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:

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}

200

The wind parameters are then given by the jump conditions for an adiabatic shock (\gamma=5/3):

T_{wind}	[2\gamma (\gamma-1)/(\gamma+1) ]M^2 = 33,333 ~K
n_{wind}	4\times 10^4 ~cm^{-3}
v_{wind}	2,000 ~km~s^{-1}

Q - shocked gas speed = shock speed? Q - does shock speed decrease with time? Q - should we get density enhancement with time along shock front? Q - how does cooling adjust shock profiles?

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 (ambient and clump medium to travel a clump radius; t_{sc}), wind crossing time (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, clump origin, simulation time & framerate (for 155 frames), are given by:

L_{x} = L_{y}	10~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}