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TransportModelCompressiblePolymer.cpp
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/*
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/TransportModelCompressiblePolymer.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/utility/miscUtilitiesBlackoil.hpp>
#include <opm/core/pressure/tpfa/trans_tpfa.h>
#include <cmath>
#include <list>
#include <opm/core/utility/ErrorMacros.hpp>
// Choose error policy for scalar solves here.
typedef Opm::RegulaFalsi<Opm::WarnAndContinueOnError> RootFinder;
class Opm::TransportModelCompressiblePolymer::ResidualEquation
{
public:
GradientMethod gradient_method;
int cell;
double s0;
double c0;
double cmax0;
double influx; // B_i sum_j b_j min(v_ij, 0)*f(s_j) - B_i q_w
double influx_polymer;
double outflux; // sum_j max(v_ij, 0) - B_i q
double porevolume0;
double porevolume;
double porosity0;
double porosity;
double B_cell0;
double B_cell;
double dtpv; // dt/pv(i)
double dps;
double rhor;
double ads0;
TransportModelCompressiblePolymer& tm;
ResidualEquation(TransportModelCompressiblePolymer& tmodel, int cell_index);
void computeResidual(const double* x, double* res) const;
void computeResidual(const double* x, double* res, double& mc, double& ff) const;
double computeResidualS(const double* x) const;
double computeResidualC(const double* x) const;
void computeGradientResS(const double* x, double* res, double* gradient) const;
void computeGradientResC(const double* x, double* res, double* gradient) const;
void computeJacobiRes(const double* x, double* dres_s_dsdc, double* dres_c_dsdc) const;
bool solveNewtonStepSC(const double*, const double*, double*) const;
bool solveNewtonStepC(const double* , const double*, double*) const;
private:
void 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;
};
class Opm::TransportModelCompressiblePolymer::ResidualCGrav {
public:
const TransportModelCompressiblePolymer& tm;
const int cell;
const double s0;
const double c0;
const double cmax0;
const double porevolume;
const double porosity;
const double dtpv; // dt/pv(i)
const double dps;
const double rhor;
double c_ads0;
double gf[2];
int nbcell[2];
mutable double last_s;
ResidualCGrav(const TransportModelCompressiblePolymer& tmodel,
const std::vector<int>& cells,
const int pos,
const double* gravflux);
double operator()(double c) const;
double computeGravResidualS(double s, double c) const;
double computeGravResidualC(double s, double c) const;
double lastSaturation() const;
};
class Opm::TransportModelCompressiblePolymer::ResidualSGrav {
public:
const ResidualCGrav& res_c_eq_;
double c;
ResidualSGrav(const ResidualCGrav& res_c_eq, const double c_init = 0.0);
double operator()(double s) const;
};
namespace
{
bool check_interval(const double* xmin, const double* xmax, double* x);
double norm(double* res)
{
return std::max(std::abs(res[0]), std::abs(res[1]));
}
// Define a piecewise linear curve along which we will look for zero of the "s" or "r" residual.
// The curve starts at "x", goes along the direction "direction" until it hits the boundary of the box of
// admissible values for "s" and "x" (which is given by "[x_min[0], x_max[0]]x[x_min[1], x_max[1]]").
// Then it joins in a straight line the point "end_point".
