NavierStokes2DPreStep.c File Reference

Pre-step function for 2D Navier Stokes equations. More...

#include <arrayfunctions.h>
#include <mathfunctions.h>
#include <matmult_native.h>
#include <physicalmodels/navierstokes2d.h>
#include <hypar.h>

Go to the source code of this file.

Functions
int	NavierStokes2DPreStep (double *u, void *s, void *m, double waqt)

Detailed Description

Pre-step function for 2D Navier Stokes equations.

Author

Debojyoti Ghosh

Definition in file NavierStokes2DPreStep.c.

Function Documentation

int NavierStokes2DPreStep	(	double *	u,
		void *	s,
		void *	m,
		double	waqt
	)

Pre-step function for the 2D Navier Stokes equations: This function is called at the beginning of each time step.

• The solution at the beginning of the step is copied into NavierStokes2D::solution for the linearized flux partitioning.
• The linearized "fast" Jacobian (representing the acoustic modes) NavierStokes2D::fast_jac is computed as:

  \begin{equation} A_f\left({\bf u}\right) = R\left({\bf u}\right)\Lambda_f\left({\bf u}\right)L\left({\bf u}\right) \end{equation}

  where \(R\) and \(L\) are the matrices of right and left eigenvectors, and,

  \begin{equation} \Lambda_f = diag\left[0,0,u+c,u-c \right] \end{equation}

  with \(c\) being the speed of sound.
  
  Reference:
• Ghosh, D., Constantinescu, E. M., Semi-Implicit Time Integration of Atmospheric Flows with Characteristic-Based Flux Partitioning, SIAM Journal on Scientific Computing, 38 (3), 2016, A1848-A1875, http://dx.doi.org/10.1137/15M1044369.

Parameters

u	Solution vector
s	Solver object of type HyPar
m	MPI object of type MPIVariables
waqt	Current simulation time

Definition at line 33 of file NavierStokes2DPreStep.c.

{
  HyPar             *solver = (HyPar*)   s;
  NavierStokes2D    *param  = (NavierStokes2D*) solver->physics;
  int               *dim    = solver->dim_local;
  int               ghosts  = solver->ghosts, dir, p;
  double            *A;
  static const int  ndims   = _MODEL_NDIMS_;
  static const int  JacSize = _MODEL_NVARS_*_MODEL_NVARS_;
  static int        index[_MODEL_NDIMS_], bounds[_MODEL_NDIMS_], offset[_MODEL_NDIMS_];
  static double     D[_MODEL_NVARS_*_MODEL_NVARS_],L[_MODEL_NVARS_*_MODEL_NVARS_],
                    R[_MODEL_NVARS_*_MODEL_NVARS_],DL[_MODEL_NVARS_*_MODEL_NVARS_];

  /* set bounds for array index to include ghost points */
  _ArrayAddCopy1D_(dim,(2*ghosts),bounds,ndims);
  /* set offset such that index is compatible with ghost point arrangement */
  _ArraySetValue_(offset,ndims,-ghosts);
  /* copy the solution to act as a reference for linearization */
  _ArrayCopy1D_(u,param->solution,(solver->npoints_local_wghosts*_MODEL_NVARS_));

  int done = 0; _ArraySetValue_(index,ndims,0);
  while (!done) {
    _ArrayIndex1DWO_(ndims,dim,index,offset,ghosts,p);

    dir = _XDIR_;
    A = (param->fast_jac + 2*JacSize*p + dir*JacSize);
    /* get the eigenvalues, and left & right eigenvectors */
    _NavierStokes2DEigenvalues_      ((u+_MODEL_NVARS_*p),D,param->gamma,dir);
    _NavierStokes2DLeftEigenvectors_ ((u+_MODEL_NVARS_*p),L,param->gamma,dir);
    _NavierStokes2DRightEigenvectors_((u+_MODEL_NVARS_*p),R,param->gamma,dir);
    /* remove the entropy modes (corresponding to eigenvalues u) */
    D[2*_MODEL_NVARS_+2] = D[3*_MODEL_NVARS_+3] = 0.0;
    /* assemble the Jacobian */
    MatMult4(_MODEL_NVARS_,DL,D,L );
    MatMult4(_MODEL_NVARS_,A ,R,DL);

    dir = _YDIR_;
    A = (param->fast_jac + 2*JacSize*p + dir*JacSize);
    /* get the eigenvalues, and left & right eigenvectors */
    _NavierStokes2DEigenvalues_      ((u+_MODEL_NVARS_*p),D,param->gamma,dir)
    _NavierStokes2DLeftEigenvectors_ ((u+_MODEL_NVARS_*p),L,param->gamma,dir);
    _NavierStokes2DRightEigenvectors_((u+_MODEL_NVARS_*p),R,param->gamma,dir);
    /* remove the entropy modes (corresponding to eigenvalues v) */
    D[1*_MODEL_NVARS_+1] = D[3*_MODEL_NVARS_+3] = 0.0;
    /* assemble the Jacobian */
    MatMult4(_MODEL_NVARS_,DL,D,L );
    MatMult4(_MODEL_NVARS_,A ,R,DL);

    _ArrayIncrementIndex_(ndims,bounds,index,done);
  }

  return(0);
}