mirror of
https://github.com/OPM/opm-simulators.git
synced 2024-12-25 08:41:00 -06:00
260 lines
11 KiB
C++
260 lines
11 KiB
C++
/*
|
|
Copyright 2013 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 <config.h>
|
|
|
|
#include <opm/autodiff/TransportSolverTwophaseAd.hpp>
|
|
#include <opm/grid/UnstructuredGrid.h>
|
|
#include <opm/core/linalg/LinearSolverInterface.hpp>
|
|
#include <opm/core/props/IncompPropertiesInterface.hpp>
|
|
#include <opm/grid/transmissibility/trans_tpfa.h>
|
|
#include <opm/common/utility/parameters/ParameterGroup.hpp>
|
|
#include <opm/common/ErrorMacros.hpp>
|
|
#include <opm/common/Exceptions.hpp>
|
|
#include <iostream>
|
|
|
|
|
|
|
|
namespace Opm
|
|
{
|
|
|
|
/// Construct solver.
|
|
/// \param[in] grid A 2d or 3d grid.
|
|
/// \param[in] props Rock and fluid properties.
|
|
/// \param[in] linsolver Linear solver for Newton-Raphson scheme.
|
|
/// \param[in] gravity Gravity vector (null for no gravity).
|
|
/// \param[in] param Parameters for the solver.
|
|
TransportSolverTwophaseAd::TransportSolverTwophaseAd(const UnstructuredGrid& grid,
|
|
const IncompPropertiesInterface& props,
|
|
const LinearSolverInterface& linsolver,
|
|
const double* gravity,
|
|
const ParameterGroup& param)
|
|
: grid_(grid),
|
|
props_(props),
|
|
linsolver_(linsolver),
|
|
ops_(grid),
|
|
gravity_(0.0),
|
|
tol_(param.getDefault("nl_tolerance", 1e-9)),
|
|
maxit_(param.getDefault("nl_maxiter", 30))
|
|
{
|
|
using namespace Opm::AutoDiffGrid;
|
|
const int nc = numCells(grid_);
|
|
allcells_.resize(nc);
|
|
for (int i = 0; i < nc; ++i) {
|
|
allcells_[i] = i;
|
|
}
|
|
if (gravity && gravity[dimensions(grid_) - 1] != 0.0) {
|
|
gravity_ = gravity[dimensions(grid_) - 1];
|
|
for (int dd = 0; dd < dimensions(grid_) - 1; ++dd) {
|
|
if (gravity[dd] != 0.0) {
|
|
OPM_THROW(std::runtime_error, "TransportSolverTwophaseAd: can only handle gravity aligned with last dimension");
|
|
}
|
|
}
|
|
V htrans(grid.cell_facepos[grid.number_of_cells]);
|
|
tpfa_htrans_compute(const_cast<UnstructuredGrid*>(&grid), props.permeability(), htrans.data());
|
|
V trans(numFaces(grid_));
|
|
tpfa_trans_compute(const_cast<UnstructuredGrid*>(&grid), htrans.data(), trans.data());
|
|
transi_ = subset(trans, ops_.internal_faces);
|
|
}
|
|
}
|
|
|
|
|
|
|
|
|
|
// Virtual destructor.
|
|
TransportSolverTwophaseAd::~TransportSolverTwophaseAd()
|
|
{
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
namespace
|
|
{
|
|
|
|
template <class ADB>
|
|
std::vector<ADB>
|
|
phaseMobility(const Opm::IncompPropertiesInterface& props,
|
|
const std::vector<int>& cells,
|
|
const typename ADB::V& sw)
|
|
{
|
|
typedef Eigen::Array<double, Eigen::Dynamic, 2, Eigen::RowMajor> TwoCol;
|
|
typedef Eigen::Array<double, Eigen::Dynamic, 4, Eigen::RowMajor> FourCol;
|
|
typedef Eigen::SparseMatrix<double> S;
|
|
typedef typename ADB::V V;
|
|
typedef typename ADB::M M;
|
|
const int nc = props.numCells();
|
|
TwoCol s(nc, 2);
|
|
s.leftCols<1>() = sw;
|
|
s.rightCols<1>() = 1.0 - s.leftCols<1>();
|
|
TwoCol kr(nc, 2);
|
|
FourCol dkr(nc, 4);
|
|
props.relperm(nc, s.data(), cells.data(), kr.data(), dkr.data());
|
|
V krw = kr.leftCols<1>();
|
|
V kro = kr.rightCols<1>();
|
|
// In dkr, columns col(0..3) are:
|
|
// dkrw/dsw dkro/dsw dkrw/dso dkrw/dso <-- partial derivatives, really.
