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specmicp/examples/reactmicp/saturated_react/leaching_kinetic.cpp
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leaching_kinetic.cpp
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// ============================================
// Leaching of a cement paste
// with kinetic dissolution of C3S
// =============================================
// This file can be used to learn how to use ReactMiCP
// Include ReactMiCP
#include "reactmicp.hpp"
#include "specmicp/adimensional/adimensional_system_solution_saver.hpp"
#include "reactmicp/systems/saturated_react/diffusive_upscaling_stagger.hpp"
#include "reactmicp/systems/saturated_react/kinetic_stagger.hpp"
// Other includes that would be needed later :
#include <Eigen/QR>
#include "physics/laws.hpp"
#include "utils/timer.hpp"
#include <functional>
#include <iostream>
#include <fstream>
// we use the following namespaces
using namespace specmicp;
using namespace reactmicp;
using namespace reactmicp::systems;
using namespace specmicp::reactmicp::systems::satdiff;
using namespace reactmicp::solver;
// We declare some functions that we will be using :
// Database
// ========
// Parse and Prepare the database
RawDatabasePtr get_database(const std::string& path_to_database);
// Boundary and initial conditions
// ===============================
// Return the chemistry constraints for the inital condition
AdimensionalSystemConstraints get_cement_initial_constraints(
RawDatabasePtr the_database,
const units::UnitsSet& units_set);
// return the chemistry constraints for the boundary condition
AdimensionalSystemConstraints get_bc_initial_constraints(
RawDatabasePtr the_database,
const units::UnitsSet& units_set);
Vector initial_compo(const Vector& publi);
void compo_from_oxyde(Vector& compo_oxyde, Vector& compo_species);
// The mesh
// ========
// There is two version
// a uniform mesh
mesh::Mesh1DPtr get_mesh(scalar_t dx);
// and a non uniform mesh
mesh::Mesh1DPtr get_mesh();
// Options
// =======
// Speciation solver options
AdimensionalSystemSolverOptions get_specmicp_options();
// Transport options
void set_transport_options(dfpmsolver::ParabolicDriverOptions& transport_options);
// Reactive Solver options
void set_reactive_solver_options(reactmicp::solver::ReactiveTransportOptions& reactive_options);
// Kinetic model and variables
// ===========================
// Kinetic variables
class C3SKineticVariables : public KineticSaturatedVariablesBase
{
public:
Vector amount_minerals; // concentration of C3S
Vector predictor; // Initial amount
Vector velocity; // dC_c3s/dt
Vector volume_fractions;
};
using C3SKineticVariablesPtr = std::shared_ptr<C3SKineticVariables>;
// The dissolution model
class C3SDissolutionModel : public KineticModelBase
{
public:
C3SDissolutionModel(RawDatabasePtr the_database, const units::UnitsSet the_units):
m_database(the_database),
m_units(the_units),
id_c3s(the_database->get_id_mineral_kinetic("C3S"))
{
if (id_c3s == no_species)
throw database::invalid_database("The database do not contain C3S !");
}
KineticSaturatedVariablesBasePtr initialize_variables(mesh::Mesh1DPtr the_mesh, scalar_t init_vol_fraction);
//! \brief Initialize a timestep
void initialize_timestep(scalar_t dt, KineticSaturatedVariablesBasePtr kinetic_variables) override;
//! \brief Restart a timestep
void restart_timestep(
index_t node,
