Initial version of compressible transport. Work in progress.

This commit is contained in:
Atgeirr Flø Rasmussen 2012-05-28 09:12:09 +02:00
parent 566eea86ec
commit e0d38cfaf8
4 changed files with 622 additions and 8 deletions

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@ -113,6 +113,7 @@ opm/core/transport/spu_explicit.c \
opm/core/transport/spu_implicit.c \
opm/core/transport/transport_source.c \
opm/core/transport/reorder/TransportModelInterface.cpp \
opm/core/transport/reorder/TransportModelCompressibleTwophase.cpp \
opm/core/transport/reorder/TransportModelTwophase.cpp \
opm/core/transport/reorder/reordersequence.cpp \
opm/core/transport/reorder/nlsolvers.c \
@ -243,6 +244,7 @@ opm/core/transport/transport_source.h \
opm/core/transport/GravityColumnSolver.hpp \
opm/core/transport/GravityColumnSolver_impl.hpp \
opm/core/transport/reorder/TransportModelInterface.hpp \
opm/core/transport/reorder/TransportModelCompressibleTwophase.hpp \
opm/core/transport/reorder/TransportModelTwophase.hpp \
opm/core/transport/reorder/nlsolvers.h \
opm/core/transport/reorder/reordersequence.h \

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@ -49,7 +49,7 @@
#include <opm/core/WellState.hpp>
#include <opm/core/transport/GravityColumnSolver.hpp>
#include <opm/core/transport/reorder/TransportModelTwophase.hpp>
#include <opm/core/transport/reorder/TransportModelCompressibleTwophase.hpp>
#include <boost/filesystem/convenience.hpp>
#include <boost/scoped_ptr.hpp>
@ -68,7 +68,7 @@
#include <vector>
#include <numeric>
#define TRANSPORT_SOLVER_FIXED 0
#define TRANSPORT_SOLVER_FIXED 1
template <class State>
@ -159,7 +159,7 @@ main(int argc, char** argv)
}
output_interval = param.getDefault("output_interval", output_interval);
}
// const int num_transport_substeps = param.getDefault("num_transport_substeps", 1);
const int num_transport_substeps = param.getDefault("num_transport_substeps", 1);
// If we have a "deck_filename", grid and props will be read from that.
bool use_deck = param.has("deck_filename");
@ -307,7 +307,7 @@ main(int argc, char** argv)
#if TRANSPORT_SOLVER_FIXED
const double nl_tolerance = param.getDefault("nl_tolerance", 1e-9);
const int nl_maxiter = param.getDefault("nl_maxiter", 30);
Opm::TransportModelTwophase reorder_model(*grid->c_grid(), *props, nl_tolerance, nl_maxiter);
Opm::TransportModelCompressibleTwophase reorder_model(*grid->c_grid(), *props, nl_tolerance, nl_maxiter);
if (use_gauss_seidel_gravity) {
reorder_model.initGravity(grav);
}
@ -427,12 +427,13 @@ main(int argc, char** argv)
}
for (int tr_substep = 0; tr_substep < num_transport_substeps; ++tr_substep) {
Opm::toWaterSat(state.saturation(), reorder_sat);
reorder_model.solve(&state.faceflux()[0], &porevol[0], &reorder_src[0],
stepsize, &reorder_sat[0]);
reorder_model.solve(&state.faceflux()[0], &state.pressure()[0], &state.surfacevol()[0],
&porevol[0], &reorder_src[0], stepsize, &reorder_sat[0]);
Opm::toBothSat(reorder_sat, state.saturation());
Opm::computeInjectedProduced(*props, state.saturation(), reorder_src, stepsize, injected, produced);
// Opm::computeInjectedProduced(*props, state.saturation(), reorder_src, stepsize, injected, produced);
if (use_segregation_split) {
reorder_model.solveGravity(columns, &porevol[0], stepsize, reorder_sat);
THROW("Segregation not implemented yet.");
// reorder_model.solveGravity(columns, &porevol[0], stepsize, reorder_sat);
Opm::toBothSat(reorder_sat, state.saturation());
}
}

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@ -0,0 +1,510 @@
/*
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/core/transport/reorder/TransportModelCompressibleTwophase.hpp>
#include <opm/core/fluid/BlackoilPropertiesInterface.hpp>
#include <opm/core/grid.h>
#include <opm/core/transport/reorder/reordersequence.h>
#include <opm/core/utility/RootFinders.hpp>
#include <opm/core/utility/miscUtilities.hpp>
#include <opm/core/pressure/tpfa/trans_tpfa.h>
#include <fstream>
#include <iterator>
#include <numeric>
namespace Opm
{
// Choose error policy for scalar solves here.