class CurveInSCPlane{
public:
CurveInSCPlane();
void 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);
void computeXOfT(double*, const double) const;
private:
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];
};
}
namespace Opm
{
TransportModelCompressiblePolymer::TransportModelCompressiblePolymer(const UnstructuredGrid& grid,
const BlackoilPropertiesInterface& props,
const PolymerProperties& polyprops,
const RockCompressibility& rock_comp,
const SingleCellMethod method,
const double tol,
const int maxit)
: grid_(grid),
props_(props),
polyprops_(polyprops),
rock_comp_(rock_comp),
darcyflux_(0),
porevolume0_(0),
porevolume_(0),
source_(0),
dt_(0.0),
inflow_c_(0.0),
tol_(tol),
maxit_(maxit),
method_(method),
adhoc_safety_(1.0),
concentration_(0),
cmax_(0),
fractionalflow_(grid.number_of_cells, -1.0),
mc_(grid.number_of_cells, -1.0),
gravity_(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)
{
const int np = props.numPhases();
const int num_cells = grid.number_of_cells;
if (props.numPhases() != 2) {
THROW("Property object must have 2 phases");
}
visc_.resize(np*num_cells);
A_.resize(np*np*num_cells);
A0_.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(num_cells, &allcells_[0], &smin_[0], &smax_[0]);
}
void TransportModelCompressiblePolymer::setPreferredMethod(SingleCellMethod method)
{
method_ = method;
}
void TransportModelCompressiblePolymer::solve(const double* darcyflux,
const std::vector<double>& initial_pressure,
const std::vector<double>& pressure,
const double* porevolume0,
const double* porevolume,
const double* source,
const double dt,
const double inflow_c,
std::vector<double>& saturation,
std::vector<double>& surfacevol,
std::vector<double>& concentration,
std::vector<double>& cmax)
{
darcyflux_ = darcyflux;
porevolume0_ = porevolume0;
porevolume_ = porevolume;
source_ = source;
dt_ = dt;
inflow_c_ = inflow_c;
toWaterSat(saturation, saturation_);
concentration_ = &concentration[0];
cmax_ = &cmax[0];
#if PROFILING
res_counts.clear();
#endif
props_.viscosity(grid_.number_of_cells, &pressure[0], NULL, &allcells_[0], &visc_[0], NULL);
props_.matrix(grid_.number_of_cells, &initial_pressure[0], NULL, &allcells_[0], &A0_[0], NULL);
props_.matrix(grid_.number_of_cells, &pressure[0], NULL, &allcells_[0], &A_[0], NULL);
// Check immiscibility requirement (only done for first cell).
if (A_[1] != 0.0 || A_[2] != 0.0) {
THROW("TransportCompressibleModelCompressibleTwophase requires a property object without miscibility.");
}
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);
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]);
}
// 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 TransportModelCompressiblePolymer::ResidualS
{
TransportModelCompressiblePolymer::ResidualEquation& res_eq_;
const double c_;
explicit ResidualS(TransportModelCompressiblePolymer::ResidualEquation& res_eq,
const double c)
: res_eq_(res_eq),
c_(c)
{
}
double operator()(double s) const
{
double x[2];
x[0] = s;
x[1] = c_;
return res_eq_.computeResidualS(x);
}
};
// Residual for concentration equation, single-cell implicit Euler transport
//
// \TODO doc me
// where ...
// Influxes are negative, outfluxes positive.
struct TransportModelCompressiblePolymer::ResidualC
{
mutable double s; // Mutable in order to change it with every operator() call to be the last computed s value.
TransportModelCompressiblePolymer::ResidualEquation& res_eq_;
explicit ResidualC(TransportModelCompressiblePolymer::ResidualEquation& res_eq)
: res_eq_(res_eq)
{}
void computeBothResiduals(const double s_arg, const double c_arg, double& res_s, double& res_c, double& mc, double& ff) const
{
double x[2];
double res[2];
x[0] = s_arg;
x[1] = c_arg;
res_eq_.computeResidual(x, res, mc, ff);
res_s = res[0];
res_c = res[1];
}
double operator()(double c) const
{
ResidualS res_s(res_eq_, 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);
s = RootFinder::solve(res_s, res_eq_.s0, 0.0, 1.0,
res_eq_.tm.maxit_, res_eq_.tm.tol_, iters_used);
double x[2];
x[0] = s;
x[1] = c;
double res = res_eq_.computeResidualC(x);
#ifdef EXTRA_DEBUG_OUTPUT
std::cout << "c = " << c << " s = " << s << " c-residual = " << res << std::endl;
#endif
return res;
}
double lastSaturation() const
{
return s;
}
};
// ResidualEquation gathers parameters to construct the residual, computes its
// value and the values of its derivatives.
