PLUTO Test Problems  4.4-patch2
Functions
init.c File Reference

Relativistic magnetized jet in axisymmetric coordinates. More...

Functions

void InitDomain (Data *d, Grid *grid)
 

Detailed Description

The jet problem is set up in axisymmetric cylindrical coordinates $ (r,z) $ as described in section 4.2.3 of Mignone, Ugliano & Bodo (2009, [MUB09] hereafter). We label ambient and jet values with the suffix "a" and "j", respectively. The ambient medium is at rest and is characterized by uniform density and pressure, $ \rho_a $ and $ p_a $. The beam enters from the lower-z boundary from a circular nozzle of radius 1, carries a constant poloidal field $ B_z $ and a (radially-varying) toroidal component $ B_\phi(R) $. Flow variables are prescribed as

\[ \left\{\begin{array}{lcl} \rho(R) &=& \rho_j \\ \noalign{\medskip} v_z(R) &=& v_j \\ \noalign{\medskip} B_\phi(R) &=& \DS \left\{\begin{array}{ll} -\gamma_j b_m R/a & \quad{\rm for}\quad r<a \\ \noalign{\medskip} -\gamma_j b_m a/R & \quad{\rm for}\quad r>a \end{array}\right. \\ \noalign{\medskip} B_z(R) &=& B_{z0}\quad\mathrm{(const)} \end{array}\right. \]

Here a is the magnetization radius while $ v_r = B_r = 0 $. The pressure distribution is found by solving the radial momentum balance between thermal, centrifugal and magnetic forces. Neglecting rotation and assuming Bz to be constant the solution is given by

\[ p(R) = p_j + b_m^2\left[1-\min\left(\frac{r^2}{a^2},1\right)\right] \]

Here $p_j=p_a$ is the jet/ambient pressure at r=1 and its value depends on the Mach number, see [MUB09].

The parameters controlling the problem is

  1. g_inputParam[MACH]: the jet Mach number $ M = v_j/cs $ where $c_s=\sqrt{\Gamma p_j/(\rho h)}$ is the sound speed and $\rho h = \rho + \Gamma p_j/(\Gamma-1)$. This is used to recover $p_j$;
  2. g_inputParam[LORENTZ]: the jet Lorentz factor;
  3. g_inpurParam[RHOJ]: the jet density;
  4. g_inpurParam[SIGMA_POL]: magnetization strength for poloidal magnetic field component (see [MUB09], Eq [65]);
  5. g_inpurParam[SIGMA_TOR]: magnetization strength for toroidal magnetic field component (see [MUB09], Eq [65]);

The different configurations are:

The following image show the (log) density map at the end of simulation for setup #01.

rmhd_jet.01.jpg
Density map at the end of the computation for configuration #01

References

Author
A. Mignone (migno.nosp@m.ne@t.nosp@m.o.inf.nosp@m.n.it)
Date
Aug 19, 2019

Function Documentation

◆ InitDomain()

void InitDomain ( Data *  d,
Grid *  grid 
)

Assign initial condition by looping over the computational domain. Called after the usual Init() function to assign initial conditions on primitive variables. Value assigned here will overwrite those prescribed during Init().