typedef RegulaFalsi<WarnAndContinueOnError> RootFinder;
TransportModelCompressibleTwophase::TransportModelCompressibleTwophase(const UnstructuredGrid& grid,
const Opm::BlackoilPropertiesInterface& props,
const double tol,
const int maxit)
: grid_(grid),
props_(props),
tol_(tol),
maxit_(maxit),
darcyflux_(0),
source_(0),
dt_(0.0),
saturation_(0),
fractionalflow_(grid.number_of_cells, -1.0),
mob_(2*grid.number_of_cells, -1.0),
ia_upw_(grid.number_of_cells + 1, -1),
ja_upw_(grid.number_of_faces, -1),
ia_downw_(grid.number_of_cells + 1, -1),
ja_downw_(grid.number_of_faces, -1)
{
if (props.numPhases() != 2) {
THROW("Property object must have 2 phases");
}
int np = props.numPhases();
int num_cells = props.numCells();
visc_.resize(np*num_cells);
A_.resize(np*np*num_cells);
smin_.resize(np*num_cells);
smax_.resize(np*num_cells);
allcells_.resize(num_cells);
for (int i = 0; i < num_cells; ++i) {
allcells_[i] = i;
}
props.satRange(props.numCells(), &allcells_[0], &smin_[0], &smax_[0]);
}
void TransportModelCompressibleTwophase::solve(const double* darcyflux,
const double* pressure,
const double* surfacevol0,
const double* porevolume,
const double* source,
const double dt,
double* saturation)
{
darcyflux_ = darcyflux;
surfacevol0_ = surfacevol0;
porevolume_ = porevolume;
source_ = source;
dt_ = dt;
saturation_ = saturation;
props_.viscosity(props_.numCells(), pressure, NULL, &allcells_[0], &visc_[0], NULL);
props_.matrix(props_.numCells(), pressure, NULL, &allcells_[0], &A_[0], NULL);
std::vector<int> seq(grid_.number_of_cells);
std::vector<int> comp(grid_.number_of_cells + 1);
int ncomp;
compute_sequence_graph(&grid_, darcyflux_,
&seq[0], &comp[0], &ncomp,
&ia_upw_[0], &ja_upw_[0]);
const int nf = grid_.number_of_faces;
std::vector<double> neg_darcyflux(nf);
std::transform(darcyflux, darcyflux + nf, neg_darcyflux.begin(), std::negate<double>());
compute_sequence_graph(&grid_, &neg_darcyflux[0],
&seq[0], &comp[0], &ncomp,
&ia_downw_[0], &ja_downw_[0]);
reorderAndTransport(grid_, darcyflux);
}
// Residual function r(s) for a single-cell implicit Euler transport
//
// [[ incompressible was: r(s) = s - s0 + dt/pv*( influx + outflux*f(s) ) ]]
//
// r(s) = s - B*z0 + dt/pv*( influx + outflux*f(s))
//
// @@@ What about the source term
//
// where influx is water influx, outflux is total outflux.
// We need the formula influx = B_i sum_{j->i} b_j v_{ij} + q_w.
// outflux = B_i sum_{i->j} b_i v_{ij} - q = sum_{i->j} v_{ij} - q (as before)
// Influxes are negative, outfluxes positive.
struct TransportModelCompressibleTwophase::Residual
{
int cell;
double s0;
double influx; // sum_j min(v_ij, 0)*f(s_j) + q_w // TODO: fix comment.
double outflux; // sum_j max(v_ij, 0) - q
// @@@ TODO: figure out change to rock-comp. terms with fluid compr.
