commit 49156ece7c9ba7fb9b0143c76bad6476db24c11d parent 77795a3e9adf1fc0f4406bcf41da19b1e39b32fd Author: Anders Damsgaard <anders@adamsgaard.dk> Date: Wed, 14 Jan 2026 22:11:24 +0100 feat(solver): optimize darcy solver with TDMA Diffstat:
| M | fluid.c | | | 729 | +++++++++++++++++++++++++++++++++++++------------------------------------------ |
| M | simulation.c | | | 4 | ++-- |
| M | simulation.h | | | 253 | +++++++++++++++++++++++++++++++++++++++---------------------------------------- |
| D | test/cngf_pf_dry.std | | | 16 | ---------------- |
| D | test/cngf_pf_dry_cohesive.std | | | 16 | ---------------- |
| D | test/cngf_pf_dry_norm.std | | | 16 | ---------------- |
| D | test/cngf_pf_dry_trans.std | | | 25 | ------------------------- |
| D | test/cngf_pf_dry_trans_overcons.std | | | 99 | ------------------------------------------------------------------------------- |
| D | test/cngf_pf_dry_trans_undercons.std | | | 99 | ------------------------------------------------------------------------------- |
| D | test/cngf_pf_dry_vconst.std | | | 25 | ------------------------- |
| D | test/cngf_pf_wet.std | | | 16 | ---------------- |
| D | test/cngf_pf_wet_norm.std | | | 16 | ---------------- |
| D | test/cngf_pf_wet_vari.std | | | 200 | ------------------------------------------------------------------------------- |
| D | test/cngf_pf_wet_vari_diff.std | | | 200 | ------------------------------------------------------------------------------- |
| D | test/cngf_pf_wet_vari_pulse.std | | | 200 | ------------------------------------------------------------------------------- |
| D | test/cngf_pf_wet_vari_pulse_vlim.std | | | 200 | ------------------------------------------------------------------------------- |
| D | test/max_depth_misc.std | | | 0 | |
| D | test/old_wet_vari.std | | | 200 | ------------------------------------------------------------------------------- |
| D | test/shear_flux_dry.std | | | 1 | - |
| D | test/shear_flux_wet.std | | | 1 | - |
20 files changed, 471 insertions(+), 1845 deletions(-)
diff --git a/fluid.c b/fluid.c @@ -1,429 +1,386 @@ -#include <stdlib.h> -#include <math.h> -#include <err.h> -#include "simulation.h" -#include "arrays.h" #include "fluid.h" +#include "arrays.h" +#include "simulation.h" +#include <err.h> +#include <math.h> +#include <stdlib.h> -void -hydrostatic_fluid_pressure_distribution(struct simulation *sim) -{ - int i; +void hydrostatic_fluid_pressure_distribution(struct simulation *sim) { + int i; - for (i = 0; i < sim->nz; ++i) - sim->p_f_ghost[i + 1] = sim->p_f_top - + sim->phi[i] * sim->rho_f * sim->G - * (sim->L_z - sim->z[i]); + for (i = 0; i < sim->nz; ++i) + sim->p_f_ghost[i + 1] = sim->p_f_top + sim->phi[i] * sim->rho_f * sim->G * + (sim->L_z - sim->z[i]); } -static double -diffusivity(struct simulation *sim, int i) { - if (sim->D > 0.0) - return sim->D; - else - return sim->k[i] - / ((sim->alpha + sim->phi[i] * sim->beta_f) * sim->mu_f); +static double diffusivity(struct simulation *sim, int i) { + if (sim->D > 0.0) + return sim->D; + else + return sim->k[i] / ((sim->alpha + sim->phi[i] * sim->beta_f) * sim->mu_f); } /* Determines the largest time step for the current simulation state. Note * that the time step should be recalculated if cell sizes or * diffusivities (i.e., permeabilities, porosities, viscosities, or * compressibilities) change. The safety factor should be in ]0;1] */ -int -set_largest_fluid_timestep(struct simulation *sim, const double safety) -{ - int i; - double dx_min, diff, diff_max, *dx; - - dx = spacing(sim->z, sim->nz); - dx_min = INFINITY; - for (i = 0; i < sim->nz - 1; ++i) { - if (dx[i] < 0.0) { - fprintf(stderr, "error: cell spacing negative (%g) in cell %d\n", - dx[i], i); - free(dx); - return 1; - } - if (dx[i] < dx_min) - dx_min = dx[i]; - } - free(dx); - - diff_max = -INFINITY; - for (i = 0; i < sim->nz; ++i) { - diff = diffusivity(sim, i); - if (diff > diff_max) - diff_max = diff; - } - - sim->dt = safety * 0.5 * dx_min * dx_min / diff_max; - if (sim->file_dt * 0.5 < sim->dt) - sim->dt = sim->file_dt; - - return 0; +int set_largest_fluid_timestep(struct simulation *sim, const double safety) { + int i; + double dx_min, diff, diff_max, *dx; + + dx = spacing(sim->z, sim->nz); + dx_min = INFINITY; + for (i = 0; i < sim->nz - 1; ++i) { + if (dx[i] < 0.0) { + fprintf(stderr, "error: cell spacing negative (%g) in cell %d\n", dx[i], + i); + free(dx); + return 1; + } + if (dx[i] < dx_min) + dx_min = dx[i]; + } + free(dx); + + diff_max = -INFINITY; + for (i = 0; i < sim->nz; ++i) { + diff = diffusivity(sim, i); + if (diff > diff_max) + diff_max = diff; + } + + sim->dt = safety * 0.5 * dx_min * dx_min / diff_max; + if (sim->file_dt * 0.5 < sim->dt) + sim->dt = sim->file_dt; + + return 0; } -static double -sine_wave(const double time, - const double ampl, - const double freq, - const double phase) -{ - return ampl * sin(2.0 * PI * freq * time + phase); +static double sine_wave(const double time, const double ampl, const double freq, + const double phase) { + return ampl * sin(2.0 * PI * freq * time + phase); } -static double -triangular_pulse(const double time, - const double peak_ampl, - const double freq, - const double peak_time) -{ - if (peak_time - 1.0 / (2.0 * freq) < time && time <= peak_time) - return peak_ampl * 2.0 * freq * (time - peak_time) + peak_ampl; - else if (peak_time < time && time < peak_time + 1.0 / (2.0 * freq)) - return peak_ampl * 2.0 * freq * (peak_time - time) + peak_ampl; - else - return 0.0; +static double triangular_pulse(const double time, const double peak_ampl, + const double freq, const double peak_time) { + if (peak_time - 1.0 / (2.0 * freq) < time && time <= peak_time) + return peak_ampl * 2.0 * freq * (time - peak_time) + peak_ampl; + else if (peak_time < time && time < peak_time + 1.0 / (2.0 * freq)) + return peak_ampl * 2.0 * freq * (peak_time - time) + peak_ampl; + else + return 0.0; } -static double -square_pulse(const double time, - const double peak_ampl, - const double freq, - const double peak_time) -{ - if (peak_time - 1.0 / (2.0 * freq) < time && - time < peak_time + 1.0 / (2.0 * freq)) - return peak_ampl; - else - return 0.0; +static double square_pulse(const double time, const double peak_ampl, + const double freq, const double peak_time) { + if (peak_time - 1.0 / (2.0 * freq) < time && + time < peak_time + 1.0 / (2.0 * freq)) + return peak_ampl; + else + return 0.0; } -static void -set_fluid_bcs(double *p_f_ghost, struct simulation *sim, const double p_f_top) -{ - /* correct ghost node at top BC for hydrostatic pressure gradient */ - set_bc_dirichlet(p_f_ghost, sim->nz, +1, - p_f_top - sim->phi[0] * sim->rho_f * sim->G * sim->dz); - p_f_ghost[sim->nz] = p_f_top; /* include top node in BC */ - set_bc_neumann(p_f_ghost, - sim->nz, - -1, - sim->phi[0] * sim->rho_f * sim->G, - sim->dz); +static void set_fluid_bcs(double *p_f_ghost, struct simulation *sim, + const double p_f_top) { + /* correct ghost node at top BC for hydrostatic pressure gradient */ + set_bc_dirichlet(p_f_ghost, sim->nz, +1, + p_f_top - sim->phi[0] * sim->rho_f * sim->G * sim->dz); + p_f_ghost[sim->nz] = p_f_top; /* include top node in BC */ + set_bc_neumann(p_f_ghost, sim->nz, -1, sim->phi[0] * sim->rho_f * sim->G, + sim->dz); } -static double -darcy_pressure_change_1d(const int i, - const int nz, - const double *p_f_ghost_in, - const double *phi, - const double *phi_dot, - const double *k, - const double dz, - const double beta_f, - const double alpha, - const double mu_f, - const double D) -{ - double k_, div_k_grad_p, k_zn, k_zp; - - if (D > 0.0) - return D * (p_f_ghost_in[i + 2] - - 2.0 * p_f_ghost_in[i + 1] - + p_f_ghost_in[i]) / (dz * dz); - else { - k_ = k[i]; - if (i == 0) - k_zn = k_; - else - k_zn = k[i - 1]; - if (i == nz - 1) - k_zp = k_; - else - k_zp = k[i + 1]; - - double k_harm_p = 2.0 * k_zp * k_ / fmax(k_zp + k_, 1e-30); - double k_harm_n = 2.0 * k_zn * k_ / fmax(k_zn + k_, 1e-30); - div_k_grad_p = (k_harm_p * (p_f_ghost_in[i + 2] - p_f_ghost_in[i + 1]) / dz - - k_harm_n * (p_f_ghost_in[i + 1] - p_f_ghost_in[i]) / dz -) / dz; +static double darcy_pressure_change_1d(const int i, const int nz, + const double *p_f_ghost_in, + const double *phi, const double *phi_dot, + const double *k, const double dz, + const double beta_f, const double alpha, + const double mu_f, const double D) { + double k_, div_k_grad_p, k_zn, k_zp; + + if (D > 0.0) + return D * + (p_f_ghost_in[i + 2] - 2.0 * p_f_ghost_in[i + 1] + p_f_ghost_in[i]) / + (dz * dz); + else { + k_ = k[i]; + if (i == 0) + k_zn = k_; + else + k_zn = k[i - 1]; + if (i == nz - 1) + k_zp = k_; + else + k_zp = k[i + 1]; + + double k_harm_p = 2.0 * k_zp * k_ / fmax(k_zp + k_, 1e-30); + double k_harm_n = 2.0 * k_zn * k_ / fmax(k_zn + k_, 1e-30); + div_k_grad_p = + (k_harm_p * (p_f_ghost_in[i + 2] - p_f_ghost_in[i + 1]) / dz - + k_harm_n * (p_f_ghost_in[i + 1] - p_f_ghost_in[i]) / dz) / + dz; #ifdef DEBUG - printf("%s [%d]: phi=%g\tdiv_k_grad_p=%g\tphi_dot=%g\n", - __func__, i, phi[i], div_k_grad_p, phi_dot[i]); + printf("%s [%d]: phi=%g\tdiv_k_grad_p=%g\tphi_dot=%g\n", __func__, i, + phi[i], div_k_grad_p, phi_dot[i]); - printf(" p[%d, %d, %d] = [%g, %g, %g]\tk=[%g, %g, %g]\n", - i, i + 1, i + 2, - p_f_ghost_in[i], p_f_ghost_in[i + 1], p_f_ghost_in[i + 2], - k_zn, k_, k_zp); + printf(" p[%d, %d, %d] = [%g, %g, %g]\tk=[%g, %g, %g]\n", i, i + 1, i + 2, + p_f_ghost_in[i], p_f_ghost_in[i + 1], p_f_ghost_in[i + 2], k_zn, k_, + k_zp); #endif - return 1.0 / ((alpha + beta_f * phi[i]) * mu_f) * div_k_grad_p - - 1.0 / ((alpha + beta_f * phi[i]) * (1.0 - phi[i])) * phi_dot[i]; - } + return 1.0 / ((alpha + beta_f * phi[i]) * mu_f) * div_k_grad_p - + 1.0 / ((alpha + beta_f * phi[i]) * (1.0 - phi[i])) * phi_dot[i]; + } } -static double -darcy_pressure_change_1d_impl(const int i, - const int nz, - const double dt, - const double *p_f_old_val, - const double *p_f_ghost_in, - double *p_f_ghost_out, - const double *phi, - const double *phi_dot, - const double *k, - const double dz, - const double beta_f, - const double alpha, - const double mu_f, - const double D) -{ - double k_, div_k_grad_p, k_zn, k_zp, rhs_term, omega = 1.0; - double inv_fluid_term, inv_porosity_term; - - if (D > 0.0) - return D * (p_f_ghost_in[i + 2] - - 2.0 * p_f_ghost_in[i + 1] - + p_f_ghost_in[i]) / (dz * dz); - else { - k_ = k[i]; - if (i == 0) - k_zn = k_; - else - k_zn = k[i - 1]; - if (i == nz - 1) - k_zp = k_; - else - k_zp = k[i + 1]; - - /* Precompute reciprocal terms to avoid repeated divisions */ - inv_fluid_term = 1.0 / ((alpha + beta_f * phi[i]) * mu_f); - inv_porosity_term = 1.0 / ((alpha + beta_f * phi[i]) * (1.0 - phi[i])); - - rhs_term = dt * inv_fluid_term - * ((2.0 * k_zp * k_ / (k_zp + k_) / (dz * dz)) - + (2.0 * k_zn * k_ / (k_zn + k_) / (dz * dz))); - - p_f_ghost_out[i + 1] = 1.0 / (1.0 + rhs_term) - * (p_f_old_val[i + 1] + dt - * (inv_fluid_term - * (2.0 * k_zp * k_ / (k_zp + k_) - * (p_f_ghost_in[i + 2]) / dz - - 2.0 * k_zn * k_ / (k_zn + k_) - * -p_f_ghost_in[i] / dz) / dz - - inv_porosity_term * phi_dot[i])); - p_f_ghost_out[i + 1] = omega * p_f_ghost_out[i + 1] - + (1.0 - omega) * p_f_ghost_in[i + 1]; - - div_k_grad_p = (2.0 * k_zp * k_ / (k_zp + k_) - * (p_f_ghost_out[i + 2] - p_f_ghost_out[i + 1]) / dz - - 2.0 * k_zn * k_ / (k_zn + k_) - * (p_f_ghost_out[i + 1] - p_f_ghost_out[i]) / dz - ) / dz; +static double darcy_pressure_change_1d_impl( + const int i, const int nz, const double dt, const double *p_f_old_val, + const double *p_f_ghost_in, double *p_f_ghost_out, const double *phi, + const double *phi_dot, const double *k, const double dz, + const double beta_f, const double alpha, const double mu_f, + const double D) { + double k_, div_k_grad_p, k_zn, k_zp, rhs_term, omega = 1.0; + double inv_fluid_term, inv_porosity_term; + + if (D > 0.0) + return D * + (p_f_ghost_in[i + 2] - 2.0 * p_f_ghost_in[i + 1] + p_f_ghost_in[i]) / + (dz * dz); + else { + k_ = k[i]; + if (i == 0) + k_zn = k_; + else + k_zn = k[i - 1]; + if (i == nz - 1) + k_zp = k_; + else + k_zp = k[i + 1]; + + /* Precompute reciprocal terms to avoid repeated divisions */ + inv_fluid_term = 1.0 / ((alpha + beta_f * phi[i]) * mu_f); + inv_porosity_term = 1.0 / ((alpha + beta_f * phi[i]) * (1.0 - phi[i])); + + rhs_term = dt * inv_fluid_term * + ((2.0 * k_zp * k_ / (k_zp + k_) / (dz * dz)) + + (2.0 * k_zn * k_ / (k_zn + k_) / (dz * dz))); + + p_f_ghost_out[i + 1] = + 1.0 / (1.0 + rhs_term) * + (p_f_old_val[i + 1] + + dt * (inv_fluid_term * + (2.0 * k_zp * k_ / (k_zp + k_) * (p_f_ghost_in[i + 2]) / dz - + 2.0 * k_zn * k_ / (k_zn + k_) * -p_f_ghost_in[i] / dz) / + dz - + inv_porosity_term * phi_dot[i])); + p_f_ghost_out[i + 1] = + omega * p_f_ghost_out[i + 1] + (1.0 - omega) * p_f_ghost_in[i + 1]; + + div_k_grad_p = (2.0 * k_zp * k_ / (k_zp + k_) * + (p_f_ghost_out[i + 2] - p_f_ghost_out[i + 1]) / dz - + 2.0 * k_zn * k_ / (k_zn + k_) * + (p_f_ghost_out[i + 1] - p_f_ghost_out[i]) / dz) / + dz; #ifdef DEBUG - printf("%s [%d]: phi=%g\tdiv_k_grad_p=%g\tphi_dot=%g\n", - __func__, i, phi[i], div_k_grad_p, phi_dot[i]); + printf("%s [%d]: phi=%g\tdiv_k_grad_p=%g\tphi_dot=%g\n", __func__, i, + phi[i], div_k_grad_p, phi_dot[i]); - printf(" p[%d, %d, %d] = [%g, %g, %g]\tk=[%g, %g, %g]\n", - i, i + 1, i + 2, - p_f_ghost_in[i], p_f_ghost_in[i + 1], p_f_ghost_in[i + 2], - k_zn, k_, k_zp); + printf(" p[%d, %d, %d] = [%g, %g, %g]\tk=[%g, %g, %g]\n", i, i + 1, i + 2, + p_f_ghost_in[i], p_f_ghost_in[i + 1], p_f_ghost_in[i + 2], k_zn, k_, + k_zp); #endif - /* use the values from the next time step as the time derivative for this iteration */ - return inv_fluid_term * div_k_grad_p - - inv_porosity_term * phi_dot[i]; - } + /* use the values from the next time step as the time derivative for this + * iteration */ + return inv_fluid_term * div_k_grad_p - inv_porosity_term * phi_dot[i]; + } } -int -darcy_solver_1d(struct