|
|
// If we want the derivatives with respect to some variable x,
|
|
// we must apply the chain rule:
|
|
// dkrw/dx = dkrw/dsw*dsw/dx + dkrw/dso*dso/dx.
|
|
// If x is sw as in our case we are left with.
|
|
// dkrw/dsw = col(0) - col(2)
|
|
// dkro/dsw = col(1) - col(3)
|
|
V dkrw = dkr.leftCols<1>() - dkr.rightCols<2>().leftCols<1>();
|
|
V dkro = dkr.leftCols<2>().rightCols<1>() - dkr.rightCols<1>();
|
|
S krwjac(nc,nc);
|
|
S krojac(nc,nc);
|
|
auto sizes = Eigen::ArrayXi::Ones(nc);
|
|
krwjac.reserve(sizes);
|
|
krojac.reserve(sizes);
|
|
for (int c = 0; c < nc; ++c) {
|
|
krwjac.insert(c,c) = dkrw(c);
|
|
krojac.insert(c,c) = dkro(c);
|
|
}
|
|
const double* mu = props.viscosity();
|
|
std::vector<M> dmw = { M(krwjac)/mu[0] };
|
|
std::vector<M> dmo = { M(krojac)/mu[1] };
|
|
|
|
std::vector<ADB> pmobc = { ADB::function(krw / mu[0], std::move(dmw)) ,
|
|
ADB::function(kro / mu[1], std::move(dmo)) };
|
|
return pmobc;
|
|
}
|
|
|
|
/// Returns fw(sw).
|
|
template <class ADB>
|
|
ADB
|
|
fluxFunc(const std::vector<ADB>& m)
|
|
{
|
|
assert (m.size() == 2);
|
|
|
|
ADB f = m[0] / (m[0] + m[1]);
|
|
|
|
return f;
|
|
}
|
|
|
|
} // anonymous namespace
|
|
|
|
|
|
/// Solve for saturation at next timestep.
|
|
/// Note that this only performs advection by total velocity, and
|
|
/// no gravity segregation.
|
|
/// \param[in] porevolume Array of pore volumes.
|
|
/// \param[in] source Transport source term. For interpretation see Opm::computeTransportSource().
|
|
/// \param[in] dt Time step.
|
|
/// \param[in, out] state Reservoir state. Calling solve() will read state.faceflux() and
|
|
/// read and write state.saturation().
|
|
void TransportSolverTwophaseAd::solve(const double* porevolume,
|
|
const double* source,
|
|
const double dt,
|
|
TwophaseState& state)
|
|
{
|
|
using namespace Opm::AutoDiffGrid;
|
|
typedef Eigen::Array<double, Eigen::Dynamic, 2, Eigen::RowMajor> TwoCol;
|
|
typedef Eigen::Map<const V> Vec;
|
|
const int nc = numCells(grid_);
|
|
const TwoCol s0 = Eigen::Map<const TwoCol>(state.saturation().data(), nc, 2);
|
|
double res_norm = 1e100;
|
|
const V sw0 = s0.leftCols<1>();
|
|
// sw1 is the object that will be changed every Newton iteration.
|
|
// V sw1 = sw0;
|
|
V sw1 = 0.5*V::Ones(nc,1);
|
|
const V dflux_all = Vec(state.faceflux().data(), numFaces(grid_), 1);
|
|
const int num_internal = ops_.internal_faces.size();
|
|
V dflux = subset(dflux_all, ops_.internal_faces);
|
|
|
|
// Upwind selection of mobilities by phase.
|
|
// We have that for a phase P
|
|
// v_P = lambda_P K (-grad p + rho_P g grad z)
|
|
// and we assume that this has the same direction as
|
|
// dh_P = -grad p + rho_P g grad z.
