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The Sod problem (Sod 1978) is an essentially one-dimensional flow discontinuity problem which provides a good test of a compressible code's ability to capture shocks and contact discontinuities with a small number of zones and to produce the correct density profile in a rarefaction. It also tests a code's ability to correctly satisfy the Rankine-Hugoniot shock jump conditions. When implemented at an angle to a multidimensional grid, it can also be used to detect irregularities in planar discontinuities produced by grid geometry or operator splitting effects.

We construct the initial conditions for the Sod problem by establishing a planar interface at some angle to the x and y axes. The fluid is initially at rest on either side of the interface, and the density and pressure jumps are chosen so that all three types of flow discontinuity (shock, contact, and rarefaction) develop. To the ``left'' and ``right'' of the interface we have

rL = 1	rR = 0.125
pL = 1	pR = 0.1

The ratio of specific heats g is chosen to be 1.4 on both sides of the interface.

We have run FLASH 1.0 on this problem using a 2D grid with 6 levels of refinement (corresponding to a finest zone size of 1/256). Shock normals parallel to the x-axis and forming and angle of 45^o with the x-axis were considered.

Plots

Density, temperature, velocity, and AMR level at t=0.2 for q=0o (GIF, Postscript)

Density, temperature, and velocity at t=0.2 for q=0o and q=45o (GIF, Postscript)

Density colormap with AMR block structure at t=0.2 for q=45o (GIF, Postscript)

References
Sod, G. 1978, J. Comp. Phys., 27, 1

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