commit 00e54a5a11a0761349e484c441d010c0ffac2b43 parent f4e8c279fa822c4104b9ddb798a4e06b9f1cdd05 Author: Anders Damsgaard <anders@adamsgaard.dk> Date: Tue, 17 Aug 2021 14:15:05 +0200 Merge branch 'ian' Diffstat:
| M | README.md | | | 7 | +++++-- |
| M | fluid.c | | | 144 | ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++--------------- |
| A | fluidtest/Makefile | | | 50 | ++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | fluidtest/fig.gp | | | 30 | ++++++++++++++++++++++++++++++ |
| M | max_depth_simple_shear.c | | | 5 | +++-- |
| M | shear_flux.c | | | 6 | ++---- |
| M | simulation.c | | | 38 | ++++++++++++++++++++++++++------------ |
| M | simulation.h | | | 2 | ++ |
| M | test/shear_flux_wet.std | | | 2 | +- |
| M | test/simple_shear_dry_vconst.std | | | 50 | +++++++++++++++++++++++++------------------------- |
| M | test/simple_shear_wet.std | | | 32 | ++++++++++++++++---------------- |
| M | test/simple_shear_wet_norm.std | | | 32 | ++++++++++++++++---------------- |
| M | test/simple_shear_wet_vari.std | | | 400 | ++++++++++++++++++++++++++++++++++++++++---------------------------------------- |
| M | test/simple_shear_wet_vari_diff.std | | | 400 | ++++++++++++++++++++++++++++++++++++++++---------------------------------------- |
| M | test/simple_shear_wet_vari_pulse.std | | | 400 | ++++++++++++++++++++++++++++++++++++++++---------------------------------------- |
| M | test/simple_shear_wet_vari_pulse_vlim.std | | | 400 | ++++++++++++++++++++++++++++++++++++++++---------------------------------------- |
16 files changed, 1094 insertions(+), 904 deletions(-)
diff --git a/README.md b/README.md @@ -12,12 +12,15 @@ Requirements are a C99-compatible compiler (e.g. `gcc` or `clang`). Run `make` and `make install` to install the programs and their man pages. +If you want to show debug output during runtime, compile with +`CFLAGS=-DDEBUG make`. + ## Usage See `man cngf-pf`, `man max_deformation_depth` and `man shear_flux` for usage information. ## Results -A preprint with model results is publically available[2]. +A paper with model results is publically available[2]. ## Author Anders Damsgaard <anders@adamsgaard.dk> @@ -26,4 +29,4 @@ ISC licensed, see LICENSE for details. ## References [1]: https://doi.org/10.1073/pnas.1219153110 -[2]: https://arxiv.org/abs/2002.02436 +[2]: https://doi.org/10.1038/s43247-020-00074-7 diff --git a/fluid.c b/fluid.c @@ -32,8 +32,7 @@ int set_largest_fluid_timestep(struct simulation *sim, const double safety) { int i; - double dx_min, diff, diff_max; - double *dx; + double dx_min, diff, diff_max, *dx; dx = spacing(sim->z, sim->nz); dx_min = INFINITY; @@ -164,15 +163,84 @@ darcy_pressure_change_1d(const int 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; + + 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]; + + rhs_term = dt / ((alpha + beta_f * phi[i]) * mu_f) + * ((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 + * (1.0 / ((alpha + beta_f * phi[i]) * mu_f) + * (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 + - 1.0 / ((alpha + beta_f * phi[i]) + * (1.0 - phi[i])) * 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(" 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 