|
|
// This may not be true for arbitrary anisotropic situations,
|
|
// but for scalar lambda and using TPFA it holds.
|
|
const V p1 = Vec(state.pressure().data(), nc, 1);
|
|
const V ndp = (ops_.ngrad * p1.matrix()).array();
|
|
const V z = cellCentroidsZToEigen(grid_);
|
|
const V ndz = (ops_.ngrad * z.matrix()).array();
|
|
assert(num_internal == ndp.size());
|
|
const double* density = props_.density();
|
|
const V dhw = ndp - ndz*(gravity_*density[0]);
|
|
const V dho = ndp - ndz*(gravity_*density[1]);
|
|
const UpwindSelector<double> upwind_w(grid_, ops_, dhw);
|
|
const UpwindSelector<double> upwind_o(grid_, ops_, dho);
|
|
|
|
// Compute more explicit and constant terms used in the equations.
|
|
const V pv = Vec(porevolume, nc, 1);
|
|
const V dtpv = dt/pv;
|
|
const V q = Vec(source, nc, 1);
|
|
const V qneg = q.min(V::Zero(nc,1));
|
|
const V qpos = q.max(V::Zero(nc,1));
|
|
const double gfactor = gravity_*(density[0] - density[1]);
|
|
const V gravflux = (gravity_ == 0.0) ? V(V::Zero(num_internal, 1))
|
|
: ndz*transi_*gfactor;
|
|
|
|
// Block pattern for variables.
|
|
// Primary variables:
|
|
// sw : one per cell
|
|
std::vector<int> bpat = { nc };
|
|
|
|
// Newton-Raphson loop.
|
|
int it = 0;
|
|
do {
|
|
// Assemble linear system.
|
|
const ADB sw = ADB::variable(0, sw1, bpat);
|
|
const std::vector<ADB> pmobc = phaseMobility<ADB>(props_, allcells_, sw.value());
|
|
const ADB fw_cell = fluxFunc(pmobc);
|
|
const std::vector<ADB> pmobf = { upwind_w.select(pmobc[0]),
|
|
upwind_o.select(pmobc[1]) };
|
|
const ADB fw_face = fluxFunc(pmobf);
|
|
const ADB flux = fw_face * (dflux - pmobf[1]*gravflux);
|
|
// const ADB fw_face = upwind_w.select(fw_cell);
|
|
// const ADB flux = fw_face * dflux;
|
|
const ADB qtr_ad = qpos + fw_cell*qneg;
|
|
const ADB transport_residual = sw - sw0 + dtpv*(ops_.div*flux - qtr_ad);
|
|
res_norm = transport_residual.value().matrix().norm();
|
|
std::cout << "Residual l2-norm = " << res_norm << std::endl;
|
|
|
|
// Solve linear system.
|
|
Eigen::SparseMatrix<double, Eigen::RowMajor> smatr;
|
|
transport_residual.derivative()[0].toSparse(smatr);
|
|
assert(smatr.isCompressed());
|
|
V ds(nc);
|
|
LinearSolverInterface::LinearSolverReport rep
|
|
= linsolver_.solve(nc, smatr.nonZeros(),
|
|
smatr.outerIndexPtr(), smatr.innerIndexPtr(), smatr.valuePtr(),
|
|
transport_residual.value().data(), ds.data());
|
|
if (!rep.converged) {
|
|
OPM_THROW(LinearSolverProblem, "Linear solver convergence error in TransportSolverTwophaseAd::solve()");
|
|
}
|
|
|
|
// Update (possible clamp) sw1.
|
|
sw1 = sw.value() - ds;
|
|
sw1 = sw1.min(V::Ones(nc,1)).max(V::Zero(nc,1));
|
|
it += 1;
|
|
} while (res_norm > tol_ && it < maxit_);
|
|
|
|
// Write to output data structure.
|
|
Eigen::Map<TwoCol> sref(state.saturation().data(), nc, 2);
|
|
sref.leftCols<1>() = sw1;
|
|
sref.rightCols<1>() = 1.0 - sw1;
|
|
}
|
|
|
|
|
|
} // namespace Opm
|