Schema_Adams_Moulton_order_3.cpp

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/*! @brief class Schema_Adams_Moulton_order_3
 *
 */
 
#include <Schema_Adams_Moulton_order_3.h>
#include <Equation_base.h>
#include <Probleme_base.h>
#include <Probleme_Couple.h>
#include <Milieu_base.h>
#include <Param.h>
#include <communications.h>
#include <Matrice_Morse.h>
 
Implemente_instanciable(Schema_Adams_Moulton_order_3,"Schema_Adams_Moulton_order_3",Schema_Adams_Moulton_base);
// XD schema_adams_moulton_order_3 schema_implicite_base schema_adams_moulton_order_3 INHERITS_BRACE not_set
// XD attr facsec_max floattant facsec_max OPT Maximum ratio allowed between time step and stability time returned by
// XD_CONT CFL condition. The initial ratio given by facsec keyword is changed during the calculation with the implicit
// XD_CONT scheme but it couldn\'t be higher than facsec_max value.NL2 Warning: Some implicit schemes do not permit high
// XD_CONT facsec_max, example Schema_Adams_Moulton_order_3 needs facsec=facsec_max=1. NL2 Advice:NL2 The calculation
// XD_CONT may start with a facsec specified by the user and increased by the algorithm up to the facsec_max limit. But
// XD_CONT the user can also choose to specify a constant facsec (facsec_max will be set to facsec value then). Faster
// XD_CONT convergence has been seen and depends on the kind of calculation: NL2-Hydraulic only or thermal hydraulic
// XD_CONT with forced convection and low coupling between velocity and temperature (Boussinesq value beta low), facsec
// XD_CONT between 20-30NL2-Thermal hydraulic with forced convection and strong coupling between velocity and
// XD_CONT temperature (Boussinesq value beta high), facsec between 90-100 NL2-Thermohydralic with natural convection,
// XD_CONT facsec around 300NL2 -Conduction only, facsec can be set to a very high value (1e8) as if the scheme was
// XD_CONT unconditionally stableNL2These values can also be used as rule of thumb for initial facsec with a facsec_max
// XD_CONT limit higher.
 
 
 
//     printOn()
/////
 
Sortie& Schema_Adams_Moulton_order_3::printOn(Sortie& s) const
{
  return  Schema_Adams_Moulton_base::printOn(s);
}
 
//// readOn
//
 
Entree& Schema_Adams_Moulton_order_3::readOn(Entree& s)
{
  return Schema_Adams_Moulton_base::readOn(s);
}
 
// Computes the average value between borne_inf and borne_sup of the degree-2 Lagrange polynomial:
// - which equals 0 at a and b
// - which equals 1 at c
static double integrate_lagrangian_basis(double a, double b, double c, double borne_inf, double borne_sup)
{
  double result  = 0.;
  double scaling = (c-a)*(c-b);
  double dt      = borne_sup-borne_inf;
 
  double prod = a*b;
  double sum  = -0.5*(a+b);
 
  double tmp_sup = borne_sup*(prod+borne_sup*(borne_sup/3.+sum));
  double tmp_inf = borne_inf*(prod+borne_inf*(borne_inf/3.+sum));
 
  result = tmp_sup-tmp_inf;
  result/=(scaling*dt);
 
  return result;
}
 
 
/*! @brief Returns the number of temporal values to keep.
 *
 * 3 temporal values: tn-1, tn, tn+1
 * 1 extra value for the implicit algorithm machinery.
 *
 */
int Schema_Adams_Moulton_order_3::nb_valeurs_temporelles() const
{
  return 4 ;
}
 
int Schema_Adams_Moulton_order_3::nb_valeurs_passees() const
{
  return 1;
}
 
int Schema_Adams_Moulton_order_3::nb_pas_dt_seuil() const
{
  return 1;
}
 
void Schema_Adams_Moulton_order_3::compute_adams_moulton_coefficients(double time_step, const DoubleTab& times) const
{
  if (nb_pas_dt()<100 && limpr() && (facteur_securite_pas()>1.0 || facsec_max_>1.0))
    {
      Cerr << finl;
      Cerr << "********************* Warning (printed only on the first 100 time steps) ************************"<< finl;
      Cerr << "The Adams Moulton order 3 scheme is recommended with a facsec and facsec_max set to 1.0 or lower."<< finl;
      Cerr << "*************************************************************************************************"<< finl;
      // See $TRUST_ROOT/tests/Reference/Schema_Adams_Moulton_order_3 test case.
    }
  assert(times.size_array() == 3); //past, present and future times, stored in ascending order inside "times" table
 
  if ( adams_moulton_coefficients_.size_array() != 3)
    {
      adams_moulton_coefficients_.resize(3,RESIZE_OPTIONS::NOCOPY_NOINIT);
    }
 
  double past_time    = times[0];
  double present_time = times[1];
  double future_time  = times[2];
 
  adams_moulton_coefficients_[0] = integrate_lagrangian_basis(present_time,future_time,past_time,present_time,future_time);
  adams_moulton_coefficients_[1] = integrate_lagrangian_basis(past_time,future_time,present_time,present_time,future_time);
  adams_moulton_coefficients_[2] = 1 -  adams_moulton_coefficients_[1] -  adams_moulton_coefficients_[0];
}