// double comp_term; // q - sum_j v_ij
double dtpv; // dt/pv(i)
const TransportModelCompressibleTwophase& tm;
explicit Residual(const TransportModelCompressibleTwophase& tmodel, int cell_index)
: tm(tmodel)
{
cell = cell_index;
s0 = tm.saturation_[cell];
const int np = tm.props_.numPhases();
const double B_cell = 1.0/tm.A_[np*np*cell + 0];
double src_flux = -tm.source_[cell];
bool src_is_inflow = src_flux < 0.0;
influx = src_is_inflow ? src_flux : 0.0;
outflux = !src_is_inflow ? src_flux : 0.0;
// comp_term = tm.source_[cell]; // Note: this assumes that all source flux is water.
dtpv = tm.dt_/tm.porevolume_[cell];
for (int i = tm.grid_.cell_facepos[cell]; i < tm.grid_.cell_facepos[cell+1]; ++i) {
const 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) {
const double b_face = tm.A_[np*np*other + 0];
influx += B_cell*b_face*flux*tm.fractionalflow_[other];
} else {
outflux += flux;
}
// comp_term -= flux;
}
}
}
double operator()(double s) const
{
// return s - s0 + dtpv*(outflux*tm.fracFlow(s, cell) + influx + s*comp_term);
return s - s0 + dtpv*(outflux*tm.fracFlow(s, cell) + influx);
}
};
void TransportModelCompressibleTwophase::solveSingleCell(const int cell)
{
Residual res(*this, cell);
int iters_used;
saturation_[cell] = RootFinder::solve(res, saturation_[cell], 0.0, 1.0, maxit_, tol_, iters_used);
fractionalflow_[cell] = fracFlow(saturation_[cell], cell);
}
void TransportModelCompressibleTwophase::solveMultiCell(const int num_cells, const int* cells)
{
// Experiment: when a cell changes more than the tolerance,
// mark all downwind cells as needing updates. After
// computing a single update in each cell, use marks
// to guide further updating. Clear mark in cell when
// its solution gets updated.
// Verdict: this is a good one! Approx. halved total time.
std::vector<int> needs_update(num_cells, 1);
// This one also needs the mapping from all cells to
// the strongly connected subset to filter out connections
std::vector<int> pos(grid_.number_of_cells, -1);
for (int i = 0; i < num_cells; ++i) {
const int cell = cells[i];
pos[cell] = i;
}
// Note: partially copied from below.
const double tol = 1e-9;
const int max_iters = 300;
// Must store s0 before we start.
std::vector<double> s0(num_cells);
// Must set initial fractional flows before we start.
// Also, we compute the # of upstream neighbours.
// std::vector<int> num_upstream(num_cells);
for (int i = 0; i < num_cells; ++i) {
const int cell = cells[i];
fractionalflow_[cell] = fracFlow(saturation_[cell], cell);
s0[i] = saturation_[cell];
// num_upstream[i] = ia_upw_[cell + 1] - ia_upw_[cell];
}
// Solve once in each cell.
// std::vector<int> fully_marked_stack;
// fully_marked_stack.reserve(num_cells);
int num_iters = 0;
int update_count = 0; // Change name/meaning to cells_updated?
do {
update_count = 0; // Must reset count for every iteration.
for (int i = 0; i < num_cells; ++i) {
// while (!fully_marked_stack.empty()) {
// // std::cout << "# fully marked cells = " << fully_marked_stack.size() << std::endl;
// const int fully_marked_ci = fully_marked_stack.back();
// fully_marked_stack.pop_back();
// ++update_count;
// const int cell = cells[fully_marked_ci];
// const double old_s = saturation_[cell];
// saturation_[cell] = s0[fully_marked_ci];
// solveSingleCell(cell);
// const double s_change = std::fabs(saturation_[cell] - old_s);
// if (s_change > tol) {
// // Mark downwind cells.
// for (int j = ia_downw_[cell]; j < ia_downw_[cell+1]; ++j) {
// const int downwind_cell = ja_downw_[j];
// int ci = pos[downwind_cell];
// ++needs_update[ci];
// if (needs_update[ci] == num_upstream[ci]) {
// fully_marked_stack.push_back(ci);
// }
// }
// }
// // Unmark this cell.
// needs_update[fully_marked_ci] = 0;
// }
if (!needs_update[i]) {
continue;
}
++update_count;
const int cell = cells[i];
const double old_s = saturation_[cell];
saturation_[cell] = s0[i];
solveSingleCell(cell);
const double s_change = std::fabs(saturation_[cell] - old_s);
if (s_change > tol) {
// Mark downwind cells.
for (int j = ia_downw_[cell]; j < ia_downw_[cell+1]; ++j) {
const int downwind_cell = ja_downw_[j];
int ci = pos[downwind_cell];
if (ci != -1) {
needs_update[ci] = 1;
}
// ++needs_update[ci];
// if (needs_update[ci] == num_upstream[ci]) {
// fully_marked_stack.push_back(ci);
// }
}
}
// Unmark this cell.
