Simpler.h

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#ifndef Simpler_included
#define Simpler_included
#include <Simple.h>
 
//Description
 
//Ref. Numerical heat Transfer Vol. 10 P. 209-228
// D. S. Jang - R. Jetli - S. Acharya
 
// Pressure convergence in the Simple algorithm (see class Simple) is slow
// because the off-diagonal terms are neglected when solving the Poisson equation
// for the pressure correction.
// The goal of the Simpler algorithm is to compute a more accurate pressure estimate
// and then apply the Simple algorithm with it.
 
// A = (M/dt + C(Uk) + D)
// Bt and -B denote the gradient and divergence operators respectively
 
// -Pressure estimation
// First evaluate the velocity field UPk by solving (Da = diagonal part of A, E = off-diagonal part):
//        Da[Uk-1]UPk = E[Uk-1]Uk-1 + Sv + Ss                        -> UPk
//
// The momentum equation can then be written as:
//        Da[Uk-1]Uk = Da[Uk-1]UPk - BtPk
// Combining this with the continuity equation (-BUk = 0):
//        (BDa-1Bt)Pk = BUPk                                -> Pk
//
//
// -Applying the Simple algorithm to find the solution (Uk,Pk)
//
// (U*k, Pk) satisfies the following momentum equation:
//        A[Uk-1]U*k = -BtPk + Sv + Ss + (M/dt)Uk-1        -> U*k
//
// p'k is evaluated by solving:
//     (BDa-1Bt)p'k = BU*k                                -> p'k
//
// The velocity correction u'k is deduced by solving:
//        Da[Uk-1] (Uk-U*k) = -Btp'k                        -> U'k
//
// The pressure field Pk is not modified by the correction p'k,
// while the velocity is updated by: Uk = U*k + U'k
//
// The algorithm can be repeated until convergence ||Uk-Uk-1|| < seuil_convergence_implicite_.
// In practice, only one iteration is needed (seuil_convergence_implicite_ = 1e6).
 
// The algorithm coded in this class (iterer_NS) differs slightly from the above description:
// In the UPk evaluation step:
//   - the pressure gradient is taken into account and the relation becomes:
//         Da[Uk-1]UPk = E[Uk-1]Uk-1 + Sv + Ss - BtPk
//
//   - solving (BDa-1Bt)Pcor = BUPk gives a pressure correction
//     and the pressure field is updated: Pk = Pk-1 + Pcor
//     (Pcor replaces the notation Pk used above)
//
//   - resu is readjusted (BtPk = BtPk-1 + BtPcor) to contain -BtPk
 
class Simpler : public Simple
{
 
  Declare_instanciable(Simpler);
 
public :
  void iterer_NS(Equation_base&, DoubleTab& current, DoubleTab& pression, double, Matrice_Morse&, double, DoubleTrav&,int nb_iter,int& converge, int& ok) override;
 
 
 
protected :
 
 
};
 
int inverser_par_diagonale(const Matrice_Morse& matrice,const DoubleTrav& resu,const DoubleTab& present,DoubleTrav& correction_en_vitesse);
 
#endif