# Spherical cloud tests

## October 19, 2015

Since we have a version of dual energy that doesn’t seem to produce wildly incorrect results, I am returning to the cloud/wind tests to see if it improves the results.

Background

These tests use the intial conditions from the Cooper et al. 2009 paper. A high density ($n_{cl} = 91$ $\mathrm{cm}^{-3}$) sphere is placed in pressure equilbrium with a low density hot wind ($n_{wind} = 0.1$ $\mathrm{cm}^{-3}$, $T_{wind} = 5 \times 10^6$ $\mathrm{K}$). The mach number of the wind is approximately 4.6 ($v_{wind} = 1200$ $\mathrm{km/s}$). The cloud is initially at rest, and its evolutuion progreses through the stages characteristic of a cloud/shock interaction: a forward shock is driven into the cloud, while another shock reflects back into the hot wind; the cloud flattens and compresses in the direction perpendicular to the flow; the forward shock initially transmitted into the cloud reaches the back and the cloud begins to expand downstream of its inital position; the cloud fragments and is destroyed by hydrodynamical instabilities.

The problem

This test has proven difficult to run with Cholla, probably for a multitude of reasons. Problems that I have looked into include:

1) The CTU and Van Leer integrators fail as a result of the transverse flux update step. I am unable to run this test in the adiabatic regime with either the CTU or VL integrator, regardless of the reconstruction technique or Riemann solver. However, I can run the test if I leave out the transverse flux update step in CTU (i.e. just do normal PPM). I don’t currently have a fix for this.

2) Dual energy may be needed for cooling. If I run this test with cooling, the code produces negative pressures relatively quickly even without the transverse flux update. Eventually the code crashes, but I’m not clear on whether the crash is caused by negative densities after the final update, or a failure of the Riemann solver in the lowest density regions. With the current implementation of dual energy the situation is improved somewhat, in the sense that the internal energy gets corrected to a positive number. However, the code still crashes, at around the same time it crashed without dual energy.

3) Failure of the exact solver? With dual energy, the crash occurs not as a result of negative densities or pressures after the final update, but because of a failure in the exact Riemann solver in a region of very low density behind the cloud. I have not spent much time on this yet, but it may be the primary problem.

Current Results

A movie of the sphere/wind test without cooling, with PPMP, the exact solver, and a simple integrator can be found at brown.as.arizona.edu/~evan/temp/sphere_wind_nocool.mov

A movie of the sphere/wind test as above but with cooling and dual energy (B14 switch) can be found at brown.as.arizona.edu/~evan/temp/sphere_wind_wcool.mov