needs_update[i] = 0;
}
// std::cout << "Iter = " << num_iters << " update_count = " << update_count
// << " # marked cells = "
// << std::accumulate(needs_update.begin(), needs_update.end(), 0) << std::endl;
} while (update_count > 0 && ++num_iters < max_iters);
// Done with iterations, check if we succeeded.
if (update_count > 0) {
THROW("In solveMultiCell(), we did not converge after "
<< num_iters << " iterations. Remaining update count = " << update_count);
}
std::cout << "Solved " << num_cells << " cell multicell problem in "
<< num_iters << " iterations." << std::endl;
}
double TransportModelCompressibleTwophase::fracFlow(double s, int cell) const
{
double sat[2] = { s, 1.0 - s };
double mob[2];
props_.relperm(1, sat, &cell, mob, 0);
mob[0] /= visc_[2*cell + 0];
mob[1] /= visc_[2*cell + 1];
return mob[0]/(mob[0] + mob[1]);
}
// Residual function r(s) for a single-cell implicit Euler gravity segregation
//
// r(s) = s - s0 + dt/pv*sum_{j adj i}( gravmod_ij * gf_ij ).
//
struct TransportModelCompressibleTwophase::GravityResidual
{
int cell;
int nbcell[2];
double s0;
double dtpv; // dt/pv(i)
double gf[2];
const TransportModelCompressibleTwophase& tm;
explicit GravityResidual(const TransportModelCompressibleTwophase& 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];
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];
}
s0 = tm.saturation_[cell];
dtpv = tm.dt_/tm.porevolume_[cell];
}
double operator()(double s) const
{
double res = s - s0;
double mobcell[2];
tm.mobility(s, cell, mobcell);
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;
}
};
void TransportModelCompressibleTwophase::mobility(double s, int cell, double* mob) const
{
double sat[2] = { s, 1.0 - s };
props_.relperm(1, sat, &cell, mob, 0);
mob[0] /= visc_[0];
mob[1] /= visc_[1];
}
void TransportModelCompressibleTwophase::initGravity(const double* grav)
{
// Set up gravflux_ = T_ij g (rho_w - rho_o) (z_i - z_j)
std::vector<double> htrans(grid_.cell_facepos[grid_.number_of_cells]);
const int nf = grid_.number_of_faces;
const int dim = grid_.dimensions;
gravflux_.resize(nf);
tpfa_htrans_compute(const_cast<UnstructuredGrid*>(&grid_), props_.permeability(), &htrans[0]);
tpfa_trans_compute(const_cast<UnstructuredGrid*>(&grid_), &htrans[0], &gravflux_[0]);
const double delta_rho = 0.0;// props_.density()[0] - props_.density()[1];
THROW("TransportModelCompressibleTwophase gravity solver not done yet."); // See line above...
for (int f = 0; f < nf; ++f) {
const int* c = &grid_.face_cells[2*f];
double gdz = 0.0;
if (c[0] != -1 && c[1] != -1) {
for (int d = 0; d < dim; ++d) {
gdz += grav[d]*(grid_.cell_centroids[dim*c[0] + d] - grid_.cell_centroids[dim*c[1] + d]);
}
}
gravflux_[f] *= delta_rho*gdz;
}
}
void TransportModelCompressibleTwophase::solveSingleCellGravity(const std::vector<int>& cells,
const int pos,
const double* gravflux)
{
const int cell = cells[pos];
GravityResidual res(*this, cells, pos, gravflux);
if (std::fabs(res(saturation_[cell])) > tol_) {
int iters_used;
saturation_[cell] = RootFinder::solve(res, smin_[2*cell], smax_[2*cell], maxit_, tol_, iters_used);
}
saturation_[cell] = std::min(std::max(saturation_[cell], smin_[2*cell]), smax_[2*cell]);
mobility(saturation_[cell], cell, &mob_[2*cell]);
}
int TransportModelCompressibleTwophase::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);
for (int ci = 0; ci < nc; ++ci) {
s0_[ci] = saturation_[cells[ci]];
}
// Solve single cell problems, repeating if necessary.