const AdimensionalSystemSolution& eq_solution,
KineticSaturatedVariablesBasePtr kinetic_variables) override;
//! \brief Return the volume fraction of kinetic (or inert) phases
scalar_t get_volume_fraction_kinetic(index_t node, KineticSaturatedVariablesBasePtr kinetic_variables) override;
//! \brief Return the velocity of the total immobile kinetic concentration for component
scalar_t get_velocity_kinetic(index_t node, index_t component, KineticSaturatedVariablesBasePtr kinetic_variables) override;
private:
scalar_t volume_fraction(scalar_t concentration);
scalar_t dy_dt(scalar_t log_IAP, scalar_t Aeff);
scalar_t m_dt {-1.0};
RawDatabasePtr m_database;
units::UnitsSet m_units;
index_t id_c3s;
};
KineticSaturatedVariablesBasePtr C3SDissolutionModel::initialize_variables(mesh::Mesh1DPtr the_mesh, scalar_t init_vol_fraction)
{
C3SKineticVariablesPtr var = std::make_shared<C3SKineticVariables>();
var->predictor.setZero(the_mesh->nb_nodes());
var->velocity.setZero(the_mesh->nb_nodes());
var->volume_fractions.setConstant(the_mesh->nb_nodes(), init_vol_fraction);
var->amount_minerals.setConstant(the_mesh->nb_nodes(),
init_vol_fraction/m_database->molar_volume_mineral_kinetic(id_c3s, m_units.length));
var->volume_fractions(0) = 0.0;
var->amount_minerals(0) = 0.0;
return std::static_pointer_cast<KineticSaturatedVariablesBase>(var);
}
void C3SDissolutionModel::initialize_timestep(scalar_t dt, KineticSaturatedVariablesBasePtr kinetic_variables)
{
m_dt = dt;
C3SKineticVariablesPtr true_kin_var = std::static_pointer_cast<C3SKineticVariables>(kinetic_variables);
true_kin_var->predictor = true_kin_var->amount_minerals;
true_kin_var->velocity.setZero();
}
void C3SDissolutionModel::restart_timestep(
index_t node,
const AdimensionalSystemSolution &eq_solution,
KineticSaturatedVariablesBasePtr kinetic_variables
)
{
C3SKineticVariablesPtr true_kin_var = std::static_pointer_cast<C3SKineticVariables>(kinetic_variables);
AdimensionalSystemSolutionExtractor extr(eq_solution, m_database, m_units);
scalar_t log_IAP = 0;
for (index_t component: m_database->range_component())
{
if (m_database->nu_mineral_kinetic(id_c3s, component) == 0.0) continue;
log_IAP += m_database->nu_mineral_kinetic(id_c3s, component)*extr.log_molality_component(component);
}
scalar_t tmp = 0;
scalar_t Aeff = 0;
scalar_t porosity = extr.porosity();
if (porosity > 0.6)
{
Aeff= 1400*1e-4/1e-3*m_database->molar_mass_mineral_kinetic(id_c3s)/m_database->molar_volume_mineral_kinetic(id_c3s)*true_kin_var->volume_fractions(node);
tmp = 1e-6*dy_dt(log_IAP, Aeff);
}
true_kin_var->velocity(node) = tmp;
tmp = true_kin_var->predictor(node) + m_dt*true_kin_var->velocity(node);
if (tmp < 1e-20) {
tmp =0.0;
true_kin_var->velocity(node) = - true_kin_var->predictor(node) / m_dt;
}
true_kin_var->amount_minerals(node) = tmp;
true_kin_var->volume_fractions(node) = tmp*m_database->molar_volume_mineral_kinetic(id_c3s, m_units.length);
}
scalar_t C3SDissolutionModel::dy_dt(scalar_t log_IAP, scalar_t Aeff)
{
scalar_t res = (-57.0 -std::log(10)*log_IAP)/21.5;
scalar_t tmp_2 = std::pow(res, 3.73);
res = - 125.3e-6*Aeff*(1.0 - std::exp(-tmp_2));
return res;
}
scalar_t C3SDissolutionModel::get_volume_fraction_kinetic(index_t node, KineticSaturatedVariablesBasePtr kinetic_variables)
{
C3SKineticVariablesPtr true_kin_var = std::static_pointer_cast<C3SKineticVariables>(kinetic_variables);
