Shocked Clump (2D)

Am investigating the interaction between a cold clump in a supernovae remnant and a shock. To model this, am injecting a supersonic wind into the boundary, whose properties are specified by the jump conditions across an adiabatic shock. The jump conditions are calculated using the following parameters in the ambient medium (note all values given are approximate; actual values are calculated to machine precision in the attached problem module):

T_{amb}	10^4 ~K
n_{amb}	10^4 ~cm^{-3}
v_{amb}	0

The sound speed of the ambient material for these parameters is (for \gamma=5/3):

C_{amb}

10 km~s^{-1}

which for a injected wind speed of v_s=2,000 ~km/s gives a Mach number of:

M_{wind}

194

The wind parameters are then given by the R-H jump conditions (see attached pdf for equations used):

T_{wind}	1e+8~ K
n_{wind}	4e+4 ~cm^{-3}
v_{wind}	1.5e+8 ~cm~s^{-1}

The clump is initially in pressure equilibrium with the ambient medium, and its properties are given by:

T_{clump}	10^2 ~K
n_{clump}	10^6 ~cm^{-3}
v_{clump}	0

The thermodynamics in the simulation is governed by an ideal EOS (with \gamma=5/3). The abundances are taken to be solar (\mu=1.3). Other parameters of interest are the clump radius (R_c), clump-ambient density contrast (\chi), clump crushing time (t_{cc}=\sqrt{\chi} R_c/v_s), sound crossing time (for sound waves in ambient and clump medium to travel a clump radius; t_{sc}), wind crossing time (for wind to travel clump radius; t_{wc}):

R_{c}	10^{16} ~cm
{\chi}	100
t_{cc}	5\times 10^{8}~s
t_{sc} (ambient medium)	10^{10}~s
t_{sc} (clump medium)	10^{11}~s
t_{wc}	5\times10^{7}~s

The domain dimensions, resolution, clump origin, simulation time & framerate (for 155 frames), are given by:

L_{x} = L_{y}	10~R_c
dx	1/64~R_c
O_{clump}	2~R_c,~ 5~R_c
t_{sim}	t_{wc}~ +~3~t_{cc}= 155\times 10^7~s
dt	10^7~s~=~1/50~t_{cc}

Run 1 - Steady inflow condition

Supersonic wind is injected each timestep over the course of the simulation.

Visualizations:

rho (cm-3)	movie
temp (K)	movie
press (Ba)	movie
Sound speed (cm/s)	movie
vx (cm/s)	movie
Density jump	image

Run 2 - Pulsed case

Supersonic wind only injected at t=0 (from lower x-boundary)

<To be added… >

Unresolved thoughts:

Q - estimate on sim runtime?

Q - location of clump center wrt grid?

Q - reflected BC differences?