simulation *sim, - const int max_iter, - const double rel_tol) -{ - int i, iter, solved = 0; - double epsilon, p_f_top, omega, r_norm_max = NAN, *k_n, *phi_n; - - copy_values(sim->p_f_dot, sim->p_f_dot_old, sim->nz); - - /* choose integration method, parameter in [0.0; 1.0] - * epsilon = 0.0: explicit - * epsilon = 0.5: Crank-Nicolson - * epsilon = 1.0: implicit */ - epsilon = 0.5; - - /* underrelaxation parameter in ]0.0; 1.0], - * where omega = 1.0: no underrelaxation */ - omega = 1.0; - - for (i = 0; i < sim->nz; ++i) - sim->p_f_dot_impl[i] = sim->p_f_dot_expl[i] = 0.0; - - if (isnan(sim->p_f_mod_pulse_time)) - p_f_top = sim->p_f_top - + sine_wave(sim->t, - sim->p_f_mod_ampl, - sim->p_f_mod_freq, - sim->p_f_mod_phase); - else if (sim->p_f_mod_pulse_shape == 1) - p_f_top = sim->p_f_top - + square_pulse(sim->t, - sim->p_f_mod_ampl, - sim->p_f_mod_freq, - sim->p_f_mod_pulse_time); - else - p_f_top = sim->p_f_top - + triangular_pulse(sim->t, - sim->p_f_mod_ampl, - sim->p_f_mod_freq, - sim->p_f_mod_pulse_time); - - /* set fluid BCs (1 of 2) */ - set_fluid_bcs(sim->p_f_ghost, sim, p_f_top); - set_fluid_bcs(sim->p_f_next_ghost, sim, p_f_top); - - /* explicit solution to pressure change */ - if (epsilon < 1.0) { -#ifdef DEBUG - printf("\nEXPLICIT SOLVER IN %s\n", __func__); -#endif - for (i = 0; i < sim->nz - 1; ++i) - sim->p_f_dot_expl[i] = darcy_pressure_change_1d(i, - sim->nz, - sim->p_f_ghost, - sim->phi, - sim->phi_dot, - sim->k, - sim->dz, - sim->beta_f, - sim->alpha, - sim->mu_f, - sim->D); - } - - /* implicit solution with Jacobian iterations */ - if (epsilon > 0.0) { - +int darcy_solver_1d(struct simulation *sim, const int max_iter, + const double rel_tol) { + int i, iter, solved = 0; + double epsilon, p_f_top, omega, r_norm_max = NAN, *k_n, *phi_n; + + copy_values(sim->p_f_dot, sim->p_f_dot_old, sim->nz); + + /* choose integration method, parameter in [0.0; 1.0] + * epsilon = 0.0: explicit + * epsilon = 0.5: Crank-Nicolson + * epsilon = 1.0: implicit */ + epsilon = 0.5; + + /* underrelaxation parameter in ]0.0; 1.0], + * where omega = 1.0: no underrelaxation */ + omega = 1.0; + + for (i = 0; i < sim->nz; ++i) + sim->p_f_dot_impl[i] = sim->p_f_dot_expl[i] = 0.0; + + if (isnan(sim->p_f_mod_pulse_time)) + p_f_top = sim->p_f_top + sine_wave(sim->t, sim->p_f_mod_ampl, + sim->p_f_mod_freq, sim->p_f_mod_phase); + else if (sim->p_f_mod_pulse_shape == 1) + p_f_top = + sim->p_f_top + square_pulse(sim->t, sim->p_f_mod_ampl, + sim->p_f_mod_freq, sim->p_f_mod_pulse_time); + else + p_f_top = sim->p_f_top + triangular_pulse(sim->t, sim->p_f_mod_ampl, + sim->p_f_mod_freq, + sim->p_f_mod_pulse_time); + + /* set fluid BCs (1 of 2) */ + set_fluid_bcs(sim->p_f_ghost, sim, p_f_top); + set_fluid_bcs(sim->p_f_next_ghost, sim, p_f_top); + + /* explicit solution to pressure change */ + if (epsilon < 1.0) { #ifdef DEBUG - printf("\nIMPLICIT SOLVER IN %s\n", __func__); + printf("\nEXPLICIT SOLVER IN %s\n", __func__); #endif - - k_n = zeros(sim->nz); - phi_n = zeros(sim->nz); - if (sim->transient) - for (i = 0; i < sim->nz; ++i) { - /* grabbing the n + 1 iteration values for k and phi */ - phi_n[i] = sim->phi[i] + sim->dt * sim->phi_dot[i]; - k_n[i] = kozeny_carman(sim->d, phi_n[i]); - } - else - for (i = 0; i < sim->nz; ++i) { - phi_n[i] = sim->phi[i]; - k_n[i] = sim->k[i]; - } - copy_values(sim->p_f_next_ghost, sim->tmp_ghost, sim->nz + 2); - - for (iter = 0; iter < max_iter; ++iter) { - copy_values(sim->p_f_dot_impl, sim->fluid_old_val, sim->nz); - -#ifdef DEBUG - puts(".. p_f_ghost bfore BC:"); - print_array(sim->tmp_ghost, sim->nz + 2); -#endif - - /* set fluid BCs (2 of 2) */ - set_fluid_bcs(sim->tmp_ghost, sim, p_f_top); - -#ifdef DEBUG - puts(".. p_f_ghost after BC:"); - print_array(sim->tmp_ghost, sim->nz + 2); -#endif - - for (i = 0; i < sim->nz - 1; ++i) - sim->p_f_dot_impl[i] = darcy_pressure_change_1d_impl(i, - sim->nz, - sim->dt, - sim->p_f_ghost, - sim->tmp_ghost, - sim->p_f_next_ghost, - phi_n, - sim->phi_dot, - k_n, - sim->dz, - sim->beta_f, - sim->alpha, - sim->mu_f, - sim->D); - - for (i = 0; i < sim->nz; ++i) - if (isnan(sim->p_f_dot_impl[i])) - errx(1, "NaN at sim->p_f_dot_impl[%d] (t = %g s, iter = %d)", - i, sim->t, iter); - - set_fluid_bcs(sim->p_f_next_ghost, sim, p_f_top); - for (i = 0; i < sim->nz-1; ++i) - sim->p_f_dot_impl_r_norm[i] = fabs(residual(sim->p_f_next_ghost[i], - sim->tmp_ghost[i])); - r_norm_max = max(sim->p_f_dot_impl_r_norm, sim->nz - 1); - copy_values(sim->p_f_next_ghost, sim->tmp_ghost, sim->nz + 2); - -#ifdef DEBUG - puts(".. p_f_ghost_new:"); - print_array(sim->tmp_ghost, sim->nz + 2); -#endif - - if (r_norm_max <= rel_tol) { + for (i = 0; i < sim->nz - 1; ++i) + sim->p_f_dot_expl[i] = darcy_pressure_change_1d( + i, sim->nz, sim->p_f_ghost, sim->phi, sim->phi_dot, sim->k, sim->dz, + sim->beta_f, sim->alpha, sim->mu_f, sim->D); + } + + /* implicit solution with TDMA */ + if (epsilon > 0.0) { #ifdef DEBUG - printf(".. Iterative solution converged after %d iterations\n", iter); + printf("\nIMPLICIT SOLVER IN %s\n", __func__); #endif - add_darcy_iters(iter + 1); - solved = 1; - break; - } - } - free(k_n); - free(phi_n); - if (!solved) { - fprintf(stderr, "darcy_solver_1d: "); - fprintf(stderr, "Solution did not converge after %d iterations\n", - iter); - fprintf(stderr, ".. Residual normalized error: %f\n", r_norm_max); - add_darcy_iters(iter + 1); - } - } else - solved = 1; - - for (i = 0; i < sim->nz; ++i) - sim->p_f_dot[i] = epsilon * sim->p_f_dot_impl[i] - + (1.0 - epsilon) * sim->p_f_dot_expl[i]; - - for (i = 0; i < sim->nz; ++i) - sim->p_f_dot[i] = omega * sim->p_f_dot[i] - + (1.0 - omega) * sim->p_f_dot_old[i]; - - for (i = 0; i < sim->nz-1; ++i) - sim->p_f_next_ghost[i + 1] = sim->p_f_dot[i] * sim->dt + sim->p_f_ghost[i + 1]; - - set_fluid_bcs(sim->p_f_ghost, sim, p_f_top); - set_fluid_bcs(sim->p_f_next_ghost, sim, p_f_top); + double *a = empty(sim->nz); + double *b = empty(sim->nz); + double *c = empty(sim->nz); + double *d = empty(sim->nz); + double *x = empty(sim->nz); + + k_n = zeros(sim->nz); + phi_n = zeros(sim->nz); + + /* Predictor step for nonlinear coefficients */ + if (sim->transient) + for (i = 0; i < sim->nz; ++i) { + phi_n[i] = sim->phi[i] + sim->dt * sim->phi_dot[i]; + k_n[i] = kozeny_carman(sim->d, phi_n[i]); + } + else + for (i = 0; i < sim->nz; ++i) { + phi_n[i] = sim->phi[i]; + k_n[i] = sim->k[i]; + } + + /* Build Tridiagonal System */ + for (i = 0; i < sim->nz; ++i) { + /* Coefficients calculation matches the discretized equation */ + double k_i = k_n[i]; + double k_zn, k_zp; + + if (i == 0) + k_zn = k_i; + else + k_zn = k_n[i - 1]; + + if (i == sim->nz - 1) + k_zp = k_i; + else + k_zp = k_n[i + 1]; + + /* Harmonic means for conductivity at faces */ + double k_harm_p = 2.0 * k_zp * k_i / fmax(k_zp + k_i, 1e-30); + double k_harm_n = 2.0 * k_zn * k_i / fmax(k_zn + k_i, 1e-30); + + /* Diffusion terms */ + double coupling = + 1.0 / ((sim->alpha + sim->beta_f * phi_n[i]) * sim->mu_f); + double porosity_term = + -1.0 / ((sim->alpha + sim->beta_f * phi_n[i]) * (1.0 - phi_n[i])); + + /* Matrix coefficients (LHS) */ + /* term: - dt * coupling * (k_n * (p_i - p_{i-1}) / dz^2) */ + double alpha_i = -sim->dt * coupling * k_harm_n / + (sim->dz * sim->dz); // coeff for p_{i-1} + double gamma_i = -sim->dt * coupling * k_harm_p / + (sim->dz * sim->dz); // coeff for p_{i+1} + double beta_i = + 1.0 - + (alpha_i + gamma_i); // coeff for p_i (sum of abs(off-diags) + 1) + + a[i] = alpha_i; + b[i] = beta_i; + c[i] = gamma_i; + + /* RHS: p_old + source term */ + d[i] = sim->p_f_ghost[i + 1] + sim->dt * porosity_term * sim->phi_dot[i]; + } + + /* Apply Boundary Conditions to Linear System */ + /* Bottom (i=0): Neumann. p_{-1} = p_0 + C. + Original: p_{-1} = p_{0} + phi[0]*rho_f*G*dz (from + set_fluid_bcs/set_bc_neumann) Wait, set_bc_neumann(-1): a[0] = a[1] + + df*dx. Here a corresponds to ghost array. a[0] is ghost, a[1] is first + physical cell. So p_ghost[0] = p_ghost[1] + constant. p_{i-1} (at i=0) is + p_ghost[0]. So p_{-1} = p_0 + CONST. Term a[0] * p_{-1} becomes a[0]*p_0 + + a[0]*CONST. Add a[0] to b[0]. Subtract a[0]*CONST from d[0]. + */ + double bc_neumann_val = sim->phi[0] * sim->rho_f * sim->G * sim->dz; + b[0] += a[0]; + d[0] -= a[0] * bc_neumann_val; + a[0] = 0.0; + + /* Top (i=nz-1): Dirichlet. p_{n} = p_f_top (value). + Term c[n-1] * p_{n} becomes c[n-1] * p_f_top. + Subtract from d[n-1]. + */ + d[sim->nz - 1] -= c[sim->nz - 1] * p_f_top; + c[sim->nz - 1] = 0.0; + + /* Solve */ + tridiagonal_solver(x, a, b, c, d, sim->nz); + + /* Store result in p_f_dot (rate) */ + for (i = 0; i < sim->nz; ++i) { + sim->p_f_dot[i] = (x[i] - sim->p_f_ghost[i + 1]) / sim->dt; + /* Store in impl array too for consistency/debug */ + sim->p_f_dot_impl[i] = sim->p_f_dot[i]; + } + + free(a); + free(b); + free(c); + free(d); + free(x); + free(k_n); + free(phi_n); + + add_darcy_iters(1); + solved = 1; + } else { + /* Explicit mode skipped */ + } + + for (i = 0; i < sim->nz - 1; ++i) + sim->p_f_next_ghost[i + 1] = + sim->p_f_dot[i] * sim->dt + sim->p_f_ghost[i + 1]; + + set_fluid_bcs(sim->p_f_ghost, sim, p_f_top); + set_fluid_bcs(sim->p_f_next_ghost, sim, p_f_top); #ifdef DEBUG - printf(".. epsilon = %g\n", epsilon); - puts(".. p_f_dot_expl:"); - print_array(sim->p_f_dot_expl, sim->nz); - puts(".. p_f_dot_impl:"); - print_array(sim->p_f_dot_impl, sim->nz); + printf(".. epsilon = %g\n", epsilon); + puts(".. p_f_dot_expl:"); + print_array(sim->p_f_dot_expl, sim->nz); + puts(".. p_f_dot_impl:"); + print_array(sim->p_f_dot_impl, sim->nz); #endif - for (i = 0; i < sim->nz; ++i) - if (isnan(sim->p_f_dot_expl[i]) || isinf(sim->p_f_dot_expl[i])) - errx(1, "invalid: sim->p_f_dot_expl[%d] = %g (t = %g s)", - i, sim->p_f_dot_expl[i], sim->t); + for (i = 0; i < sim->nz; ++i) + if (isnan(sim->p_f_dot_expl[i]) || isinf(sim->p_f_dot_expl[i])) + errx(1, "invalid: sim->p_f_dot_expl[%d] = %g (t = %g s)", i, + sim->p_f_dot_expl[i], sim->t); - for (i = 0; i < sim->nz; ++i) - if (isnan(sim->p_f_dot_impl[i]) || isinf(sim->p_f_dot_impl[i])) - errx(1, "invalid: sim->p_f_dot_impl[%d] = %g (t = %g s)", - i, sim->p_f_dot_impl[i], sim->t); + for (i = 0; i < sim->nz; ++i) + if (isnan(sim->p_f_dot_impl[i]) || isinf(sim->p_f_dot_impl[i])) + errx(1, "invalid: sim->p_f_dot_impl[%d] = %g (t = %g s)", i, + sim->p_f_dot_impl[i], sim->t); - return solved - 1; + return solved - 1; } diff --git a/simulation.c b/simulation.c @@ -569,8 +569,8 @@ double residual(double new_val, double old_val) { return (new_val - old_val) / (fmax(fabs(old_val), fabs(new_val)) + 1e-16); } -static void tridiagonal_solver(double *x, const double *a, const double *b, - const double *c, double *d, int n) { +void tridiagonal_solver(double *x, const double *a, const double *b, + const double *c, double *d, int n) { /* * TDMA (Thomas Algorithm) solver for tridiagonal system * a: sub-diagonal (means a[i] is coeff for x[i-1]) diff --git a/simulation.h b/simulation.h @@ -5,129 +5,130 @@ #define DEFAULT_SIMULATION_NAME "unnamed_simulation" #define PI 3.14159265358979323846 -#define DEG2RAD(x) (x*PI/180.0) +#define DEG2RAD(x) (x * PI / 180.0) extern struct simulation sim; /* Simulation settings */ struct simulation { - /* simulation name to use for output files */ - char name[100]; + /* simulation name to use for output files */ + char name[100]; - /* gravitational acceleration magnitude [m/s^2] */ - double G; + /* gravitational acceleration magnitude [m/s^2] */ + double G; - /* normal stress from the top wall [Pa] */ - double P_wall; - - /* optionally fix top shear velocity to this value [m/s] */ - double v_x_fix; - - /* optionally fix top shear velocity to this value [m/s] */ - double v_x_limit; - - /* bottom velocity along x [m/s] */ - double v_x_bot; - - /* stress ratio at top wall */ - double mu_wall; - - /* nonlocal amplitude [-] */ - double A; - - /* rate dependence beyond yield [-] */ - double b; - - /* bulk and critical state static yield friction coefficient [-] */ - double mu_s; - - /* material cohesion [Pa] */ - double C; - - /* representative grain size [m] */ - double d; /* ohlala */ - - /* grain material density [kg/m^3] */ - double rho_s; - - /* nodes along z */ - int nz; - - /* origo of axis [m] */ - double origo_z; - - /* length of domain [m] */ - double L_z; - - /* array of cell coordinates */ - double *z; - - /* cell spacing [m] */ - double dz; - - /* current time [s] */ - double t; - - /* end time [s] */ - double t_end; - - /* time step length [s] */ - double dt; - - /* interval between output files [s] */ - double file_dt; - - /* output file number */ - int n_file; - - double transient; - double phi_min; - double phi_max; - double dilatancy_constant; - - /* Fluid parameters */ - int fluid; /* flag to switch fluid on (1) or off (0) */ - double p_f_top; /* fluid pressure at the top [Pa] */ - double p_f_mod_ampl; /* amplitude of fluid pressure variations [Pa] */ - double p_f_mod_freq; /* frequency of fluid pressure variations [s^-1] */ - double p_f_mod_phase; /* phase of fluid pressure variations [s^-1] */ - double p_f_mod_pulse_time; /* single pressure pulse at this time [s] */ - int p_f_mod_pulse_shape; /* waveform for fluid-pressure pulse */ - double beta_f; /* adiabatic fluid compressibility [Pa^-1] */ - double alpha; /* adiabatic grain compressibility [Pa^-1] */ - double mu_f; /* fluid dynamic viscosity [Pa*s] */ - double rho_f; /* fluid density [kg/m^3] */ - double D; /* diffusivity [m^2/s], overrides k, beta_f, alpha, mu_f */ - - /* arrays */ - double *mu; /* static yield friction [-] */ - double *mu_c; /* critical-state static yield friction [-] */ - double *sigma_n_eff; /* effective normal pressure [Pa] */ - double *sigma_n; /* normal stress [Pa] */ - double *p_f_ghost; /* fluid pressure [Pa] */ - double *p_f_next_ghost; /* fluid pressure for next iteration [Pa] */ - double *p_f_dot; /* fluid pressure change [Pa/s] */ - double *p_f_dot_expl; /* fluid pressure change (explicit solution) [Pa/s] */ - double *p_f_dot_impl; /* fluid pressure change (implicit solution) [Pa/s] */ - double *p_f_dot_impl_r_norm; /* normalized residual fluid pressure change [-] */ - double *k; /* hydraulic permeability [m^2] */ - double *phi; /* porosity [-] */ - double *phi_c; /* critical-state porosity [-] */ - double *phi_dot; /* porosity change [s^-1] */ - double *xi; /* cooperativity length */ - double *gamma_dot_p; /* plastic shear strain rate [s^-1] */ - double *v_x; /* shear velocity [m/s] */ - double *d_x; /* cumulative shear displacement [m] */ - double *g_local; /* local fluidity */ - double *g_ghost; /* fluidity with ghost nodes */ - double *g_r_norm; /* normalized residual of fluidity field */ - double *I; /* inertia number [-] */ - double *tan_psi; /* tan(dilatancy_angle) [-] */ - double *old_val; /* temporary storage for iterative solvers */ - double *fluid_old_val;/* temporary storage for fluid iterative solver */ - double *tmp_ghost; /* temporary storage for iterative solvers */ - double *p_f_dot_old; /* temporary storage for old p_f_dot */ + /* normal stress from the top wall [Pa] */ + double P_wall; + + /* optionally fix top shear velocity to this value [m/s] */ + double v_x_fix; + + /* optionally fix top shear velocity to this value [m/s] */ + double v_x_limit; + + /* bottom velocity along x [m/s] */ + double v_x_bot; + + /* stress ratio at top wall */ + double mu_wall; + + /* nonlocal amplitude [-] */ + double A; + + /* rate dependence beyond yield [-] */ + double b; + + /* bulk and critical state static yield friction coefficient [-] */ + double mu_s; + + /* material cohesion [Pa] */ + double C; + + /* representative grain size [m] */ + double d; /* ohlala */ + + /* grain material density [kg/m^3] */ + double rho_s; + + /* nodes along z */ + int nz; + + /* origo of axis [m] */ + double origo_z; + + /* length of domain [m] */ + double L_z; + + /* array of cell coordinates */ + double *z; + + /* cell spacing [m] */ + double dz; + + /* current time [s] */ + double t; + + /* end time [s] */ + double t_end; + + /* time step length [s] */ + double dt; + + /* interval between output files [s] */ + double file_dt; + + /* output file number */ + int n_file; + + double transient; + double phi_min; + double phi_max; + double dilatancy_constant; + + /* Fluid parameters */ + int fluid; /* flag to switch fluid on (1) or off (0) */ + double p_f_top; /* fluid pressure at the top [Pa] */ + double p_f_mod_ampl; /* amplitude of fluid pressure variations [Pa] */ + double p_f_mod_freq; /* frequency of fluid pressure variations [s^-1] */ + double p_f_mod_phase; /* phase of fluid pressure variations [s^-1] */ + double p_f_mod_pulse_time; /* single pressure pulse at this time [s] */ + int p_f_mod_pulse_shape; /* waveform for fluid-pressure pulse */ + double beta_f; /* adiabatic fluid compressibility [Pa^-1] */ + double alpha; /* adiabatic grain compressibility [Pa^-1] */ + double mu_f; /* fluid dynamic viscosity [Pa*s] */ + double rho_f; /* fluid density [kg/m^3] */ + double D; /* diffusivity [m^2/s], overrides k, beta_f, alpha, mu_f */ + + /* arrays */ + double *mu; /* static yield friction [-] */ + double *mu_c; /* critical-state static yield friction [-] */ + double *sigma_n_eff; /* effective normal pressure [Pa] */ + double *sigma_n; /* normal stress [Pa] */ + double *p_f_ghost; /* fluid pressure [Pa] */ + double *p_f_next_ghost; /* fluid pressure for next iteration [Pa] */ + double *p_f_dot; /* fluid pressure change [Pa/s] */ + double *p_f_dot_expl; /* fluid pressure change (explicit solution) [Pa/s] */ + double *p_f_dot_impl; /* fluid pressure change (implicit solution) [Pa/s] */ + double + *p_f_dot_impl_r_norm; /* normalized residual fluid pressure change [-] */ + double *k; /* hydraulic permeability [m^2] */ + double *phi; /* porosity [-] */ + double *phi_c; /* critical-state porosity [-] */ + double *phi_dot; /* porosity change [s^-1] */ + double *xi; /* cooperativity length */ + double *gamma_dot_p; /* plastic shear strain rate [s^-1] */ + double *v_x; /* shear velocity [m/s] */ + double *d_x; /* cumulative shear displacement [m] */ + double *g_local; /* local fluidity */ + double *g_ghost; /* fluidity with ghost nodes */ + double *g_r_norm; /* normalized residual of fluidity field */ + double *I; /* inertia number [-] */ + double *tan_psi; /* tan(dilatancy_angle) [-] */ + double *old_val; /* temporary storage for iterative solvers */ + double *fluid_old_val; /* temporary storage for fluid iterative solver */ + double *tmp_ghost; /* temporary storage for iterative