mirror of
https://github.com/OPM/opm-simulators.git
synced 2025-02-25 18:55:30 -06:00
Added Newton step as first step in Splitting s-c residual solver.
This commit is contained in:
Xavier Raynaud
@@ -259,7 +259,6 @@ namespace Opm
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outflux = !src_is_inflow ? dflux : 0.0;
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dtpv = tm.dt_/tm.porevolume_[cell];
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porosity = tm.porosity_[cell];
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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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@@ -284,6 +283,31 @@ namespace Opm
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}
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}
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void computeExplicitStep(const double* xmin, const double* xmax, double* x) const {
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double ff = tm.fracFlow(s0, c0, cell);
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double mc = tm.computeMc(c0);
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double dps = tm.polyprops_.dps;
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//In this explicit step, we do not compute absorption and take ads0=ads
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// double rhor = tm.polyprops_.rhor;
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// double ads0 = tm.polyprops_.adsorbtion(std::max(c0, cmax0));
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// double ads = tm.polyprops_.adsorbtion(std::max(c, cmax0));
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x[0] = s0 - dtpv*(outflux*ff + influx);
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x[1] = 1./(x[0] - dps)*((s0 - dps)*c0 - dtpv*(outflux*ff*mc + influx_polymer)); // + rhor*((1.0 - porosity)/porosity)*(ads - ads0)
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// We check that the values we obtain remains admissible (this is not guaranted for an explicit step)
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if (x[0] < xmin[0]) {
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x[0] = xmin[0];
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} else if (x[0] > xmax[0]) {
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x[0] = xmax[0];
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}
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if (x[1] < xmin[1]) {
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x[1] = xmin[1];
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} else if (x[1] > xmax[1]) {
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x[1] = xmax[1];
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}
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}
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void computeResidual(const double* x, double* res) const
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{
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double s = x[0];
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@@ -301,12 +325,81 @@ namespace Opm
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}
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// Compute gradient using finite difference.
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void computeGradient(const double* x, double* res, double* gradient, const int& method) const
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// If method == 1, use finite diference
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// If method == 2, use analytic expresions
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bool solveNewtonStep(const double* x, double* x_new, const int& gradient_method) {
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// If gradient_method == 1, use finite difference
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// If gradient_method == 2, use analytic expresions
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double res[2];
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double res_s_ds_dc[2];
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double res_c_ds_dc[2];
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if (gradient_method == 1) {
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double epsi = 1e-8;
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double res_epsi[2];
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double x_epsi[2];
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computeResidual(x, res);
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x_epsi[0] = x[0] + epsi;
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x_epsi[1] = x[1];
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computeResidual(x_epsi, res_epsi);
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res_s_ds_dc[0] = (res_epsi[0] - res[0])/epsi;
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x_epsi[0] = x[0];
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x_epsi[1] = x[1] + epsi;
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computeResidual(x_epsi, res_epsi);
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res_s_ds_dc[1] = (res_epsi[0] - res[0])/epsi;
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x_epsi[0] = x[0] + epsi;
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x_epsi[1] = x[1];
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computeResidual(x_epsi, res_epsi);
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res_c_ds_dc[0] = (res_epsi[1] - res[1])/epsi;
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x_epsi[0] = x[0];
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x_epsi[1] = x[1] + epsi;
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computeResidual(x_epsi, res_epsi);
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res_c_ds_dc[1] = (res_epsi[1] - res[1])/epsi;
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} else if (gradient_method == 2) {
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double s = x[0];
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double c = x[1];
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double ff_ds_dc[2];
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double ff = tm.fracFlowWithDer(s, c, cell, ff_ds_dc);
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double mc_dc;
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double mc = tm.computeMcWithDer(c, &mc_dc);
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double dps = tm.polyprops_.dps;
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double rhor = tm.polyprops_.rhor;
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double ads0 = tm.polyprops_.adsorbtion(std::max(c0, cmax0));
