2D circular explosion test
The 2D explosion test of L&W centres around the production of an unstable contact layer, which is crossed by a reflected shock wave. Performing this essentially circular explosion with Cartesian coordinates means that the reflection at the origin of the spherical shock is also reasonably challenging.
The less dissipative highresolution shock capturing upwind methods, such as PPM, VH1, and Fyris, tend to produce the greatest amound of interface breakup, and the source of the grid noise that seeds the interface breakup appears to lie in the initial boundary definition of the high pressure circular region at t = 0.0. In disspative schemes, the initial 'pixelisation' of the circle on the square grid is lost, wheras in the high resolution nondissipative methods the signature of this pattern survives to late times and the interface breaks up more.
Here a second test with the inital circular boundary is smoothed more heavily with a gaussian kernel with a FWHM of 2.0 cells is compared, and the late time interface breakup is less. The standard test is run with a smothing of FWHM 1.0 cells.
Assymmetry in the late time interface breakup is due to the standard asymmetric split sweep operator used by Fyris (like VH1, PPM). When a symmetric split sweep operator is used, as the expense of extra memory, then the initial grid symmetry is preserved and the late time interface remains symmetric, like the WENO and CLAW codes. (See 2D implosion results for description of symmetric sweeps)
Initial conditions
Inside region: r < 0.4
 Density = 1.000
 Pressure = 1.000
 Velocity = 0.000
Outside region
 Density = 0.125
 Pressure = 0.1
 Radial velocity = 0.000
Ending condition
 Time, t = 3.2
Grid
 Domain: 0.0 < x <1.5, 0.0 < y < 1.5
 400 x 400 cells
Hydrodynamics settings
 Adiabatic index: Gamma = 1.4
 >CFL number: 0.8, initial step 0.4 (standard)
 Flattening: minimum 0.0, maximum 1.0 (standard)
The code and configuration files for Fyris to run the 2D explosion problem will be available soon.
Results
Smoothed FWHM = 1.0
min = 0.0 max = Auto Scale


Density, t = 0.0

Density, t = 0.2

Density, t = 0.8

Density, t = 1.6

Density, t = 2.4

Density, t = 3.2

Smoothed boundary FWHM = 2.0
min = 0.0 max = Auto Scale


Density, t = 0.0

Density, t = 0.2

Density, t = 0.8

Density, t = 1.6

Density, t = 2.4

Density, t = 3.2

Symmetric sweeps, smoothed FWHM = 1.0
min = 0.0 max = Auto Scale


Density, t = 0.0

Density, t = 0.2

Density, t = 0.8

Density, t = 1.6

Density, t = 2.4

Density, t = 3.2