return true_kin_var->volume_fractions(node);
}
scalar_t C3SDissolutionModel::get_velocity_kinetic(index_t node, index_t component, KineticSaturatedVariablesBasePtr kinetic_variables)
{
C3SKineticVariablesPtr true_kin_var = std::static_pointer_cast<C3SKineticVariables>(kinetic_variables);
return m_database->nu_mineral_kinetic(id_c3s, component)*true_kin_var->velocity(node);
}
// ==============
// Output
// ==============
// Many information is generated throughout a computation and we can't save everything
// The reactmicp runner can call a function to output the desired information
// Here the output function is a member function for convenience
class OutputPolicy
{
public:
// Initialise the output
// SimulationInformation contain basic information from the simulation
OutputPolicy(const SimulationInformation& simul_info,
mesh::Mesh1DPtr the_mesh,
RawDatabasePtr the_database,
units::UnitsSet the_units):
m_mesh(the_mesh),
m_database(the_database),
m_units(the_units)
{
// Open the files
// Save the pH
out_c_ph.open(simul_info.complete_filepath("ph", suffix));
// Save the total aqueous concentration of HCO3[-]
out_c_hco3.open(simul_info.complete_filepath("c_hco3", suffix));
// save the total solid concentration of s_ca
out_s_ca.open(simul_info.complete_filepath("s_ca", suffix));
// Save the volume fraction of calcite
out_calcite.open(simul_info.complete_filepath("calcite", suffix));
// Save the porosity
out_poro.open(simul_info.complete_filepath("poro", suffix));
out_kin_vol_frac.open(simul_info.complete_filepath("kin_vol_frac", suffix));
// save useful indices from the database
m_id_hco3 = m_database->get_id_component("HCO3[-]");
m_id_ca = m_database->get_id_component("Ca[2+]");
m_id_calcite = m_database->get_id_mineral("Calcite");
}
void output(scalar_t time, VariablesBasePtr variables)
{
SaturatedVariablesPtr true_var = cast_var_from_base(variables);
out_c_ph << time;
out_c_hco3 << time;
out_s_ca << time;
out_calcite << time;
out_poro << time;
out_kin_vol_frac << time;
for (index_t node: m_mesh->range_nodes())
{
// Again AdimensionalSystemSolutionExtractor is used to obtain information about the speciation system
AdimensionalSystemSolutionExtractor extractor(true_var ->equilibrium_solution(node), m_database, m_units);
out_c_ph << "\t" << extractor.pH();
out_c_hco3 << "\t" << true_var->aqueous_concentration(node, m_id_hco3);
out_s_ca << "\t" << true_var->solid_concentration(node, m_id_ca);
out_calcite << "\t" << extractor.volume_fraction_mineral(m_id_calcite);
out_poro << "\t" << extractor.porosity();
out_kin_vol_frac << "\t" << std::static_pointer_cast<C3SKineticVariables>(true_var->kinetic_variables())->volume_fractions(node);
}
out_c_hco3 << std::endl;
out_c_ph << std::endl;
out_s_ca << std::endl;
out_calcite << std::endl;
out_poro << std::endl;
out_kin_vol_frac << std::endl;
}
private:
mesh::Mesh1DPtr m_mesh;
RawDatabasePtr m_database;
units::UnitsSet m_units;
std::string suffix { "dat" };
std::ofstream out_c_ph;
std::ofstream out_c_hco3;
std::ofstream out_s_ca;
std::ofstream out_calcite;
std::ofstream out_poro;
std::ofstream out_kin_vol_frac;
index_t m_id_hco3;
index_t m_id_ca;
index_t m_id_calcite;
};
// ===================
// MAIN
// ===================
int main()
{
// initialize eigen
// This is needed if OpenMP is used
Eigen::initParallel();
// Setup the log
// The output will be on cerr
specmicp::logger::ErrFile::stream() = &std::cerr;
