Hydrodynamics allows for an effective description of macroscopic matter
providing the matter is in local
thermal equilibrium.
Jets are ubiquitous in extragalactic radio sources associated with
active galactic nuclei. Although to explain their origin GR
magnetohydrodynamics is needed, to study the morphology of the jet a SR
hydrodynamics is sufficient. The following is a simulation of a 2D
planar
jet (
) moving
through
an extragalactic medium (
).
The first image/movie below shows the log of the fluid density of a the
jet. The second image/movie shows a 3D view of the domain. In order to
visualize the fluid flow one can trace test particles
trajectories.
I started with random uniform particle distribution and regularly added
particles into the jet source. The third image/movie shows the motion
of the
tracers.
Since the jet is symmetric it is sufficient only to use half of the
domain for calculations and to use reflection boundary conditions at
the symmetry axis.
The computational domain is (20,55)x(0,21) and the resolution is
3000x840 cells.
Note the presence of an external bow shock and the vortices due to
the KelvinHelmholtz instability.
These are the results of simulations of
a relativistic wind accretion onto a Schwarzschild BH. The models are
taken from the paper by Font et. al.
A
NUMERICAL STUDY OF RELATIVISTIC BONDIHOYLE ACCRETION ONTO A MOVING
BLACK HOLE:AXISYMMETRIC COMPUTATIONS IN A SCHWARZSCHILD
BACKGROUND,494,297316 (1998)
Here is the table from the paper describing the models (I think that r_{min}(r_{a})
for model MC2 should be 0.57  0.44 would be below the Schwarzschild
radius)
Model  cs_{∞}  G  Μ_{∞}  v_{∞}  r_{a}(M)  r_{min}(r_{a})  r_{max}(r_{a})  t_{f}(M) 
MA1...  0.1  1.1  1.5  0.15  30.8  0.125  10.0  4000 
MA2...  0.1  1.1  5.0  0.5  3.8  0.57  10.0  750 
MB1...  0.1  4/3  1.5  0.15  30.8  0.125  10.0  4000 
MB2...  0.1  4/3  5.0  0.5  3.8  0.57  10.0  750 
MC1...  0.1  5/3  1.5  0.15  30.8  0.125  10.0  2000 
MC2...  0.1  5/3  5.0  0.5  3.8  0.44  10.0  750 
UA1...  0.31  1.1  1.5  0.47  3.2  0.69  9.38  200 
UA2...  0.31  1.1  3.0  0.93  1.04  2.12  28.85  110 
UB0...  0.57  4/3  0.6  0.34  2.2  1.0  13.64  200 
UB1...  0.57  4/3  1.5  0.86  0.92  2.39  32.61  200 
UC0...  0.81  5/3  0.6  0.49  1.1  2.0  27.27  200 
cs_{∞}  asymptotic sound speed
(i.e., at the outer boundary) 
G  adiabatic exponent 
Μ_{∞}  asymptotic Mach number at
infinity 
v_{∞}  asymptotic flow velocity 
r_{a}(M)  accretion radius 
r_{min}(r_{a})  inner boundary in units of
accretion radius 
r_{max}(r_{a})  outer boundary in units of accretion radius 
t_{f}(M)  final time at which the simulation was stopped 

Wind accreation schematics. The outer circle is the outer boundary. The small circle in the middle represents the inner boundary with the black hole. 
First is the simulation of the model MC2 performed on a 200x100 grid (r,theta) using EddingtonFinkelstein ingoing coordinates. The grid is logarithmic in rdirection and uniform in theta. The inner radius is located at r=1.75M and the outer radius is at r=100M. In this simulation (unlike in the paper) I put vacuum in the whole domain except at the ghost zones in the upper hemisphere at initial time. The vacuum was a true vacuum, i.e., all the variables were set to zero. It is a bit tricky to evolve such a setup but the method I implemented seemed to work fine. Since this is log_{10} plot I added 1.e3 to the density so vacuum would be represented by the value 3.
The next simulation is for the model MB1. This particular one is done in Schwarzschild coordinates but the results do not change when using EddingtonFinkelstein ingoing coordinates. The simulation shows that if a stationary state is reached it would be qualitatively different than the one for the model MC2 which is unexpected. I performed many simulations in both types of coordinate systems with different resolutions, domain sizes and flux approximations. All result in the same behaviour, i.e., the detachment of the initially formed shock and its dispersion. My computed accretion rates for all tested models agree to those published until the t_{f}(M) for each simulation. My evolution of the model MC1 shows similar behaviour  a hint of it might be even present in the paper  the simulation of C1 shows a detached shock but the simulation was stopped at t=2000M.