Sod shock tube

The Sod shock tube is a 1D Riemann problem commonly used to test numerical methods for solving hyperbolic conservation laws, particularly the Euler equations in gas dynamics. It was introduced by Gary A. Sod in 1978 as a benchmark problem for capturing shock waves, rarefaction waves, and contact discontinuities.

This is the basic test case that all compressible solvers has to reproduce.

The Sod shock tube consists of a 1D domain where a diaphragm initially separates two regions of gas with different pressure and density. At time t = 0, the diaphragm is removed, and the gas evolves according to the compressible Euler equations.

The benchmark is reproduced with a time step of 1e-4 s, and a mesh resolution of 0.02 for a tube of air with total length of 1 m.

The stabilization parameters are the tau 2001 and the 1998 discontinuity capturing.

Details can be found in the setup.txt, props.txt, fluid_ic_bc.hpp, and mesh.geo files.

Results

Results obtained with Gales are in good agreement with the exact and reference solution.

Reference

Park & Munz “Multiple pressure variables methods for
fluid fl
ow at all Mach numbers” (2005) Int. J. Numer. Meth. Fluids