// And only Warning and error messages will be printed
specmicp::stdlog::ReportLevel() = specmicp::logger::Warning;
// The database
// -------------
// Obtain the database
RawDatabasePtr the_database = get_database("../data/cemdata.js");
// SpecMiCP options
// ----------------
// Set the options
AdimensionalSystemSolverOptions specmicp_options = get_specmicp_options();
units::UnitsSet units_set = specmicp_options.units_set;
// The mesh
// --------
// Obtain the mesh
mesh::Mesh1DPtr the_mesh = get_mesh(0.0050); // uniform
//mesh::Mesh1DPtr the_mesh = get_mesh(); // non uniform
index_t nb_nodes = the_mesh->nb_nodes(); // just boilerplate to make things easier
// Print the mesh
io::print_mesh("out_carbo_mesh.dat", the_mesh, units::LengthUnit::centimeter);
// Initial and boundary conditions
// --------------------------------
// Obtain the initial constraints
// Note : the database is modified at this point
// Only the relevant components are kept at this point
AdimensionalSystemConstraints cement_constraints = get_cement_initial_constraints(the_database, units_set);
// Freeze the database
the_database->freeze_db();
// Obtain the initial condition
AdimensionalSystemSolution cement_solution = solve_equilibrium(
the_database,
cement_constraints,
specmicp_options);
if(not the_database->is_valid())
throw std::runtime_error("The database has been changed during the initial condition computation");
// Just to check that everything is ok !
AdimensionalSystemSolutionExtractor extractor(cement_solution, the_database, units_set);
std::cout << "Porosity : " << extractor.porosity() << std::endl;
std::cout << "Water volume fraction " << extractor.volume_fraction_water() << std::endl;
//return EXIT_SUCCESS;
// Obtain the boundary conditions
AdimensionalSystemConstraints bc_constraints = get_bc_initial_constraints(
the_database,
specmicp_options.units_set
);
AdimensionalSystemSolution bc_solution = solve_equilibrium(
the_database,
bc_constraints,
specmicp_options
);
if(not the_database->is_valid())
throw std::runtime_error("The database has been changed during the boundary conditions computation");
// The constraints
// --------------
// Boundary condition
// 'list_fixed_nodes' lists the node with fixed composition
std::vector<index_t> list_fixed_nodes = {0};
// list_constraints lists the different speciation constraints in the system
// Note : the total concentrations are computed from the initial solution,
// and thus different total concentrations do not constitute a reason to create different constraints
std::vector<specmicp::AdimensionalSystemConstraints> list_constraints = {cement_constraints,
bc_constraints};
// index_constraints links a node to the set of constraints that will be used
std::vector<int> index_constraints(nb_nodes, 0);
index_constraints[0] = 1; // Boundary conditions
// This is the list of initial composition
std::vector<specmicp::AdimensionalSystemSolution> list_initial_composition = {cement_solution, bc_solution};
// This list links a node to its initial conditions
std::vector<int> index_initial_state(nb_nodes, 0);
index_initial_state[0] = 1; // boundary condition
// Variables
// -----------
// Create the main set of variables
// They will be initialized using the list of initial composition
satdiff::SaturatedVariablesPtr variables =
satdiff::init_variables(the_mesh, the_database, units_set,
list_fixed_nodes,