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]; + } +} + 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; + 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 @@ -208,6 +276,7 @@ darcy_solver_1d(struct simulation *sim, /* 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) { @@ -226,16 +295,29 @@ darcy_solver_1d(struct simulation *sim, sim->alpha, sim->mu_f, sim->D); - } /* implicit solution with Jacobian iterations */ if (epsilon > 0.0) { #ifdef DEBUG - printf("\nEXPLICIT SOLVER IN %s\n", __func__); + printf("\nIMPLICIT SOLVER IN %s\n", __func__); #endif - copy_values(sim->p_f_ghost, sim->tmp_ghost, sim->nz + 2); + + 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); @@ -254,27 +336,32 @@ darcy_solver_1d(struct simulation *sim, #endif for (i = 0; i < sim->nz - 1; ++i) - sim->p_f_dot_impl[i] = darcy_pressure_change_1d(i, - sim->nz, - sim->tmp_ghost, - sim->phi, - sim->phi_dot, - sim->k, - sim->dz, - sim->beta_f, - sim->alpha, - sim->mu_f, - sim->D); + 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); - for (i = 0; i < sim->nz - 1; ++i) - sim->p_f_dot_impl_r_norm[i] = fabs(residual(sim->p_f_dot_impl[i], - sim->fluid_old_val[i])); + 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:"); @@ -289,25 +376,30 @@ darcy_solver_1d(struct simulation *sim, 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); + iter); fprintf(stderr, ".. Residual normalized error: %f\n", r_norm_max); } - } else { + } 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]; - set_fluid_bcs(sim->p_f_ghost, sim, p_f_top); - 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); #ifdef DEBUG printf(".. epsilon = %g\n", epsilon); puts(".. p_f_dot_expl:"); diff --git a/fluidtest/Makefile b/fluidtest/Makefile @@ -0,0 +1,50 @@ +BIN = ../cngf-pf +BIN2 = ../max_depth_simple_shear + +PERMEABILITY = 2e-17 +GRAIN_COMPRESSIBILITY = 1e-8 +FLUID_PRESSURE_TOP = 100e3 +FLUID_PRESSURE_AMPL = 80e3 +FLUID_PRESSURE_FREQ != echo "1.0/(3600*24)" | bc -l +EFF_NORMAL_STRESS_TOP = 200e3 + +timeseries.pdf: fig.gp timeseries.txt + sh -c '\ + out=$$($(BIN2) \ + -k $(PERMEABILITY) \ + -P $(GRAIN_COMPRESSIBILITY) \ + -O $(FLUID_PRESSURE_TOP) \ + -a $(FLUID_PRESSURE_AMPL) \ + -q $(FLUID_PRESSURE_FREQ) \ + ); \ + echo $$out; \ + max_def_depth=$$(echo $$out | cut -d" " -f1); \ + skin_depth=$$(echo $$out | cut -d" " -f2); \ + gnuplot -e "skin_depth=$$skin_depth; max_def_depth=$$max_def_depth" \ + fig.gp > $@' + +timeseries.txt: sim.output00000.txt + /bin/sh -c '\ + rm -f $@; \ + for f in sim.output*.txt; do \ + tail -n 1 "$$f" | cut -f2- >> $@; \ + done' + +sim.output00000.txt: $(BIN) + /bin/sh -c '\ + $(BIN) -L 8.0 \ + -n $(EFF_NORMAL_STRESS_TOP) \ + -f 0.40 \ + -F \ + -k $(PERMEABILITY) \ + -P $(GRAIN_COMPRESSIBILITY) \ + -O $(FLUID_PRESSURE_TOP) \ + -a $(FLUID_PRESSURE_AMPL) \ + -q $(FLUID_PRESSURE_FREQ) \ + -I $$( echo "60*10" | bc -l ) \ + -e $$( echo "3600*24*7" | bc -l ) sim' + +clean: + rm -f *.txt timeseries.pdf + +.PHONY: clean diff --git a/fluidtest/fig.gp b/fluidtest/fig.gp @@ -0,0 +1,30 @@ +#!