TY - JOUR
T1 - Towards an Accurate and Robust Roe-Type Scheme for All Mach Number Flows
AU - Xie , Wenjia
AU - Zhang , Ye
AU - Chang , Qing
AU - Li , Hua
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 132
EP - 167
PY - 2019
DA - 2019/01
SN - 11
DO - http://doi.org/10.4208/aamm.OA-2018-0141
UR - https://global-sci.org/intro/article_detail/aamm/12925.html
KW - Roe scheme, low Mach number, numerical shock instability.
AB - <p style="text-align: justify;">We propose an accurate and robust Roe-type scheme applied to the compressible Euler system at all Mach numbers. To study the occurrence of unstable modes during the shock wave computation, a shock instability analysis of several Roe-type schemes is carried out. This analysis approach allows proposing a simple and effective modification to eliminate shock instability of the Roe method for hypersonic flows. A desirable feature of this modification is that it does not resort to any additional numerical dissipation on linear degenerate waves to suppress the shock instability. With an all Mach correction strategy, the modified Roe-type scheme is further extended to solve flow problems at all Mach numbers. Numerical results that are obtained for various test cases indicate that the new scheme has a good performance in terms of accuracy and robustness.</p>