Two-Dimensional Riemann problem. More...

#include "pluto.h"

Include dependency graph for init.c:

Functions
void	Init (double *us, double x1, double x2, double x3)

void	Analysis (const Data d, Grid grid)

void	UserDefBoundary (const Data d, RBox box, int side, Grid *grid)

Detailed Description

Two-Dimensional Riemann problem.

Sets the initial condition for a 2D Riemann problem in terms of 4 four constant states at each corner of the computational domain.

For example, the top right corner, $x > 0$ , $y > 0$ , is denoted with PP and its initial values are:

$\rho = \rho_{\rm PP} \,,\quad\quad P = P_{\rm PP} \,,\quad\quad v_x = v_{x\,{\rm PP}} \,,\quad\quad v_y = v_{y\,{\rm PP}}\,.$

Similar conditions hold for the bottom right corner ( $x > 0$ , $y < 0$ ; PM), the top left ( $x < 0$ , $y > 0$ ; MP), and the bottom left ( $x < 0$ , $y < 0$ ; MM). The 4 flow quantities of each corner are defined by the 16 parameters that are read from pluto.ini.

DN_PP, PR_PP, VX_PP, VY_PP
DN_MP, PR_MP, VX_MP, VY_MP
DN_PM, PR_PM, VX_PM, VY_PM
DN_MM, PR_MM, VX_MM, VY_MM
Configurations #01, #02 and #05 involve the interaction between four contact discontinuities (see fig. below).
Configurations #03 and #04 (with AMR) involve the interaction of shocks.

Final state for configuration #05.

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

Date: Sept 15, 2014

References

C. W. Schulz-Rinne, "Classification of the Riemann problem for two-dimensional gas dynamics", SIAM J. Math. Anal., 24 (1993), pp. 76-88.
C. W. Schulz-Rinne, J. P. Collins and H. M. Glaz, "Numerical solution of the Riemann problem for two-dimensional gas dynamics", SIAM J. Sci. Comp., 14 (1993), pp. 1394-1414.

Definition in file init.c.

Function Documentation

void Analysis	(	const Data *	d,
		Grid *	grid
	)

Perform runtime data analysis.

Parameters

[in]	d	the PLUTO Data structure
[in]	grid	pointer to array of Grid structures

Definition at line 102 of file init.c.

 {
 
 }

void Init	(	double *	us,
		double	x1,
		double	x2,
		double	x3
	)

The Init() function can be used to assign initial conditions as as a function of spatial position.

Parameters

[out]	v	a pointer to a vector of primitive variables
[in]	x1	coordinate point in the 1st dimension
[in]	x2	coordinate point in the 2nd dimension
[in]	x3	coordinate point in the 3rdt dimension

The meaning of x1, x2 and x3 depends on the geometry:

$\begin{array}{cccl} x_1 & x_2 & x_3 & \mathrm{Geometry} \\ \noalign{\medskip} \hline x & y & z & \mathrm{Cartesian} \\ \noalign{\medskip} R & z & - & \mathrm{cylindrical} \\ \noalign{\medskip} R & \phi & z & \mathrm{polar} \\ \noalign{\medskip} r & \theta & \phi & \mathrm{spherical} \end{array}$

Variable names are accessed by means of an index v[nv], where nv = RHO is density, nv = PRS is pressure, nv = (VX1, VX2, VX3) are the three components of velocity, and so forth.

Definition at line 55 of file init.c.

 {
   double x,y;
 
   x = x1;
   y = x2;
   #if EOS == IDEAL
    g_gamma = 1.4;
   #elif EOS == ISOTHERMAL
    g_isoSoundSpeed = 1.0;
   #endif
 
   if (x > 0.0 && y > 0.0){
     us[RHO] = g_inputParam[DN_PP];
     #if EOS == IDEAL
      us[PRS] = g_inputParam[PR_PP];
     #endif
     us[VX1] = g_inputParam[VX_PP];
     us[VX2] = g_inputParam[VY_PP];
   }else if(x < 0.0 && y > 0.0){
     us[RHO] = g_inputParam[DN_MP];
     #if EOS == IDEAL
      us[PRS] = g_inputParam[PR_MP];
     #endif
     us[VX1] = g_inputParam[VX_MP];
     us[VX2] = g_inputParam[VY_MP];
   }else if(x < 0.0 && y < 0.0){
     us[RHO] = g_inputParam[DN_MM];
     #if EOS == IDEAL
      us[PRS] = g_inputParam[PR_MM];
     #endif
     us[VX1] = g_inputParam[VX_MM];
     us[VX2] = g_inputParam[VY_MM];
   }else if(x > 0.0 && y < 0.0){
     us[RHO] = g_inputParam[DN_PM];
     #if EOS == IDEAL
      us[PRS] = g_inputParam[PR_PM];
     #endif
     us[VX1] = g_inputParam[VX_PM];
     us[VX2] = g_inputParam[VY_PM];
   }   
 }

void UserDefBoundary	(	const Data *	d,
		RBox *	box,
		int	side,
		Grid *	grid
	)

Assign user-defined boundary conditions.

Parameters

[in,out]	d	pointer to the PLUTO data structure containing cell-centered primitive quantities (d->Vc) and staggered magnetic fields (d->Vs, when used) to be filled.
[in]	box	pointer to a RBox structure containing the lower and upper indices of the ghost zone-centers/nodes or edges at which data values should be assigned.
[in]	side	specifies the boundary side where ghost zones need to be filled. It can assume the following pre-definite values: X1_BEG, X1_END, X2_BEG, X2_END, X3_BEG, X3_END. The special value side == 0 is used to control a region inside the computational domain.
[in]	grid	pointer to an array of Grid structures.

Assign user-defined boundary conditions in the lower boundary ghost zones. The profile is top-hat:

$V_{ij} = \left\{\begin{array}{ll} V_{\rm jet} & \quad\mathrm{for}\quad r_i < 1 \\ \noalign{\medskip} \mathrm{Reflect}(V) & \quad\mathrm{otherwise} \end{array}\right.$

where $V_{\rm jet} = (\rho,v,p)_{\rm jet} = (1,M,1/\Gamma)$ and M is the flow Mach number (the unit velocity is the jet sound speed, so $ v = M$ ).

Assign user-defined boundary conditions:

left side (x beg): constant shocked values
bottom side (y beg): constant shocked values for x < 1/6 and reflective boundary otherwise.
top side (y end): time-dependent boundary: for $x < x_s(t) = 10 t/\sin\alpha + 1/6 + 1.0/\tan\alpha$ we use fixed (post-shock) values. Unperturbed values otherwise.

Definition at line 112 of file init.c.

116 { }

Functions

Detailed Description

Function Documentation