ssa_test_linear.cc

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// Copyright (C) 2010--2018, 2021, 2022, 2024 Ed Bueler, Constantine Khroulev, and David Maxwell
//
// This file is part of PISM.
//
// PISM 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.
//
// PISM 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 PISM; if not, write to the Free Software
// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
 
/* This file implements a test case for the ssa: linear flow. The rheology is
   linear (i.e. n=1 in the Glen flow law) and the basal shear stress is also
   linear viscous flow. The geometry consists of a constant surface slope in
   the positive x-direction, and dirichlet conditions leading to an exponential
   solution are imposed along the entire boundary.
*/
 
 
#include <memory>
static char help[] =
  "\nSSA_TEST_EXP\n"
  "  Testing program for the finite element implementation of the SSA.\n"
  "  Does a time-independent calculation.  Does not run IceModel or a derived\n"
  "  class thereof.Also may be used in a PISM\n"
  "  software (regression) test.\n\n";
 
#include <cmath>
 
#include "pism/stressbalance/ssa/SSAFD.hh"
#include "pism/stressbalance/ssa/SSAFEM.hh"
#include "pism/stressbalance/ssa/SSATestCase.hh"
#include "pism/util/Context.hh"
#include "pism/util/error_handling.hh"
#include "pism/util/petscwrappers/PetscInitializer.hh"
#include "pism/util/pism_options.hh"
 
namespace pism {
namespace stressbalance {
 
std::shared_ptr<Grid> ssa_test_linear_grid(std::shared_ptr<Context> ctx, int Mx, int My) {
  return SSATestCase::grid(ctx, Mx, My, 50e3, 50e3, grid::CELL_CORNER, grid::NOT_PERIODIC);
}
std::shared_ptr<Grid> ssa_test_linear_grid(std::shared_ptr<Context> ctx, int Mx, int My) {…}
 
class SSATestCaseExp: public SSATestCase
{
public:
  SSATestCaseExp(std::shared_ptr<SSA> ssa)
    : SSATestCase(ssa) {
    L     = units::convert(m_sys, 50, "km", "m"); // 50km half-width
    H0    = 500;                      // meters
    dhdx  = 0.005;                    // pure number
    nu0   = units::convert(m_sys, 30.0, "MPa year", "Pa s");
    tauc0 = 1.e4;               // 1kPa
  }
  SSATestCaseExp(std::shared_ptr<SSA> ssa) {…}
 
protected:
  virtual void initializeSSACoefficients();
 
  virtual void exactSolution(int i, int j,
    double x, double y, double *u, double *v);
 
  double L, H0, dhdx, nu0, tauc0;
};
class SSATestCaseExp: public SSATestCase {…};
 
void SSATestCaseExp::initializeSSACoefficients() {
 
  // Force linear rheology
  m_ssa->strength_extension->set_notional_strength(nu0 * H0);
  m_ssa->strength_extension->set_min_thickness(4000*10);
 
  // Set constants for most coefficients.
  m_geometry.ice_thickness.set(H0);
  m_geometry.ice_surface_elevation.set(H0);
  m_geometry.bed_elevation.set(0.0);
  m_tauc.set(tauc0);
 
 
  // Set boundary conditions (Dirichlet all the way around).
  m_bc_mask.set(0.0);
 
  array::AccessScope list{&m_bc_values, &m_bc_mask};
 
  for (auto p = m_grid->points(); p; p.next()) {
    const int i = p.i(), j = p.j();
 
    double myu, myv;
    const double myx = m_grid->x(i), myy=m_grid->y(j);
 
    bool edge = ((j == 0) || (j == (int)m_grid->My() - 1) ||
                 (i == 0) || (i == (int)m_grid->Mx() - 1));
    if (edge) {
      m_bc_mask(i,j) = 1;
      exactSolution(i,j,myx,myy,&myu,&myv);
      m_bc_values(i,j).u = myu;
      m_bc_values(i,j).v = myv;
    }
  }
 
  m_bc_values.update_ghosts();
  m_bc_mask.update_ghosts();
}
void SSATestCaseExp::initializeSSACoefficients() {…}
 
 
void SSATestCaseExp::exactSolution(int /*i*/, int /*j*/, double x, double /*y*/,
                                   double *u, double *v) {
  double tauc_threshold_velocity = m_config->get_number("basal_resistance.pseudo_plastic.u_threshold",
                                                        "m second-1");
  double v0 = units::convert(m_sys, 100.0, "m year^-1", "m second^-1");
  // double alpha=log(2.)/(2*L);
  double alpha = sqrt((tauc0/tauc_threshold_velocity) / (4*nu0*H0));
  *u = v0*exp(-alpha*(x-L));
  *v = 0;
}
void SSATestCaseExp::exactSolution(int /*i*/, int /*j*/, double x, double /*y*/, {…}
 
} // end of namespace stressbalance
} // end of namespace pism
 
int main(int argc, char *argv[]) {
 
  using namespace pism;
  using namespace pism::stressbalance;
 
  MPI_Comm com = MPI_COMM_WORLD;  // won't be used except for rank,size
  petsc::Initializer petsc(argc, argv, help);
 
  com = PETSC_COMM_WORLD;
 
  /* This explicit scoping forces destructors to be called before PetscFinalize() */
  try {
    std::shared_ptr<Context> ctx = context_from_options(com, "ssa_test_linear");
    Config::Ptr config = ctx->config();
 
    std::string usage = "\n"
      "usage:\n"
      "  run ssa_test_linear -Mx <number> -My <number> -ssa_method <fd|fem>\n"
      "\n";
 
    bool stop = show_usage_check_req_opts(*ctx->log(), "ssa_test_linear", {}, usage);
 
    if (stop) {
      return 0;
    }
 
    // Parameters that can be overridden by command line options
    unsigned int Mx = config->get_number("grid.Mx");
    unsigned int My = config->get_number("grid.My");
 
    auto method      = config->get_string("stress_balance.ssa.method");
    auto output_file = config->get_string("output.file");
 
    bool write_output = config->get_string("output.size") != "none";
 
    // Use a pseudo-plastic law with linear till
    config->set_flag("basal_resistance.pseudo_plastic.enabled", true);
    config->set_number("basal_resistance.pseudo_plastic.q", 1.0);
 
    // The finite difference code uses the following flag to treat the non-periodic grid correctly.
    config->set_flag("stress_balance.ssa.compute_surface_gradient_inward", true);
 
    auto grid = ssa_test_linear_grid(ctx, Mx, My);
    SSATestCaseExp testcase(SSATestCase::solver(grid, method));
    testcase.init();
    testcase.run();
    testcase.report("linear");
    if (write_output) {
      testcase.write(output_file);
    }
  }
  catch (...) {
    handle_fatal_errors(com);
    return 1;
  }
 
  return 0;
}
int main(int argc, char *argv[]) {…}