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double ads;
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double ads_dc;
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if (c < cmax0) {
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ads = tm.polyprops_.adsorbtion(cmax0);
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ads_dc = 0;
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} else {
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ads = tm.polyprops_.adsorbtionWithDer(c, &ads_dc);
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}
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res[0] = s - s0 + dtpv*(outflux*ff + influx);
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res[1] = (s - dps)*c - (s0 - dps)*c0
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+ rhor*((1.0 - porosity)/porosity)*(ads - ads0)
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+ dtpv*(outflux*ff*mc + influx_polymer);
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res_s_ds_dc[0] = 1 + dtpv*outflux*ff_ds_dc[0];
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res_s_ds_dc[1] = dtpv*outflux*ff_ds_dc[1];
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res_c_ds_dc[0] = c + dtpv*outflux*(ff_ds_dc[0])*mc;
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res_c_ds_dc[1] = s - dps + rhor*((1.0 - porosity)/porosity)*ads_dc
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+ dtpv*outflux*(ff_ds_dc[1]*mc + ff*mc_dc);
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}
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double det = res_s_ds_dc[0]*res_c_ds_dc[1] - res_c_ds_dc[0]*res_s_ds_dc[1];
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if (std::abs(det) < 1e-8) {
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return false;
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} else {
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x_new[0] = x[0] - (res[0]*res_c_ds_dc[1] - res[1]*res_s_ds_dc[1])/det;
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x_new[1] = x[1] - (res[1]*res_s_ds_dc[0] - res[0]*res_c_ds_dc[0])/det;
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return true;
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}
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}
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void computeGradient(const double* x, double* res, double* gradient, const int& gradient_method) const
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// If gradient_method == 1, use finite difference
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// If gradient_method == 2, use analytic expresions
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{
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if (method == 1) {
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if (gradient_method == 1) {
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double epsi = 1e-8;
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double res_epsi[2];
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double x_epsi[2];
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@@ -330,7 +423,7 @@ namespace Opm
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computeResidual(x_epsi, res_epsi);
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gradient[1] = (res_epsi[1] - res[1])/epsi;
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}
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} else if (method == 2) {
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} else if (gradient_method == 2) {
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double s = x[0];
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double c = x[1];
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double ff_ds_dc[2];
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@@ -499,7 +592,7 @@ namespace Opm
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// the tolerance for 1d solver is set as a function of the residual
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// The tolerance falsi_tol is improved by (reduc_factor_falsi_tol * "previous residual") at each step
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double falsi_tol;
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double reduc_factor_falsi_tol = 1e-5;
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double reduc_factor_falsi_tol = 1e-4;
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const double gradient_method = 2; // method to compute derivative ( 1: finite difference, 2: formulae)
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int iters_used_falsi = 0;
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const int max_iters_split = 20;
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@@ -509,14 +602,18 @@ namespace Opm
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Residual residual(*this, cell);
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double x[2] = {saturation_[cell], concentration_[cell]};
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double res[2];
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residual.computeResidual(x, res);
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if (norm(res) < tol) {
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cmax_[cell] = std::max(cmax_[cell], concentration_[cell]);
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fractionalflow_[cell] = fracFlow(saturation_[cell], concentration_[cell], cell);
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mc_[cell] = computeMc(concentration_[cell]);
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return;
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}
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bool res_s_done;
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double x_min[2] = {0.0, 0.0};
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double x_min[2] = {polyprops_.dps, 0.0};
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double x_max[2] = {1.0, polyprops_.c_max_limit};
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double t;
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double t_max;
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@@ -524,6 +621,13 @@ namespace Opm
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double direction[2];
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double end_point[2];
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double gradient[2];
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bool unsuccessfull_newton_step;
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double x_new[2];
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double res_new[2];
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// // Update x=(s, c) with an explicit solver.