double max_s_change = 0.0;
int num_iters = 0;
do {
max_s_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]] };
saturation_[cells[ci]] = s0_[ci];
solveSingleCellGravity(cells, ci, &col_gravflux[0]);
saturation_[cells[ci2]] = s0_[ci2];
solveSingleCellGravity(cells, ci2, &col_gravflux[0]);
max_s_change = std::max(max_s_change, std::max(std::fabs(saturation_[cells[ci]] - old_s[0]),
std::fabs(saturation_[cells[ci2]] - old_s[1])));
}
// std::cout << "Iter = " << num_iters << " max_s_change = " << max_s_change << std::endl;
} while (max_s_change > tol_ && ++num_iters < maxit_);
if (max_s_change > tol_) {
THROW("In solveGravityColumn(), we did not converge after "
<< num_iters << " iterations. Delta s = " << max_s_change);
}
return num_iters + 1;
}
void TransportModelCompressibleTwophase::solveGravity(const std::vector<std::vector<int> >& columns,
const double* pressure,
const double* porevolume,
const double dt,
std::vector<double>& saturation)
{
// Initialize mobilities.
const int nc = grid_.number_of_cells;
std::vector<int> cells(nc);
for (int c = 0; c < nc; ++c) {
cells[c] = c;
}
mob_.resize(2*nc);
std::vector<double> boths;
Opm::toBothSat(saturation, boths);
props_.relperm(cells.size(), &boths[0], &cells[0], &mob_[0], 0);
props_.viscosity(props_.numCells(), pressure, NULL, &allcells_[0], &visc_[0], NULL);
for (int c = 0; c < nc; ++c) {
mob_[2*c + 0] /= visc_[2*c + 0];
mob_[2*c + 1] /= visc_[2*c + 1];
}
// Set up other variables.
porevolume_ = porevolume;
dt_ = dt;
saturation_ = &saturation[0];
// Solve on all columns.
int num_iters = 0;
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;
}
} // namespace Opm
/* Local Variables: */
/* c-basic-offset:4 */
/* End: */

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@ -0,0 +1,101 @@
/*
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/>.
*/
#ifndef OPM_TRANSPORTMODELCOMPRESSIBLETWOPHASE_HEADER_INCLUDED
#define OPM_TRANSPORTMODELCOMPRESSIBLETWOPHASE_HEADER_INCLUDED
#include <opm/core/transport/reorder/TransportModelInterface.hpp>
#include <vector>
struct UnstructuredGrid;
namespace Opm
{
class BlackoilPropertiesInterface;
class TransportModelCompressibleTwophase : public TransportModelInterface
{
public:
TransportModelCompressibleTwophase(const UnstructuredGrid& grid,
const Opm::BlackoilPropertiesInterface& props,
const double tol,
const int maxit);
void solve(const double* darcyflux,
const double* pressure,
const double* surfacevol0,
const double* porevolume,
const double* source,
const double dt,
double* saturation);
virtual void solveSingleCell(const int cell);
virtual void solveMultiCell(const int num_cells, const int* cells);
void initGravity(const double* grav);
void solveSingleCellGravity(const std::vector<int>& cells,
const int pos,
const double* gravflux);
int solveGravityColumn(const std::vector<int>& cells);
void solveGravity(const std::vector<std::vector<int> >& columns,
const double* pressure,
const double* porevolume,
const double dt,
std::vector<double>& saturation);
private:
const UnstructuredGrid& grid_;
const BlackoilPropertiesInterface& props_;
std::vector<int> allcells_;
std::vector<double> visc_;
std::vector<double> A_;
std::vector<double> smin_;
std::vector<double> smax_;
double tol_;
double maxit_;
const double* darcyflux_; // one flux per grid face
const double* surfacevol0_; // one per phase per cell
const double* porevolume_; // one volume per cell
const double* source_; // one source per cell
double dt_;
double* saturation_; // one per cell
std::vector<double> fractionalflow_; // = m[0]/(m[0] + m[1]) per cell
// For gravity segregation.
std::vector<double> gravflux_;
std::vector<double> mob_;
std::vector<double> s0_;
// Storing the upwind and downwind graphs for experiments.
std::vector<int> ia_upw_;
std::vector<int> ja_upw_;
std::vector<int> ia_downw_;
std::vector<int> ja_downw_;
struct Residual;
double fracFlow(double s, int cell) const;
struct GravityResidual;
void mobility(double s, int cell, double* mob) const;
};
} // namespace Opm
#endif // OPM_TRANSPORTMODELCOMPRESSIBLETWOPHASE_HEADER_INCLUDED