hll_speed.c File Reference

Compute the outermost wave speeds for HLL-based solvers. More...

#include "pluto.h"

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Macros
#define	DAVIS_ESTIMATE   YES
#define	EINFELDT_ESTIMATE   NO
#define	ROE_ESTIMATE   NO

Functions
void	HLL_Speed (double **vL, double **vR, double *a2L, double *a2R, double *SL, double *SR, int beg, int end)

Detailed Description

Compute the outermost wave speeds for HLL-based solvers.

HLL_Speed() computes an estimate to the leftmost and rightmost wave signal speeds bounding the Riemann fan based on the input states ::vR and ::vL. Depending on the estimate, several variants are possible.

Authors

A. Mignone (migno.nosp@m.ne@p.nosp@m.h.uni.nosp@m.to.i.nosp@m.t)

Date

June 6, 2013

Definition in file hll_speed.c.

Macro Definition Documentation

#define DAVIS_ESTIMATE   YES

Definition at line 19 of file hll_speed.c.

#define EINFELDT_ESTIMATE   NO

Definition at line 20 of file hll_speed.c.

#define ROE_ESTIMATE   NO

Definition at line 21 of file hll_speed.c.

Function Documentation

void HLL_Speed	(	double **	vL,
		double **	vR,
		double *	a2L,
		double *	a2R,
		double *	SL,
		double *	SR,
		int	beg,
		int	end
	)

Compute leftmost (SL) and rightmost (SR) speed for the Riemann fan.

Parameters

[in]	vL	left state for the Riemann solver
[in]	vR	right state for the Riemann solver
[in]	a2L	1-D array containing the square of the sound speed for the left state
[in]	a2R	1-D array containing the square of the sound speed for the right state
[out]	SL	the (estimated) leftmost speed of the Riemann fan
[out]	SR	the (estimated) rightmost speed of the Riemann fan
[in]	beg	starting index of computation
[in]	end	final index of computation

Switches:

ROE_ESTIMATE (YES/NO), DAVIS_ESTIMATE (YES/NO). TVD_ESTIMATE (YES/NO) JAN_HLL (YES/NO)

These switches set how the wave speed estimates are going to be computed. Only one can be set to 'YES', and the rest of them must be set to 'NO'

ROE_ESTIMATE: b_m = (0, (u_R - c_R, u_L - c_L, u_{roe} - c_{roe})) b_m = (0, (u_R + c_R, u_L + c_L, u_{roe} + c_{roe}))

where u_{roe} and c_{roe} are computed using Roe averages.

DAVIS_ESTIMATE: b_m = (0, (u_R - c_R, u_L - c_L)) b_m = (0, (u_R + c_R, u_L + c_L))

Definition at line 24 of file hll_speed.c.

{
  int    i;
  double scrh, s, c;
  double aL, dL;
  double aR, dR;
  double dvx, dvy, dvz;
  double a_av, du, vx;
  static double *sl_min, *sl_max;
  static double *sr_min, *sr_max;

  if (sl_min == NULL){
    sl_min = ARRAY_1D(NMAX_POINT, double);
    sl_max = ARRAY_1D(NMAX_POINT, double);

    sr_min = ARRAY_1D(NMAX_POINT, double);
    sr_max = ARRAY_1D(NMAX_POINT, double);
  }

/* ----------------------------------------------
              DAVIS Estimate  
   ---------------------------------------------- */

  #if DAVIS_ESTIMATE == YES

   MaxSignalSpeed (vL, a2L, sl_min, sl_max, beg, end);
   MaxSignalSpeed (vR, a2R, sr_min, sr_max, beg, end);
   for (i = beg; i <= end; i++) {

     SL[i] = MIN(sl_min[i], sr_min[i]);
     SR[i] = MAX(sl_max[i], sr_max[i]);

     aL = sqrt(a2L[i]);
     aR = sqrt(a2R[i]);

     scrh  = fabs(vL[i][VXn]) + fabs(vR[i][VXn]);    
     scrh /= aL + aR;

     g_maxMach = MAX(scrh, g_maxMach); 
   }

  #endif

/* ----------------------------------------------
        Einfeldt Estimate for wave speed 
   ---------------------------------------------- */

  #if EINFELDT_ESTIMATE == YES

   for (i = beg; i <= end; i++) {

     aL = sqrt(a2L[i]);
     aR = sqrt(a2R[i]);

     dL   = sqrt(vL[i][RHO]);
     dR   = sqrt(vR[i][RHO]);
     a_av = 0.5*dL*dR/( (dL + dR)*(dL + dR));
     du   = vR[i][VXn] - vL[i][VXn];
     scrh = (dR*aL*aL + dR*aR*aR)/(dL + dR);
     scrh += a_av*du*du;
      
     SL[i] = (dl*ql[VXn] + dr*qr[VXn])/(dl + dr);
  
     bmin = MIN(0.0, um[VXn] - sqrt(scrh));
     bmax = MAX(0.0, um[VXn] + sqrt(scrh));      
   }
  #endif

/* ----------------------------------------------
              Roe-like Estimate  
   ---------------------------------------------- */

  #if ROE_ESTIMATE  == YES
   
   for (i = beg; i <= end; i++) {

     aL = sqrt(a2L[i]);
     aR = sqrt(a2R[i]);

     s = 1.0/(1.0 + sqrt(vR[i][RHO]/vL[i][RHO]));
     c = 1.0 - s;

     vx = s*vL[i][VXn] + c*vR[i][VXn];

/* ************************************************************
     The following definition of the averaged sound speed
     is equivalent to original formulation given by Roe;
     here we just simplify the expression without explicitly 
     computing the Enthalpy:                                 
   ************************************************************ */
   
     EXPAND(dvx = vL[i][VX1] - vR[i][VX1];  ,
            dvy = vL[i][VX2] - vR[i][VX2];  ,
            dvz = vL[i][VX3] - vR[i][VX3];)

     scrh = EXPAND(dvx*dvx, + dvy*dvy, + dvz*dvz);
  
     a_av = sqrt(s*aL2 + c*aR2 + 0.5*s*c*gmm1*scrh);

     SL[i] = MIN(vL[i][VXn] - aL, vx - a_av);
     SR[i] = MAX(vR[i][VXn] + aR, vx + a_av);

     scrh = (fabs(vL[i][VXn]) + fabs(vR[i][VXn]))/(aL + aR);
     g_maxMach = MAX(scrh, g_maxMach);

   }
  #endif
   
}

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