Spherical adaptive mesh simulations

Initial results of following 15 solar mass star post bounce evolution in 2-d spherical coordinates.

QuickTime Movies
[density w/ and w/o blocks]

When running with a spherical grid (r, theta), where the grid spacings are uniform, the computational zones do not have a constant aspect ratio. Rather, the zones are very elongated in the radial direction near the origin, and very flat (in r) at the outer edge of the domain. This is illustrated in the figure below, when the minimum radius is 1.e8, and the maxium radius is 1.e12.

Using an adaptive mesh does not help things, since the refinement cuts a block in half in each spatial dimension, preserving the aspect ratio. So while adapting makes the zones have a higher resolution, they still suffer from the same aspect ratio problems.

We can instead use a logarithmic spacing in the radial zones. In this case, each zone will be some constant factor wider in the radial direction than the one below it. The same grid as above, but using a logarithmic spacing in the radial direction is shown below.

We've modifed FLASH to use such a spacing on a 2-d adaptive spherical mesh for the SN II mixing problem.

Cartesian simulations

15 solar mass star undergoing a Type II supernova explosion, post bounce. We are interested in studying the mixing at the hydrogen interface as the shock wave moves outward. These images are ~ 6.8 hours after the start of the explosion. A Rayleigh-Taylor instability sets up at the hydrogen interface, just behind the shock wave. The blue boxes in the second image show our AMR block structure. Each block contains 256 computational zones. The effective resolution of these calculations varies as the shock moves outwards from the origin, but starts at 3.81e8 cm. The flow on axis is an artifact of the axisymmetric geometry, and does not interfere with the mixing, which is the focus of these calculations. These simulations are in 2-d axisymmetric geometry, and are being used to tune our refinement strategy for upcoming 3-d calculations.

For this work, FLASH was modified to better simulation cylindrical geometries, with the addition of new, third-order accurate prolongation routines and better flux conservation averaging routines. Furthermore, speedups of > 400x to the multipole poisson solver were made, so the gravity solve is now a small fraction of the runtime.

QuickTime Movies
[density] [density w/ AMR blocks]

Presentation from Supernova Science Center meeting
[OpenOffice.org formant] [postscript]

A large fraction of the computational domain, showing the shock at about 1.35e13 cm, and the Rayleigh-Taylor instability behind it.

A close up view of the entire RT region at the same time.

A zoom in of some of the mixing.

The same zoom in with the AMR blocks shown. Each block is 256 computational zones.

Support for this work was provided by the Scientific Discovery through Advanced Computing (SciDAC) program of the DOE, grant number DE-FC02-01ER41176