On Alternative Setups of the Double Mach Reflection Problem

Abstract

The double Mach reflection (DMR) problem is an important test case for the assessment of the resolution of Euler codes. The initial and boundary conditions specified in the conventional setup of the problem result in the formation of undesirable numerical artefacts which interfere with the solution. In this study, two alternative setups are proposed to prevent the manifestations of such artefacts. The first setup involves modifying the computational domain to simplify the boundary conditions while the second setup involves modifying the initial conditions to make the problem more conducive to run on uniform Cartesian grids and foregoing the problematic boundary conditions altogether. Both setups employ a modified two-step initialization procedure to obtain clean, artefact-free results. These methods are robust and easy to implement. The DMR problem was simulated using a 7th order finite-volume WENO-based solver developed using OpenFOAM to demonstrate that the proposed methods can be used for the assessment of higher order methods. The proposed methods have yielded good results and complete removal of the artefacts is observed in some cases. The simulations were performed with two different numerical flux schemes to determine the dependency of the flux schemes on the performance of the setups. Lastly, the second setup was found to be superior than the first one in terms of effectively removing the numerical artefacts.