A Few Benchmark Test Cases for Higher-order Euler Solvers

摘要

There have been great efforts on the development of higher-order numericalschemes for compressible Euler equations. The traditional tests mostlytargeting on the strong shock interactions alone may not be adequate to testthe performance of higher-order schemes. This study will introduce a few testcases with a wide range of wave structures for testing higher-order schemes. Asreference solutions, all test cases will be calculated by our recentlydeveloped two-stage fourth-order gas-kinetic scheme (GKS). All examples areselected so that the numerical settings are very simple and any high orderaccurate scheme can be straightly used for these test cases, and compare theirperformance with the GKS solutions. The examples include highly oscillatorysolutions and the large density ratio problem in one dimensional case;hurricane-like solutions, interactions of planar contact discontinuities (thecomposite of entropy wave and vortex sheets) sheets with large Mach numberasymptotic, interaction of planar rarefaction waves with transition fromcontinuous flows to the presence of shocks, and other types of interactions oftwo-dimensional planar waves. The numerical results from the fourth-ordergas-kinetic scheme provide reference solutions only. These benchmark test caseswill help CFD developers to validate and further develop their schemes to ahigher level of accuracy and robustness.