Underexpanded jet. 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

Underexpanded jet.

The domain is initialized with a static medium, whereas in the bottom boundary the following conditions are applied (see Section 5.2 of [Mig07])

$P_{\rm jet} = \frac{P_{\rm ratio}}{\Gamma}\left(\frac{2}{\Gamma + 1}\right)^{\Gamma/(\Gamma - 1)} \,,\quad \rho_{\rm jet} = \rho_{\rm ratio}\left(\frac{2}{\Gamma + 1}\right)^{1/(\Gamma - 1)} \,,\quad v_{\rm jet} = \sqrt{\frac{\Gamma P_{\rm jet}}{\rho_{\rm jet}}}\,.$

The runtime parameters that are read from pluto.ini are

g_inputParam[DN_RATIO]: sets the value of $\rho_{\rm ratio}$ ;
g_inputParam[PR_RATIO]: sets the value of $P_{\rm ratio}$ ;

Configurations:

#01: Second order accuracy;
#02: Third order accuracy;

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

Date: July 09, 2014

References:

[Mig07]: "PLUTO: a numerical code for computational astrophysics", Mignone et al., ApJS (2007), 170, 228

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 53 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 37 of file init.c.

 {
   g_gamma = 5./3.;
 
   us[RHO] = 1.0;
   us[VX1] = 0.0;
   us[VX2] = 0.0;
   us[VX3] = 0.0;
   us[PRS] = 1.0/g_gamma;
   us[TRC] = 0.0;
 
 }

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 61 of file init.c.

 {
   int     i, j, k;
   double  *R;
   real    pjet, dnjet, vjet;
   real    scrh;
 
   scrh = 1.0/(g_gamma - 1.0);
 
   R     = grid[IDIR].xgc;
   pjet  = g_inputParam[PR_RATIO]*pow(2.0/(g_gamma + 1.0),g_gamma*scrh)/g_gamma;
   dnjet = g_inputParam[DN_RATIO]*pow(2.0/(g_gamma + 1.0),scrh);
   vjet  = sqrt(g_gamma*pjet/dnjet);
 
   if (side == X2_BEG){
 
     X2_BEG_LOOP(k,j,i){
 
       if (R[i] <= 1.) {
         d->Vc[RHO][k][j][i] = dnjet;
         d->Vc[VX1][k][j][i] = 0.;
         d->Vc[VX2][k][j][i] = vjet;
         d->Vc[PRS][k][j][i] = pjet;
       } else {
         d->Vc[RHO][k][j][i] =  d->Vc[RHO][k][2*JBEG - j - 1][i];
         d->Vc[VX1][k][j][i] =  d->Vc[VX1][k][2*JBEG - j - 1][i];
         d->Vc[VX2][k][j][i] = -d->Vc[VX2][k][2*JBEG - j - 1][i];
         d->Vc[PRS][k][j][i] =  d->Vc[PRS][k][2*JBEG - j - 1][i];
       }
     }
   } 
 }

Functions

Detailed Description

Function Documentation