TransportModelCompressiblePolymer::ResidualEquation::ResidualEquation(TransportModelCompressiblePolymer& tmodel, int cell_index)
: tm(tmodel)
{
gradient_method = Analytic;
cell = cell_index;
const int np = tm.props_.numPhases();
s0 = tm.saturation_[cell];
c0 = tm.concentration_[cell];
cmax0 = tm.cmax_[cell];
double src_flux = -tm.source_[cell];
bool src_is_inflow = src_flux < 0.0;
B_cell0 = 1.0/tm.A0_[np*np*cell + 0];
B_cell = 1.0/tm.A_[np*np*cell + 0];
// Not clear why we multiply by B_cell source terms.
influx = src_is_inflow ? src_flux : 0.0;
outflux = !src_is_inflow ? src_flux : 0.0;
porevolume0 = tm.porevolume0_[cell];
porevolume = tm.porevolume_[cell];
const double vol_cell = tm.grid_.cell_volumes[cell];
porosity0 = porevolume0/vol_cell;
porosity = porevolume/vol_cell;
dtpv = tm.dt_/porevolume;
dps = tm.polyprops_.deadPoreVol();
rhor = tm.polyprops_.rockDensity();
tm.polyprops_.adsorption(c0, cmax0, ads0);
double mc;
tm.computeMc(tm.inflow_c_, mc);
influx_polymer = src_is_inflow ? src_flux*mc : 0.0;
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) {
const double b_face =tm.A_[np*np*other+ 0];
influx += B_cell*b_face*flux*tm.fractionalflow_[other];
influx_polymer += flux*tm.fractionalflow_[other]*tm.mc_[other];
} else {
outflux += flux; // Because B_cell*b_face = 1 for outflow faces
}
}
}
}
void TransportModelCompressiblePolymer::ResidualEquation::computeResidual(const double* x, double* res) const
{
double dres_s_dsdc[2];
double dres_c_dsdc[2];
double mc;
double ff;
computeResAndJacobi(x, true, true, false, false, res, dres_s_dsdc, dres_c_dsdc, mc, ff);
}
void TransportModelCompressiblePolymer::ResidualEquation::computeResidual(const double* x, double* res, double& mc, double& ff) const
{
double dres_s_dsdc[2];
double dres_c_dsdc[2];
computeResAndJacobi(x, true, true, false, false, res, dres_s_dsdc, dres_c_dsdc, mc, ff);
}
double TransportModelCompressiblePolymer::ResidualEquation::computeResidualS(const double* x) const
{
double res[2];
double dres_s_dsdc[2];
double dres_c_dsdc[2];
double mc;
double ff;
computeResAndJacobi(x, true, false, false, false, res, dres_s_dsdc, dres_c_dsdc, mc, ff);
return res[0];
}
double TransportModelCompressiblePolymer::ResidualEquation::computeResidualC(const double* x) const
{
double res[2];
double dres_s_dsdc[2];
double dres_c_dsdc[2];
double mc;
double ff;
computeResAndJacobi(x, false, true, false, false, res, dres_s_dsdc, dres_c_dsdc, mc, ff);
return res[1];
}
void TransportModelCompressiblePolymer::ResidualEquation::computeGradientResS(const double* x, double* res, double* gradient) const
// If gradient_method == FinDif, use finite difference
// If gradient_method == Analytic, use analytic expresions
{
double dres_c_dsdc[2];
double mc;
double ff;
computeResAndJacobi(x, true, true, true, false, res, gradient, dres_c_dsdc, mc, ff);
}
void TransportModelCompressiblePolymer::ResidualEquation::computeGradientResC(const double* x, double* res, double* gradient) const
// If gradient_method == FinDif, use finite difference
// If gradient_method == Analytic, use analytic expresions
{
double dres_s_dsdc[2];
double mc;
double ff;
computeResAndJacobi(x, true, true, false, true, res, dres_s_dsdc, gradient, mc, ff);
}
// Compute the Jacobian of the residual equations.
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{