Comparison between Two HLL-type Riemann Solvers for Strong Shock Calculation on ALE Framework

This paper investigates solution behaviors under the strong shock interaction for moving mesh schemes based on the one-dimensional HLL-type Riemann solvers. Numerical experiments show that some schemes which updates the flow parameters directly on the moving mesh without using interpolation, may suffer from severe instability such as grid distortion. But the HLL solver can be free from such failings. It is well known that the numerical schemes on a fixed grid that can capture contact discontinuity accurately usually suffer from some disastrous carbuncle phenomenon, while others, such as the HLL scheme, are free from this kind of shock instability. Due to such high similarity, a research to combine the grid deformation and the numerical shock instability is developed. Furthermore, in order to unveil the cause of producing these failings, a HLL-type solver (denoted as the HLLS) with shear wave is constructed for inviscid, compressible gas flows and implemented into the arbitrary Lagrangian Eulerian (ALE) method. With the vorticity viscosity vanishing, the ALE HLLS scheme produce some numerical instability phenomena. This result indicates that viscosity associated to the shear wave may be unique reason to cause the instability or nonphysical deformation.