Piso.h

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#ifndef Piso_included
#define Piso_included
 
#include <Navier_Stokes_std.h>
#include <Simpler.h>
 
//Description
 
// Ref. Journal of Computational Physics 62 P. 40-65
// R. I. Issa
 
// A = (M/dt + C(Uk) + D)
// Bt and -B denote the gradient and divergence operators respectively
// delta_x denotes the Laplacian operator
// H denotes the convection+diffusion operator
 
// The PISO (Pressure Implicit Splitting Operator) algorithm is non-iterative
// and consists of three steps * ** and ***.
// The steps of the algorithm are:
 
// -PREDICTION STEP
//
// Find the velocity field U* satisfying the momentum equation (with pressure Pn)
//        (rho/dt)*(U*-Un) = H(U*) - BtP + S
// U* does not satisfy the continuity equation
 
// The prediction step is performed by solving the following system:
//        AU* = -BtPn + Sv + Ss + (M/dt)Un                -> U*
 
 
// -FIRST CORRECTION STEP
//
// Find U** and P* satisfying the momentum equation and continuity equation (from U* and Un)
//        (rho/dt)*(U**-Un) = H(U*) - BtP* + S
//        delta_x U** = 0
 
// To stabilise the system, the diagonal part of convection-diffusion is treated implicitly
//        (rho/dt-Ao)*U** - (rho/dt)*Un = H'(U*) -BtP* + S with H(U) = H'(U) + AoU
// Subtracting the prediction equation:
//        (rho/dt-Ao)*(U**-U*) = -Bt(P*-Pn)        and on the other hand delta_x U** = 0
//
// The first correction step is performed by solving (Da = rho/dt-Ao):
//        (BDa-1Bt)P' = BU*                                -> P' -> P* = Pn + P'
// then   Da[Un]U' = -BtP'                                -> U' -> U** = U* + U'
 
 
//-SECOND CORRECTION STEP
//
// Find U*** and P** satisfying the momentum equation and continuity equation (from U** and Un)
//        (rho/dt)*(U***-Un) = H(U**) - BtP** + S
//        delta_x U*** = 0
 
// To stabilise the system, the diagonal part of convection-diffusion is treated implicitly
//        (rho/dt-Ao)*U*** - (rho/dt)*Un = H'(U**) -BtP** + S
// Subtracting the reformulated first correction equation from the reformulated second correction equation:
//        (rho/dt-Ao)*(U***-U**) = H'(U**-U*) -Bt(P**-P*)        and on the other hand delta_x U*** = 0 and delta_x U** = 0
//
// The second correction step is performed by solving (E = H'):
//        (BDa-1Bt)P'' =  (BDa-1E)U'                        -> P'' -> P** = P* + P''
//         DaU'' = EU' -BtP''                                -> U'' -> U*** = U** + U''
 
// Note: Additional correction steps can be performed.
// The implementation here continues corrections (compt_max-1 maximum)
// unless the residual increases compared to the previous correction.
 
class Piso : public Simpler
{
  Declare_instanciable(Piso);
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 nb_corrections_max_ = 21; // maximum number of corrections to refine the projection
  int avancement_crank_ = 0;   // not pure PISO but rather Crank-Nicolson
  int with_sources_ = 0;   // include source terms in the pressure matrix -> more implicit terms, fewer PISO terms
 
  Entree& lire(const Motcle&, Entree&) override;
 
private:
  virtual void iterer_NS_PolyMAC_CDO(Navier_Stokes_std& eqn,DoubleTab& current,DoubleTab& pression, double dt, Matrice_Morse& matrice, int& ok);
  // IBM stuff
  void add_penality_term(Navier_Stokes_std& , DoubleTrav& resu , DoubleTrav& gradP);
  void correct_incr_pressure(Navier_Stokes_std& , DoubleTrav& secmem);
  void correct_gradP(Navier_Stokes_std& , DoubleTrav& gradP);
  void correct_pressure(Navier_Stokes_std& , DoubleTab& , DoubleTab& );
};
 
//Description
// Ref. G. Fauchet
 
// The IMPLICITE algorithm is non-iterative and consists of two steps * and **.
// The steps of the algorithm are:
 
// -PREDICTION STEP
//
// Find the velocity field U* satisfying the momentum equation (with pressure Pn)
// As in the PISO algorithm, the diffusion term is expressed implicitly
// and the convection term semi-implicitly.
 
//         (U*-Un)/dt = H(U*) - BtPn + Sv + Ss
// U* does not satisfy the continuity equation
 
// The prediction step is performed by solving the following system:
//        AU* = -BtPn + Sv + Ss + (M/dt)Un                -> U*
 
// -CORRECTION STEP
//
// The momentum equation at step n+1 can be written:
//         (Un+1-Un)/dt = H(Un+1) - BtPn+1 + Sv + Ss
// Subtracting the momentum equation written for U* and neglecting
// the convection and diffusion terms on U' = Un+1 - U*, we get:
//         (Un+1-U*)/dt = -BtP'        with P' = Pn+1 - Pn
//
// The correction step is performed by solving (M = mass matrix):
//        (BM-1Bt)dt*P' = BU*                                -> dt*P' -> P'
//         Un+1 = U* -dt*BtP'                                -> Un+1
//
// Note: The mass matrix is constant, therefore the system (BM-1Bt) is assembled only once.
class Implicite : public Piso
{
  Declare_instanciable(Implicite);
};
 
#endif /* Piso_included */