RealVector HyperbolicEquationUpwindRHSFunction::evalF(Real time, RealVector& y, IntegerVector& ref){
Real dx = (xL - x0) / Nx;
Integer elem_ref = ref.sum();
RealVector F(elem_ref);
F.fill(0.0);
Integer idx = 0;
if (ref(0) == 1){
F(idx) = bc_func->getValue(time);
idx += 1;
}
for (Integer i = 1; i <= Nx-2; ++i){
if (ref(i) == 1){
Real yi = y(i);
Real a = flux_func->evalFderivative(time,yi);
if ( a > 0.0 ){
Real yi_prec = y(i-1);
F(idx) = 1.0/dx * ( flux_func->evalF(time,yi_prec) - flux_func->evalF(time,yi) );
}
else{
Real yi_succ = y(i+1);
F(idx) = 1.0/dx * ( flux_func->evalF(time,yi) - flux_func->evalF(time,yi_succ) );
}
idx += 1;
}
}
return F;
}
RealMatrixSparse HyperbolicEquationUpwindRHSFunction::evaldFdY(Real time, RealVector& y,IntegerVector& ref){
// this is not the exact Jacobian!
Integer y_size = y.size();
Integer elem_ref = ref.sum();
RealMatrixSparse J(elem_ref,elem_ref);
Integer col = 0;
Real epsi = 1.e-3;
Real iepsi = 1.0 / 1.e-3;
RealVector F = evalF(time,y,ref);
for (Integer j = 0; j < y_size; ++j){
if(ref(j) == 1){
RealVector yd = y;
yd(j) = yd(j) + epsi;
RealVector Fd = evalF(time,yd,ref);
for(Integer i=0; i< Fd.size(); i++){
J.insert(i,col) = (Fd[i] - F[i]) * iepsi;
}
col = col + 1;
}
}
return J;
}
RealVector HyperbolicEquationRusanovFlux::evalF(Real time, RealVector& y, IntegerVector& ref){
Real dx = (xL - x0) / Nx;
Integer elem_ref = ref.sum();
RealVector F(elem_ref);
F.fill(0.0);
Integer idx = 0;
if (ref(0) == 1){
Integer i=0;
Real y0 = bc_func->getValue(time);
Real yi_succ = y(i+1);
Real f_deriv_i = fabs(flux_func-> evalFderivative(time,y0));
Real f_deriv_isucc = fabs(flux_func-> evalFderivative(time,yi_succ));
Real f_prev = flux_func->evalF(time,y0);
Real f_succ = 0.5*(flux_func->evalF(time,y0) + flux_func->evalF(time,yi_succ) - ( std::max( f_deriv_i, f_deriv_isucc))*(yi_succ-y0));
F(0) = - 1.0/dx * (f_succ - f_prev );
idx += 1;
}
for (Integer i = 1; i < Nx-1; ++i){
if (ref(i) == 1){
//! We use a finite volume method with Rusanov flux
Real yi = y(i);
Real yi_succ = y(i+1);
Real yi_prev = y(i-1);
Real f_deriv_i = fabs(flux_func-> evalFderivative(time,yi));
Real f_deriv_isucc = fabs(flux_func-> evalFderivative(time,yi_succ));
Real f_deriv_iprev = fabs(flux_func-> evalFderivative(time,yi_prev));
Real f_prev = 0.5*(flux_func->evalF(time,yi_prev) + flux_func->evalF(time,yi) - (std::max( f_deriv_i, f_deriv_iprev))*(yi-yi_prev));
Real f_succ = 0.5*(flux_func->evalF(time,yi) + flux_func->evalF(time,yi_succ) - ( std::max( f_deriv_i, f_deriv_isucc))*(yi_succ-yi));
F(idx) = - 1.0/dx * (f_succ - f_prev );
idx += 1;
}
}
if(ref(Nx-1)==1){
Real yn = y(Nx-1);
Real yi_prev = y(Nx-2);
Real f_deriv_i = fabs(flux_func-> evalFderivative(time,yn));
Real f_deriv_iprev = fabs(flux_func-> evalFderivative(time,yi_prev));
Real f_prev = 0.5*(flux_func->evalF(time,yi_prev) + flux_func->evalF(time,yn) - (std::max( f_deriv_i, f_deriv_iprev))*(yn-yi_prev));
Real f_succ = flux_func->evalF(time,yn);
F(idx) = - 1.0/dx * (f_succ - f_prev );
}
return F;
}
int GenerateNumbComponentsRestabFile::ComponentsRestab( std::vector<std::unique_ptr<ISolverData>>&& vect_solution){
DataCube datacube;
///====================================
/// Set Description
///====================================
{
IndexDescription index;
index.label = "timeStep";
index.name = "iTimeStep";
datacube.list_of_index_description.add(index);
}
{
Restab::VariableDescription var;
var.label = "number_of_components";
datacube.list_of_variable_description.add(var);
}
///====================================
/// Add Step Values
///====================================
MapInteger step_index_values;
MapReal step_var_values;
Integer num_solution = vect_solution.size();
//!Steps
for(Integer i = 1; i < num_solution; i++){
step_index_values.clear();
step_var_values.clear();
step_index_values.insert(KeyInteger("timeStep",i));
IntegerVector ref = vect_solution[i]->getNumbComponentsSolve();
Integer numb_comp = ref.sum();
step_var_values.insert(KeyReal("number_of_components" ,numb_comp));
datacube.table_of_index_values.add(step_index_values);
datacube.table_of_variable_values.add(step_var_values);
}
///======================================
/// Write Results
///======================================
String filename = "Componentsresult";
//! Description
String filenameDesc = filename + ".restab.desc";
String text_desc = datacube.toStringDescription();
//std::cout << text_desc << "\n";
datacube.writeDescription(filenameDesc);
//! Data
String filenameData = filename + ".restab";
String text_data = datacube.toStringData();
//std::cout << text_data << "\n";
datacube.writeData(filenameData);
//======================================
return 0;
}