list_initial_composition,
index_initial_state);
std::shared_ptr<C3SDissolutionModel> kinetic_model = std::make_shared<C3SDissolutionModel>(the_database, units_set);
variables->kinetic_variables() = kinetic_model->initialize_variables(the_mesh, 0.2);
// Staggers
// ---------
// This section initialize the staggers
// The equilibrium stagger
// - - - - - - - - - - - -
std::shared_ptr<KineticStagger> kinetic_stagger =
std::make_shared<satdiff::KineticStagger>(kinetic_model, list_constraints, index_constraints, specmicp_options);
// The transport stagger
// - - - - - - - - - - -
std::shared_ptr<SaturatedTransportStagger> transport_stagger =
std::make_shared<satdiff::SaturatedTransportStagger>(variables, list_fixed_nodes);
set_transport_options(transport_stagger->options_solver());
// The upscaling stagger
// - - - - - - - - - - -
CappedPowerLawParameters upscaling_param;
upscaling_param.d_eff_0 = 2.726e-12*1e4;
upscaling_param.cap = 1e10*1e6;
upscaling_param.exponent = 3.32;
upscaling_param.porosity_0 = 0.25;
upscaling_param.porosity_res = 0.02;
CappedPowerLaw upscaling_law(upscaling_param);
UpscalingStaggerPtr upscaling_stagger =
std::make_shared<DiffusiveUpscalingStagger>(upscaling_law.get_law(),the_database, units_set);
// Solver
// ------
// This section initialize the reactive transport solver
ReactiveTransportSolver solver(transport_stagger, kinetic_stagger, upscaling_stagger);
set_reactive_solver_options(solver.get_options());
transport_stagger->initialize(variables);
kinetic_stagger->initialize(variables);
upscaling_stagger->initialize(variables);
// Some basic information about the simulation
// First argument : the name of the simulation
// Second argument : the output function will be called every 3600s
SimulationInformation simul_info("kincarbo", 1800);
simul_info.output_prefix = "out_kincarbo_";
// Runner
// -------
// Create the runner : loop through the timestep
ReactiveTransportRunner runner(solver, 0.1, 100.0, simul_info);
// Create the output class
OutputPolicy output_policy(simul_info, the_mesh, the_database, specmicp_options.units_set);
// and bind it to the runner
runner.set_output_policy(std::bind(&OutputPolicy::output, &output_policy, std::placeholders::_1, std::placeholders::_2));
// Solve the problem
runner.run_until(10*24*3600, cast_var_to_base(variables));
if(not the_database->is_valid())
throw std::runtime_error("The database has been changed during the computation");
AdimensionalSystemSolutionSaver saver(the_database);
saver.save_solutions(simul_info.complete_filepath("solutions", "dat"), variables->equilibrium_solutions());
// output information at the end of the timestep
io::print_minerals_profile(the_database, variables, the_mesh, simul_info.complete_filepath("profiles_end", "dat"));
io::print_components_total_aqueous_concentration(the_database, variables,
the_mesh, specmicp_options.units_set,
simul_info.complete_filepath("c_profiles_end", "dat"));
io::print_components_total_solid_concentration(the_database, variables,
the_mesh, specmicp_options.units_set,
simul_info.complete_filepath("s_profiles_end", "dat"));
}
AdimensionalSystemSolverOptions get_specmicp_options()
{
AdimensionalSystemSolverOptions options;
options.solver_options.maxiter_maxstep = 100;
options.solver_options.maxstep = 20.0;
options.solver_options.threshold_cycling_linesearch = 1e-6;
options.solver_options.set_tolerance(1e-8, 1e-14);
