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

Run description: supersonic wind is injected into the left edge of the computational domain each timestep over the course of the simulation.

Note that we must initialize the left and right state of the "Riemann problem" (where the discontinuity corresponds to the interface between the grid and the boundary zones) which generates a shock traveling to the right into the grid at 2,000 km/s. In other words, we solve the jump conditions across a 2,000 km/s shock using the pre-shock values of the gas in the grid to initialize the boundary zones (the "post-shock" gas). If the incoming flow does not match the jump condition values exactly, additional waves will be generated once the incoming flow collides with the ambient gas in the box. To illustrate this, see the following image which shows an initial inflow at the boundary that has slightly different values than those specified by the jump conditions, compared to the true values (right).

The shock front in the right panel shows some oscillations, but these are to be expected given the numerical scheme. Currently, am using a PPL interpolation method, but will see if PPM reduces these oscillations further in a future run.

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?