_dc = -mu_w_eff*mu_w_eff*inv_mu_w_eff_dc;
*der = mu_w_eff/mu_p_eff + c*mu_w_eff_dc/mu_p_eff - c*mu_p_eff_dc*mu_w_eff/(mu_p_eff*mu_p_eff);
return c*mu_w_eff/mu_p_eff;
}
} // namespace Opm
/* Local Variables: */
/* c-basic-offset:4 */
/* End: */