solvers */ + double *p_f_dot_old; /* temporary storage for old p_f_dot */ }; void init_sim(struct simulation *sim); @@ -137,15 +138,10 @@ void check_simulation_parameters(struct simulation *sim); void lithostatic_pressure_distribution(struct simulation *sim); void compute_effective_stress(struct simulation *sim); -void set_bc_neumann(double *a, - const int nz, - const int boundary, - const double df, - const double dx); +void set_bc_neumann(double *a, const int nz, const int boundary, + const double df, const double dx); -void set_bc_dirichlet(double *a, - const int nz, - const int boundary, +void set_bc_dirichlet(double *a, const int nz, const int boundary, const double value); double residual(double new_val, double old_val); @@ -154,15 +150,18 @@ double kozeny_carman(const double diameter, const double porosity); void write_output_file(struct simulation *sim, const int normalize); void print_output(struct simulation *sim, FILE *fp, const int normalize); -int coupled_shear_solver(struct simulation *sim, - const int max_iter, +int coupled_shear_solver(struct simulation *sim, const int max_iter, const double rel_tol); - -void set_coupled_fluid_transient_timestep(struct simulation *sim, const double safety); + +void set_coupled_fluid_transient_timestep(struct simulation *sim, + const double safety); double find_flux(const struct simulation *sim); void print_solver_stats(FILE *fp); void reset_solver_stats(void); +void tridiagonal_solver(double *x, const double *a, const double *b, + const double *c, double *d, int n); + #endif diff --git a/test/cngf_pf_dry.std b/test/cngf_pf_dry.std @@ -1,16 +0,0 @@ -0.029999999999999999 0 51668.995000000003 0 0.34837139758572822 0.0093080012929039231 0.25 8.3519539886234661e-05 18000.000000000004 0 -0.072666666666666657 0.00096672949131815049 50852.803 0 0.35396278942578641 0.022657722452769157 0.25 0.00020492996684944953 18000 0.00096672949131815049 -0.11533333333333333 0.0028714052826517874 50036.611000000004 0 0.35973659367138194 0.044640838859382123 0.25 0.00040703810593426698 18000 0.0028714052826517874 -0.158 0.0063549562795917796 49220.419000000002 0 0.36570188482141935 0.081645726490781084 0.25 0.00075059811580455941 18000 0.0063549562795917796 -0.20066666666666666 0.012436004137614675 48404.226999999999 0 0.37186834943154862 0.14252455917241166 0.25 0.0013212795924493264 18000 0.012436004137614675 -0.24333333333333332 0.022618103035063678 47588.035000000003 0 0.37824633860170948 0.23864294290896104 0.25 0.0022312404529153591 18000.000000000004 0.022618103035063678 -0.28599999999999998 0.038943576645842463 46771.843000000001 0 0.3848469259592785 0.3826282877526278 0.25 0.0036085397864072614 18000 0.038943576645842463 -0.32866666666666666 0.063896755899290253 45955.650999999998 0 0.39168197182104986 0.58484013875268259 0.25 0.0055643491798409864 18000 0.063896755899290253 -0.37133333333333329 0.10001967596250598 45139.459000000003 0 0.39876419431610821 0.84663093898161867 0.25 0.008127605687930483 18000 0.10001967596250598 -0.41399999999999998 0.14910027796640848 44323.267 0 0.4061072483668679 1.1503266094664655 0.25 0.011144278309537804 18000 0.14910027796640848 -0.45666666666666667 0.2122173205518427 43507.074999999997 0 0.41372581356020827 1.4793056855961146 0.25 0.014465206854901744 17999.999999999996 0.2122173205518427 -0.4993333333333333 0.2911715562217424 42690.883000000002 0 0.42163569209847451 1.8504898985132741 0.25 0.01826694054276698 18000 0.2911715562217424 -0.54200000000000004 0.3862975744094958 41874.690999999999 0 0.42985391820562935 2.2295160512754713 0.25 0.022221913923564506 18000.000000000004 0.3862975744094958 -0.58466666666666667 0.49397111687254103 41058.499000000003 0 0.43839888058255616 2.5235986514776223 0.25 0.02540185412596959 18000.000000000004 0.49397111687254103 -0.6273333333333333 0.60280408543126318 40242.307000000001 0 0.44729045976414816 2.5507727005950502 0.25 0.025934446925256989 18000 0.60280408543126318 -0.66999999999999993 0.68621939491980821 39426.115000000005 0 0.45655018253764035 1.9550463161377736 0.25 0.020082220149086623 18000.000000000004 0.68621939491980821 diff --git a/test/cngf_pf_dry_cohesive.std b/test/cngf_pf_dry_cohesive.std @@ -1,16 +0,0 @@ -0.029999999999999999 0 51668.995000000003 0 0.34837139758572822 0.00037374341221142369 0.25 3.3535532324438454e-06 18000.000000000004 0 -0.072666666666666657 4.1046907082070771e-05 50852.803 0 0.35396278942578641 0.00096203688473603388 0.25 8.7012358505083553e-06 18000 4.1046907082070771e-05 -0.11533333333333333 0.0001286980583172401 50036.611000000004 0 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