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// residual.computeExplicitStep(x_min, x_max, x);
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// residual.computeResidual(x, res);
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if (std::abs(res[0]) < std::abs(res[1])) {
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falsi_tol = std::max(reduc_factor_falsi_tol*std::abs(res[0]), tol);
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@@ -552,79 +656,123 @@ namespace Opm
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}
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while ((norm(res) > tol) && (iters_used_split < max_iters_split)) {
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if (res_s_done) { // solve for c-residual
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if (res[1] < 0) {
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// We update the bounding box (Here we assume that the curve res_s(s,c)=0 is
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// increasing). We do it only for a significantly large res[1]
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// if (res[1] < -tol ) {
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// x_min[0] = x[0];
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// x_min[1] = x[1];
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// }
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//
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end_point[0] = x_max[0];
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end_point[1] = x_max[1];
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residual.setup(x, direction, end_point, x_min, x_max, false, t_max, t_out);
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if (residual(t_out) >= 0) {
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t_max = t_out;
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}
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// We first try a Newton step
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if (residual.solveNewtonStep(x, x_new, gradient_method)) {
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residual.computeResidual(x_new, res_new);
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unsuccessfull_newton_step = false;
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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]) {
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unsuccessfull_newton_step = true;
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} else {
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// We update the bounding box (Here we assume that the curve res_s(s,c)=0 is increasing)
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// if (res[1] > tol) {
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// x_max[0] = x[0];
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// x_max[1] = x[1];
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// }
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//
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end_point[0] = x_min[0];
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end_point[1] = x_min[1];
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residual.setup(x, direction, end_point, x_min, x_max, false, t_max, t_out);
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if (residual(t_out) <= 0) {
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t_max = t_out;
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x[0] = x_new[0];
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x[1] = x_new[1];
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res[0] = res_new[0];
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res[1] = res_new[1];
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if (std::abs(res[0]) < std::abs(res[1])) {
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falsi_tol = std::max(reduc_factor_falsi_tol*std::abs(res[0]), tol);
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if (std::abs(res[0]) > tol) {
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if (res[0] < 0) {
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direction[0] = x_max[0] - x[0];
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direction[1] = x_min[1] - x[1];
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} else {
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direction[0] = x_min[0] - x[0];
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direction[1] = x_max[1] - x[1];
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}
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res_s_done = false; // means that we will start by finding zero of s-residual.
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}
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} else {
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falsi_tol = std::max(reduc_factor_falsi_tol*std::abs(res[1]), tol);
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if (std::abs(res[1]) > tol) {
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if (res[1] < 0) {
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direction[0] = x_max[0] - x[0];
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direction[1] = x_max[1] - x[1];
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}
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} else {
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direction[0] = x_min[0] - x[0];
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direction[1] = x_min[1] - x[1];
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}
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res_s_done = true; // means that we will start by finding zero of c-residual.
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}
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}
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t = modifiedRegulaFalsi(residual, 0., t_max, max_iters_falsi, falsi_tol, iters_used_falsi);
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if (std::abs(residual(t)) > falsi_tol) {
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std::cout << "modifiedRegulaFalsi did not produce result under tolerance." << std::endl;
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}
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residual.compute_new_x(x, t);
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residual.computeGradient(x, res, gradient, gradient_method);
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falsi_tol = std::max(reduc_factor_falsi_tol*std::abs(res[1]), tol);
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direction[0] = gradient[1];
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direction[1] = -gradient[0];
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res_s_done = false;
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} else { // solve for s residual
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if (res[0] < 0) {
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end_point[0] = x_max[0];
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end_point[1] = x_min[1];
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residual.setup(x, direction, end_point, x_min, x_max, true, t_max, t_out);
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if (residual(t_out) >= 0) {
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t_max = t_out;
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}
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} else {
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end_point[0] = x_min[0];
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end_point[1] = x_max[1];
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residual.setup(x, direction, end_point, x_min, x_max, true, t_max, t_out);
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if (residual(t_out) <= 0) {
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t_max = t_out;