options.solver_options.disable_condition_check();
options.solver_options.disable_descent_direction();
options.solver_options.enable_non_monotone_linesearch();
options.solver_options.enable_scaling();
options.system_options.non_ideality_tolerance = 1e-14;
options.system_options.cutoff_total_concentration = 1e-10;
options.units_set.length = units::LengthUnit::centimeter;
return options;
}
void set_transport_options(dfpmsolver::ParabolicDriverOptions& transport_options)
{
transport_options.maximum_iterations = 450;
transport_options.quasi_newton = 3;
transport_options.residuals_tolerance = 1e-8;
transport_options.step_tolerance = 1e-14;
transport_options.absolute_tolerance = 1e-18;
transport_options.alpha = 1.0;
//transport_options.linesearch = dfpmsolver::ParabolicLinesearch::Strang;
transport_options.sparse_solver = SparseSolver::SparseLU;
//transport_options.sparse_solver = SparseSolver::GMRES;
transport_options.threshold_stationary_point = 1e-4;
}
void set_reactive_solver_options(reactmicp::solver::ReactiveTransportOptions& reactive_options)
{
reactive_options.maximum_iterations = 100; //500;
reactive_options.residuals_tolerance = 1e-2;
reactive_options.good_enough_tolerance = 1.0;
reactive_options.absolute_residuals_tolerance = 1e-14;
reactive_options.implicit_upscaling = true;
}
RawDatabasePtr get_database(const std::string& path_to_database) {
database::Database the_database(path_to_database);
std::map<std::string, std::string> swapping({
{"H[+]","HO[-]"},
{"Si(OH)4", "SiO(OH)3[-]"},
{"Al[3+]","Al(OH)4[-]"}
});
the_database.swap_components(swapping);
the_database.remove_gas_phases();
return the_database.get_database();
}
AdimensionalSystemConstraints get_cement_initial_constraints(
RawDatabasePtr the_database,
const units::UnitsSet& units_set)
{
Vector oxyde_compo(4);
oxyde_compo << 66.98, 21.66, 7.19, 2.96;
Vector species_compo;
compo_from_oxyde(oxyde_compo, species_compo);
scalar_t mult = 1e-6;
species_compo *= 0.85e-2;
Formulation formulation;
formulation.mass_solution = 1.0;
formulation.amount_minerals = {
{"C3S", species_compo(0)},
{"C2S", species_compo(1)},
{"C3A", species_compo(2)},
{"Gypsum", species_compo(3)},
{"Calcite", species_compo(0)*1e-3}
};
formulation.extra_components_to_keep = {"HCO3[-]"};
formulation.concentration_aqueous =
{
{"Na[+]", mult*1.0298},
{"K[+]", mult*0.0801},
{"Cl[-]", mult*0.0001},
{"HO[-]", mult*1.8298}
},
formulation.minerals_to_keep = {
"Portlandite",
"CSH,jennite",
"CSH,tobermorite",
"SiO2(am)",
"Calcite",
"Al(OH)3(mic)",
"C3AH6",
"C3ASO_41H5_18",
"C3ASO_84H4_32",
"C4AH19",
"C4AH13",
"C2AH7_5",
"CAH10",
"Monosulfoaluminate",
"Tricarboaluminate",
"Monocarboaluminate",
"Hemicarboaluminate",
"Straetlingite",
"Gypsum",
"Ettringite",
//"Thaumasite"
};
Dissolver dissolver(the_database);
dissolver.set_units(units_set);
AdimensionalSystemConstraints constraints;
constraints.set_charge_keeper(1);
constraints.total_concentrations = dissolver.dissolve(formulation);
std::cout << constraints.total_concentrations << std::endl;
constraints.set_saturated_system();
constraints.set_inert_volume_fraction(0.2);
return constraints;
}
AdimensionalSystemConstraints get_bc_initial_constraints(
RawDatabasePtr the_database,
const units::UnitsSet& units_set)
{
const scalar_t rho_w = laws::density_water(units::celsius(25.0), units_set.length, units_set.mass);
const scalar_t nacl = 0.3*rho_w;
