Two-phase shock-tube problems and numerical methods of solution

The study involves the flow of compressible gas in a porous bed: We are interested in exploring the solution to a shock-tube problem that also includes a discontinuous jump in the porosity of the bed. The averaging process that is used to derive the governing system of equations introduces terms that prevent the equations taking a standard conservation form. The purpose of this work is to explore how the porosity jump effects the solution to the Riemann problem and to assess whether standard conservative and nonconservative numerical methods can provide the correct solution to the Riemann problem. The study illustrates serious shortfalls in the numerical solution to these problems using standard techniques. By exploring the exact solution, the author suggests how the standard numerical methods can be modified to provide the correct solution to these systems.