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}
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}
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t = modifiedRegulaFalsi(residual, 0., t_max, max_iters_falsi, falsi_tol, iters_used_falsi);
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if (std::abs(residual(t)) > falsi_tol) {
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std::cout << "modifiedRegulaFalsi did not produce result under tolerance." << std::endl;
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}
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residual.compute_new_x(x, t);
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residual.computeGradient(x, res, gradient, gradient_method);
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falsi_tol = std::max(reduc_factor_falsi_tol*std::abs(res[0]), tol);
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res_s_done = true;
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direction[0] = -gradient[1];
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direction[1] = gradient[0];
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} else {
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unsuccessfull_newton_step = true;
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}
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iters_used_split += 1;
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if (unsuccessfull_newton_step) {
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if (res_s_done) { // solve for c-residual
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if (res[1] < 0) {
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// We update the bounding box (Here we assume that the curve res_s(s,c)=0 is
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// increasing). We do it only for a significantly large res[1]
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// if (res[1] < -tol ) {
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// x_min[0] = x[0];
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// x_min[1] = x[1];
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// }
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//
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end_point[0] = x_max[0];
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end_point[1] = x_max[1];
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residual.setup(x, direction, end_point, x_min, x_max, false, t_max, t_out);
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if (residual(t_out) >= 0) {
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t_max = t_out;
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}
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} else {
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// We update the bounding box (Here we assume that the curve res_s(s,c)=0 is increasing)
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// if (res[1] > tol) {
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// x_max[0] = x[0];
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// x_max[1] = x[1];
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// }
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//
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end_point[0] = x_min[0];
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end_point[1] = x_min[1];
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residual.setup(x, direction, end_point, x_min, x_max, false, t_max, t_out);
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if (residual(t_out) <= 0) {
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t_max = t_out;
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}
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}
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t = modifiedRegulaFalsi(residual, 0., t_max, max_iters_falsi, falsi_tol, iters_used_falsi);
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if (std::abs(residual(t)) > falsi_tol) {
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std::cout << "modifiedRegulaFalsi did not produce result under tolerance." << std::endl;
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}
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residual.compute_new_x(x, t);
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residual.computeGradient(x, res, gradient, gradient_method);
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falsi_tol = std::max(reduc_factor_falsi_tol*std::abs(res[1]), tol);
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direction[0] = gradient[1];
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direction[1] = -gradient[0];
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res_s_done = false;
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} else { // solve for s residual
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if (res[0] < 0) {
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end_point[0] = x_max[0];
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end_point[1] = x_min[1];
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residual.setup(x, direction, end_point, x_min, x_max, true, t_max, t_out);
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if (residual(t_out) >= 0) {
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t_max = t_out;
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}
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} else {
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end_point[0] = x_min[0];
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end_point[1] = x_max[1];
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residual.setup(x, direction, end_point, x_min, x_max, true, t_max, t_out);
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if (residual(t_out) <= 0) {
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t_max = t_out;
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}
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}
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t = modifiedRegulaFalsi(residual, 0., t_max, max_iters_falsi, falsi_tol, iters_used_falsi);
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if (std::abs(residual(t)) > falsi_tol) {
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std::cout << "modifiedRegulaFalsi did not produce result under tolerance." << std::endl;
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}
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residual.compute_new_x(x, t);
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residual.computeGradient(x, res, gradient, gradient_method);
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falsi_tol = std::max(reduc_factor_falsi_tol*std::abs(res[0]), tol);
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res_s_done = true;
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direction[0] = -gradient[1];
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direction[1] = gradient[0];
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}
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iters_used_split += 1;
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}
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}
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if ((iters_used_split >= max_iters_split) && (norm(res) >= tol)) {
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solveSingleCellBracketing(cell);
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std::cout << "splitting did not work" << std::endl;
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std::cout << "cell number" << cell << std::endl;
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} else {
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concentration_[cell] = x[1];
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cmax_[cell] = std::max(cmax_[cell], concentration_[cell]);
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