NavierStokes2DModifiedSolution.c File Reference

Compute the modified solution for the well-balanced treatment of gravitational source terms. More...

#include <basic.h>
#include <arrayfunctions.h>
#include <physicalmodels/navierstokes2d.h>
#include <mpivars.h>
#include <hypar.h>

Go to the source code of this file.

Functions
int	NavierStokes2DModifiedSolution (double *uC, double *u, int d, void *s, void *m, double waqt)

Detailed Description

Compute the modified solution for the well-balanced treatment of gravitational source terms.

Author

Debojyoti Ghosh

Definition in file NavierStokes2DModifiedSolution.c.

Function Documentation

NavierStokes2DModifiedSolution()

int NavierStokes2DModifiedSolution	(	double *	uC,
		double *	u,
		int	d,
		void *	s,
		void *	m,
		double	waqt
	)

This function computes the modified solution for the well-balanced treatment of the gravitational source terms. The modified solution vector is given by

\begin{equation} {\bf u}^* = \left[\begin{array}{c} \rho \varrho^{-1}\left(x,y\right) \\ \rho u \varrho^{-1}\left(x,y\right) \\ \rho v \varrho^{-1}\left(x,y\right) \\ e^* \end{array}\right] \end{equation}

where

\begin{equation} e^* = \frac{p \varphi^{-1}\left(x,y\right)}{\gamma-1} + \frac{1}{2}\rho \varrho^{-1}\left(x,y\right) \left(u^2+v^2\right) \end{equation}

\(\varrho\) and \(\varphi\) are computed in NavierStokes2DGravityField(). For flows without gravity, \({\bf u}^* = {\bf u}\).

References:

• Ghosh, D., Constantinescu, E.M., Well-Balanced Formulation of Gravitational Source Terms for Conservative Finite-Difference Atmospheric Flow Solvers, AIAA Paper 2015-2889, 7th AIAA Atmospheric and Space Environments Conference, June 22-26, 2015, Dallas, TX, http://dx.doi.org/10.2514/6.2015-2889
• Ghosh, D., Constantinescu, E.M., A Well-Balanced, Conservative Finite-Difference Algorithm for Atmospheric Flows, AIAA Journal, 54 (4), 2016, pp. 1370-1385, http://dx.doi.org/10.2514/1.J054580.

Parameters

uC	Array to hold the computed modified solution
u	Solution vector array
d	spatial dimension (not used)
s	Solver object of type HyPar
m	MPI object of time MPIVariables
waqt	Current simulation time

Definition at line 31 of file NavierStokes2DModifiedSolution.c.

{
  HyPar           *solver = (HyPar*)          s;
  NavierStokes2D  *param  = (NavierStokes2D*) solver->physics;

  int     ghosts  = solver->ghosts;
  int     *dim    = solver->dim_local;
  int     ndims   = solver->ndims;
  int     index[ndims], bounds[ndims], offset[ndims];

  /* set bounds for array index to include ghost points */
  _ArrayCopy1D_(dim,bounds,ndims);
  int i; for (i=0; i<ndims; i++) bounds[i] += 2*ghosts;

  /* set offset such that index is compatible with ghost point arrangement */
  _ArraySetValue_(offset,ndims,-ghosts);

  int done = 0; _ArraySetValue_(index,ndims,0);
  double inv_gamma_m1 = 1.0 / (param->gamma-1.0);

  while (!done) {
    int p; _ArrayIndex1DWO_(ndims,dim,index,offset,ghosts,p);
    double rho, uvel, vvel, E, P;
    _NavierStokes2DGetFlowVar_((u+_MODEL_NVARS_*p),rho,uvel,vvel,E,P,param->gamma);
    uC[_MODEL_NVARS_*p+0] = u[_MODEL_NVARS_*p+0] * param->grav_field_f[p];
    uC[_MODEL_NVARS_*p+1] = u[_MODEL_NVARS_*p+1] * param->grav_field_f[p];
    uC[_MODEL_NVARS_*p+2] = u[_MODEL_NVARS_*p+2] * param->grav_field_f[p];
    uC[_MODEL_NVARS_*p+3] = (P*inv_gamma_m1)*(1.0/param->grav_field_g[p]) + (0.5*rho*(uvel*uvel+vvel*vvel))*param->grav_field_f[p];
    _ArrayIncrementIndex_(ndims,bounds,index,done);
  }

  return(0);
}