/usr/bin/env gnuplot + +set terminal pdfcairo color size 17.8 cm, 10.0 cm font ",10" + +set colorsequence podo +set multiplot + +file_interval=60*10 +plot_interval=60*60 +inc=plot_interval/file_interval +L_z=8.0 +set yrange [4.0:0.0] +set ytics 1.0 + +t0 = 48*inc - 1 +tend = 72*inc - 1 + +filename(t) = sprintf('sim.output%05d.txt', t) +#set origin 0.095, 0.09 +#set size 0.14, 0.23 +set xlabel "{/:Normal Water pressure [kPa]}" font ",8" offset 0,1.3 +set ylabel "" +unset arrow +xmin = 0 +xmax = 200.0 +set arrow from xmin,skin_depth to xmax,skin_depth nohead lc black front +set xrange [xmin:xmax] +set xtics 100 offset 0,0.5 +set ytics 2 offset 0.5 +plot for [t = t0:tend:inc*2] filename(t) u ($4/1e3):(L_z - $1):(t*file_interval/(24.*3600.)) w l lc palette lw 1 t "" diff --git a/max_depth_simple_shear.c b/max_depth_simple_shear.c @@ -82,7 +82,8 @@ zbrent(struct simulation *sim, double tol) { int iter; - double a, b, c, d, e, min1, min2, fa, fb, fc, p, q, r, s, tol1, xm; + double a, b, c, d = NAN, e = NAN, min1, min2, + fa, fb, fc, p, q, r, s, tol1, xm; a = x1; b = x2; @@ -154,6 +155,7 @@ zbrent(struct simulation *sim, warnx("error: %s: exceeded maximum number of iterations", __func__); free_arrays(sim); exit(12); + return NAN; } @@ -168,7 +170,6 @@ main(int argc, char *argv[]) #ifdef BENCHMARK_PERFORMANCE clock_t t_begin, t_end; double t_elapsed; - #endif #ifdef __OpenBSD__ diff --git a/shear_flux.c b/shear_flux.c @@ -23,11 +23,9 @@ usage(void) static double find_flux(FILE *f) { - int i; - double pos, vel, pos_prev, vel_prev, flux; + int i = 0; + double pos, vel, pos_prev, vel_prev, flux = 0.0; - i = 0; - flux = 0.0; while (fscanf(f, "%lf\t%lf%*[^\n]", &pos, &vel) == 2) { if (i++ > 0) flux += (vel + vel_prev) / 2.0 * (pos - pos_prev); diff --git a/simulation.c b/simulation.c @@ -9,7 +9,7 @@ /* iteration limits for solvers */ #define MAX_ITER_GRANULAR 100000 -#define MAX_ITER_DARCY 10000 +#define MAX_ITER_DARCY 1000000 #define MAX_ITER_STRESS 20000 /* tolerance criteria when in velocity driven or velocity limited mode */ @@ -47,7 +47,6 @@ init_sim(struct simulation *sim) /* Henann and Kamrin 2016 */ /* sim->mu_s = 0.3819; */ /* sim->C = 0.0; */ - /* Damsgaard et al 2013 */ sim->mu_s = tan(DEG2RAD(22.0)); sim->C = 0.0; @@ -149,6 +148,7 @@ prepare_arrays(struct simulation *sim) sim->sigma_n_eff = zeros(sim->nz); sim->sigma_n = zeros(sim->nz); sim->p_f_ghost = zeros(sim->nz + 2); + sim->p_f_next_ghost = zeros(sim->nz + 2); sim->p_f_dot = zeros(sim->nz); sim->p_f_dot_expl = zeros(sim->nz); sim->p_f_dot_impl = zeros(sim->nz); @@ -181,6 +181,7 @@ free_arrays(struct simulation *sim) free(sim->sigma_n_eff); free(sim->sigma_n); free(sim->p_f_ghost); + free(sim->p_f_next_ghost); free(sim->p_f_dot); free(sim->p_f_dot_expl); free(sim->p_f_dot_impl); @@ -492,15 +493,21 @@ compute_porosity_change(struct simulation *sim) sim->phi_dot[i] = sim->tan_psi[i] * sim->gamma_dot_p[i] * sim->phi[i]; } +double +kozeny_carman(const double diameter, const double porosity) +{ + return pow(diameter, 2.0) / 180.0 + * pow(porosity, 3.0) + / pow(1.0 - porosity, 2.0); +} + static void compute_permeability(struct simulation *sim) { int i; for (i = 0; i < sim->nz; ++i) - sim->k[i] = pow(sim->d, 2.0) / 180.0 - * pow(sim->phi[i], 3.0) - / pow(1.0 - sim->phi[i], 