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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 challening.

The less dissipative high resolution shock capturing upwind methods, such as PPM, VH1, 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 non-dissipative 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.

• Left and Bottom boundaries are reflecting, Top and Right boundaries are free.

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

Density, t = 0.0	Density, t = 0.2
Density, t = 0.8	Density, t = 1.6
Density, t = 2.4	Density, t = 3.2
min = 0.0 max = Auto Scale

Smoothed Boundary FWHM = 2.0

Density, t = 0.0	Density, t = 0.2
Density, t = 0.8	Density, t = 1.6
Density, t = 2.4	Density, t = 3.2
min = 0.0 max = Auto Scale

Symmetric Sweeps, Smoothed FWHM = 1.0

Density, t = 0.0	Density, t = 0.2
Density, t = 0.8	Density, t = 1.6
Density, t = 2.4	Density, t = 3.2
min = 0.0 max = Auto Scale