const scalar_t kcl = 0.28*rho_w;
Vector total_concentrations;
total_concentrations.setZero(the_database->nb_component());
total_concentrations(the_database->get_id_component("K[+]")) = kcl;
total_concentrations(the_database->get_id_component("Cl[-]")) = nacl + kcl;
total_concentrations(the_database->get_id_component("Na[+]")) = nacl;
total_concentrations(the_database->get_id_component("SiO(OH)3[-]")) = 0.0001*rho_w;
AdimensionalSystemConstraints constraints;
constraints.add_fixed_activity_component(the_database->get_id_component("HO[-]"), -10.3);
constraints.set_charge_keeper(the_database->get_id_component("HCO3[-]"));
constraints.total_concentrations = total_concentrations;
constraints.set_saturated_system();
constraints.disable_surface_model();
constraints.fixed_fugacity_cs ={};
return constraints;
}
AdimensionalSystemSolution get_bc_initial_compo(
RawDatabasePtr the_database,
const AdimensionalSystemConstraints& constraints,
const AdimensionalSystemSolverOptions& options
)
{
Vector variables;
AdimensionalSystemSolver solver(the_database,
constraints,
options);
micpsolver::MiCPPerformance perf = solver.solve(variables, true);
if (perf.return_code <= micpsolver::MiCPSolverReturnCode::NotConvergedYet)
throw std::runtime_error("Failed to solve initial composition");
std::cout << variables << std::endl;
return solver.get_raw_solution(variables);
}
void compo_from_oxyde(Vector& compo_oxyde, Vector& compo_species)
{
constexpr double M_CaO = 56.08;
constexpr double M_SiO2 = 60.09;
constexpr double M_Al2O3 = 101.96;
constexpr double M_SO3 = 80.06;
Eigen::MatrixXd compo_in_oxyde(4, 4);
Vector molar_mass(4);
molar_mass << 1.0/M_CaO, 1.0/M_SiO2, 1.0/M_Al2O3, 1.0/M_SO3;
compo_oxyde = compo_oxyde.cwiseProduct(molar_mass);
//C3S C2S C3A Gypsum
compo_in_oxyde << 3, 2, 3, 1, // CaO
1, 1, 0, 0, // SiO2
0, 0, 1, 0, // Al2O3
0, 0, 0, 1; // SO3
Eigen::ColPivHouseholderQR<Eigen::MatrixXd> solver(compo_in_oxyde);
compo_species = solver.solve(compo_oxyde);
}
Vector initial_compo(const Vector& publi)
{
Matrix publi_stochio(5,5);
publi_stochio << 1, 0, 0, 0, 0,
9, 6, 0, 0, 0,
3, 0, 1, 1, 0,
3, 0, 1, 3, 0,
0, 0, 0, 0, 1;
Matrix cemdata_stochio(5, 5);
cemdata_stochio << 1, 0, 0, 0, 0,
1.0/0.6, 1.0, 0, 0, 0,
3, 0, 1, 1, 0,
3, 0, 1, 3, 0,
0, 0, 0, 0, 1;
Vector oxyde;
Eigen::ColPivHouseholderQR<Matrix> solver(publi_stochio);
oxyde = solver.solve(publi);
Vector for_cemdata = cemdata_stochio*oxyde;
return for_cemdata;
}
mesh::Mesh1DPtr get_mesh(scalar_t dx)
{
const scalar_t total_length = 0.75/2.0 + dx; //cm
const scalar_t height = 20.0;
index_t nb_nodes = total_length/dx + 1;
return mesh::uniform_axisymmetric_mesh1d(nb_nodes, total_length, dx, height);
}
mesh::Mesh1DPtr get_mesh()
{
Vector radius(71);
const scalar_t height = 20;
radius <<
3.751,
3.750,
3.745,
3.740,
3.735,
3.730,
3.720,
3.710,
3.700,
3.690,
3.680,
3.670,
3.660,
3.645,
3.630,
3.615,
3.600,
3.580,
3.560,
3.540,
3.520,
3.500,
3.475,
3.450,
3.425,
3.400,
3.375,
3.350,
3.325,
3.300,
3.275,
3.250,
3.225,
3.200,
3.175,
3.150,
3.125,
3.100,
3.050,
3.025,
3.000,
2.950,
2.900,
2.850,
2.800,
2.750,
2.700,
2.650,
2.600,
2.550,
2.500,
2.450,
2.400,
2.350,
2.300,
2.250,
2.200,
2.150,
2.100,
2.050,
2.000,
1.950,
1.900,
1.850,
1.800,
1.750,
1.700,
1.650,
1.600,
1.550,
1.500
;
radius = radius/10;
return mesh::axisymmetric_mesh1d(radius, height);
}
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