Two material Sod shock

We consider the two-material variant of the one-dimensional Sod shock tube problem. As usual, the computational domain is [0, 1] with an interface initially located at x = 0.5. The initial conditions for left material are (rho_l, p_l, u_l, gamma_l) = (1, 2, 0, 2) and (rho_r, p_r, u_r, gamma_r) = (0.125, 0.1, 0, 1.4) for the right material. We point out that this test case is a genuine two-material problems since the polytropic index is different for the left and the right material. The total simulated time is 0.2 s.

The simulation is performed with a unifrorm grid of 0.005 m element size, a time step of 1e-3 s, the compressible non-diagonal tau of 2019, and the 2006 discontinuity capturing operator. Mesh file is mesh.geo, and setup of the simulation can be found in setup.txt file.

The two materials are air and a custom fluid with gamma = 2, and molar mass = 0.035, as specified in the props.txt file.

The initial and boundary conditions are assigned in the fluid_ic_bc.hpp file.

The comparison of the Gales simulation with the reference solution is reported in the following Figures.

Reference

Stéphane Galera, Pierre-Henri Maire, Jérôme Breil “A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction” (2010) J. Comp. Phys.