Volume 11, Issue 1
Towards an Accurate and Robust Roe-Type Scheme for All Mach Number Flows

Wenjia Xie, Ye Zhang, Qing Chang & Hua Li

Adv. Appl. Math. Mech., 11 (2019), pp. 132-167.

Published online: 2019-01

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  • Abstract

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 to propose 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.

  • Keywords

Roe scheme low Mach number numerical shock instability.

  • AMS Subject Headings

35L65 65M08 76M12 76L05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-11-132, author = {Wenjia Xie, Ye Zhang, Qing Chang and Hua Li}, title = {Towards an Accurate and Robust Roe-Type Scheme for All Mach Number Flows}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {1}, pages = {132--167}, abstract = {

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 to propose 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0141}, url = {http://global-sci.org/intro/article_detail/aamm/12925.html} }
TY - JOUR T1 - Towards an Accurate and Robust Roe-Type Scheme for All Mach Number Flows AU - Wenjia Xie, Ye Zhang, Qing Chang & Hua Li JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 132 EP - 167 PY - 2019 DA - 2019/01 SN - 11 DO - http://dor.org/10.4208/aamm.OA-2018-0141 UR - https://global-sci.org/intro/aamm/12925.html KW - Roe scheme KW - low Mach number KW - numerical shock instability. AB -

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 to propose 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.

Wenjia Xie, Ye Zhang, Qing Chang & Hua Li. (1970). Towards an Accurate and Robust Roe-Type Scheme for All Mach Number Flows. Advances in Applied Mathematics and Mechanics. 11 (1). 132-167. doi:10.4208/aamm.OA-2018-0141
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