2.0); + sim->k[i] = kozeny_carman(sim->d, sim->phi[i]); } /* NEW FUNCTIONS END */ @@ -541,7 +548,12 @@ compute_effective_stress(struct simulation *sim) if (sim->fluid) for (i = 0; i < sim->nz; ++i) { - sim->sigma_n_eff[i] = sim->sigma_n[i] - sim->p_f_ghost[i + 1]; + /* average of current and next step pressure values for effective stress - may not be optimal */ + sim->sigma_n_eff[i] = sim->sigma_n[i] + - ((sim->p_f_ghost[i + 1] + + sim->p_f_next_ghost[i + 1]) + / 2.0); + /* sim->sigma_n_eff[i] = sim->sigma_n[i] - sim->p_f_ghost[i + 1]; */ if (sim->sigma_n_eff[i] < 0) errx(1, "%s: sigma_n_eff[%d] is negative with value %g\n", __func__, i, sim->sigma_n_eff[i]); @@ -673,8 +685,7 @@ implicit_1d_jacobian_poisson_solver(struct simulation *sim, const double rel_tol) { int iter, i; - double r_norm_max = NAN; - double *tmp; + double r_norm_max = NAN, *tmp; for (iter = 0; iter < max_iter; ++iter) { #ifdef DEBUG @@ -803,6 +814,9 @@ coupled_shear_solver(struct simulation *sim, int i, coupled_iter, stress_iter = 0; double r_norm_max, vel_res_norm = NAN, mu_wall_orig = sim->mu_wall; + copy_values(sim->p_f_ghost, sim->p_f_next_ghost, sim->nz + 2); + compute_effective_stress(sim); /* Eq. 9 */ + do { /* stress iterations */ coupled_iter = 0; do { /* coupled iterations */ @@ -827,8 +841,8 @@ coupled_shear_solver(struct simulation *sim, compute_friction(sim); /* Eq. 4 */ /* step 5, Eq. 13 */ - if (sim->fluid) - if (darcy_solver_1d(sim, MAX_ITER_DARCY, rel_tol)) + if (sim->fluid && (sim->t > 0) ) + if (darcy_solver_1d(sim, MAX_ITER_DARCY, 1e-3 * rel_tol)) exit(11); /* step 6 */ @@ -869,7 +883,7 @@ coupled_shear_solver(struct simulation *sim, for (i = 0; i < sim->nz; ++i) sim->g_r_norm[i] = fabs(residual(sim->phi_dot[i], sim->old_val[i])); r_norm_max = max(sim->g_r_norm, sim->nz); - if (r_norm_max <= rel_tol) + if (r_norm_max <= rel_tol && coupled_iter > 0) break; if (coupled_iter++ >= max_iter) { @@ -893,7 +907,7 @@ coupled_shear_solver(struct simulation *sim, vel_res_norm = (sim->v_x_fix - sim->v_x[sim->nz - 1]) / (sim->v_x[sim->nz - 1] + 1e-12); } - sim->mu_wall *= 1.0 + (vel_res_norm * 1e-2); + sim->mu_wall *= 1.0 + (vel_res_norm * 1e-3); } if (++stress_iter > MAX_ITER_STRESS) { fprintf(stderr, "error: stress solution did not converge:\n"); diff --git a/simulation.h b/simulation.h @@ -106,6 +106,7 @@ struct simulation { 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] */ @@ -148,6 +149,7 @@ void set_bc_dirichlet(double *a, const double value); double residual(double new_val, double old_val); +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); diff --git a/test/shear_flux_wet.std b/test/shear_flux_wet.std @@ -1 +1 @@ -0.00022711336009603655 +0.00022713620374911894 diff --git a/test/simple_shear_dry_vconst.std b/test/simple_shear_dry_vconst.std @@ -1,25 +1,25 @@ -0 0 139129.5 0 0.36846050173498257 2.521180462250813e-06 0.25 1.3786086085057726e-08 51263.725376137256 0 -0.041666666666666664 2.3679004279723009e-07 138332.4375 0 0.37058354716071024 5.6829610271335227e-06 0.25 3.1164440064760098e-08 51263.725376137249 2.3679004279723009e-07 -0.083333333333333329 6.6085812182676643e-07 137535.375 0 0.37273120007225236 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