Three material shock tube

The three-material shock-tube problem of two helium gases and one air gas modeled by an ideal-gas EOS is an extension of the two-material shock-tube problem. Reflective boundary conditions are applied at x = 0 and x = 1. The initial condition is listed in Table.

Two shock waves move towards the left and right boundaries while two rarefaction waves approach to each other. Finally, at t = 0.1 these two rarefaction waves impact and interact with each other, as shown in Figures below.

Helium and air properties are set in the props.txt file.

Computations are made with 1e-4 s of time step over a grid with 5e-4 m of element size as designed in the mesh.geo file.

Initial and boundary conditions are set according to Table above in fluid_ic_bc.hpp file.

The compressible non-diagonal tau 2001 and the 2006 discontinuity capturing operator are employed as specified in setup.txt file.

Results well agree with the reference solution.

Reference

Shucheng Pan, Luhui Han, Xiangyu Hu, Nikolaus A. Adams “A conservative interface-interaction method for compressible multi-material flows” (2018) j. Comp. Phy.