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 and data files for the fiducial case described here):

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 a "Riemann problem" (where the Riemann interface lies along the boundary between the grid and ghost zones) such that the generated wave fan consists of a shock traveling to the right into the grid at 2,000 km/s. In other words, we initialize the boundary zones (the "post-shock" gas) with the values specified by the jump conditions across a 2,000 km/s shock. The pre-shock values correspond to the fluid variables in the grid. 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 (left), compared to the true values (right).

The shock front in the right panel shows some oscillations, but these are 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:

(note time slider is in units of the crushing time)

n (cm-2)	movie​
T (K)	movie​
P (Ba)	movie​
Mach	movie​
Schleiren	movie​

Run 2 - PPM vs. PPL scheme

This run was just to see if the choice of solver can significantly change the simulation. To check this, here is a line plot of the density vs. position for the PPM method (the previous simulation used PPL):

and a comparison of the final frame:

Run 3 - Pulsed case

Supersonic wind only injected at t=0.

<To be added… >

Run 4 - Mach Comparison (Mach 100 vs. 200 vs. 300)

Run 5 - Mach Comparison (Mach 1.5, 6, 10)

Run 6 - AMR tests

This set of runs is meant to see how to adequately track the shock front with AMR and the clump. As the resolution in the ambient medium goes down with AMR, we wish to provide adequate resolution around the shock front as to not degrade the solution. Am doing a quick test of an AMR simulation of the fiducial initial conditions with the resolution of the ambient medium decreased by a factor of 4, plus two levels of refinement on the clump and refinement triggered by density gradients.

Estimate ~ 3 hours per frame with cooling turned on at same resolution above (on 24 processors).

Run 7 - Prelim 3D run

Unresolved thoughts:

Q - reflected BC differences - due to pressure/density protection, or position of clump wrt to grid?

Q - size scales needing to resolve (i.e. instabilities and their wavelengths)?

Q - examine cooling cases (cooling lengths/timescales, temperature ranges for various cooling tables in astrobear, modifying the abundances statically as well as dynamically, what options for tracking ionizations, etc., radiative shock physics — shock structures in steady state solutions, additional instabilities that arise when cooling is possible)

Reference Papers