Volume 8, Issue 4
Osher Flux with Entropy Fix for Two-Dimensional Euler Equations

Huajun Zhu, Xiaogang Deng, Meiliang Mao, Huayong Liu & Guohua Tu

Adv. Appl. Math. Mech., 8 (2016), pp. 670-692.

Published online: 2018-05

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  • Abstract

We compare in this paper the properties of Osher flux with O-variant and P-variant (Osher-O flux and Osher-P flux) in finite volume methods for the twodimensional Euler equations and propose an entropy fix technique to improve their robustness. We consider both first-order and second-order reconstructions. For inviscid hypersonic flow past a circular cylinder, we observe different problems for different schemes: A first-order Osher-O scheme on quadrangular grids yields a carbuncle shock, while a first-order Osher-P scheme results in a dislocation shock for high Mach number cases. In addition, a second-order Osher scheme can also yield a carbuncle shock or be unstable. To improve the robustness of these schemes we propose an entropy fix technique, and then present numerical results to show the effectiveness of the proposed method. In addition, the influence of grid aspects ratio, relative shock position to the grid and Mach number on shock stability are tested. Viscous heating problem and double Mach reflection problem are simulated to test the influence of the entropy fix on contact resolution and boundary layer resolution.

  • Keywords

Osher flux, entropy fix, Euler equation, finite volume method, ”carbuncle” shock.

  • AMS Subject Headings

65M06, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-670, author = {}, title = {Osher Flux with Entropy Fix for Two-Dimensional Euler Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {4}, pages = {670--692}, abstract = {

We compare in this paper the properties of Osher flux with O-variant and P-variant (Osher-O flux and Osher-P flux) in finite volume methods for the twodimensional Euler equations and propose an entropy fix technique to improve their robustness. We consider both first-order and second-order reconstructions. For inviscid hypersonic flow past a circular cylinder, we observe different problems for different schemes: A first-order Osher-O scheme on quadrangular grids yields a carbuncle shock, while a first-order Osher-P scheme results in a dislocation shock for high Mach number cases. In addition, a second-order Osher scheme can also yield a carbuncle shock or be unstable. To improve the robustness of these schemes we propose an entropy fix technique, and then present numerical results to show the effectiveness of the proposed method. In addition, the influence of grid aspects ratio, relative shock position to the grid and Mach number on shock stability are tested. Viscous heating problem and double Mach reflection problem are simulated to test the influence of the entropy fix on contact resolution and boundary layer resolution.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m469}, url = {http://global-sci.org/intro/article_detail/aamm/12109.html} }
TY - JOUR T1 - Osher Flux with Entropy Fix for Two-Dimensional Euler Equations JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 670 EP - 692 PY - 2018 DA - 2018/05 SN - 8 DO - http://dor.org/10.4208/aamm.2014.m469 UR - https://global-sci.org/intro/aamm/12109.html KW - Osher flux, entropy fix, Euler equation, finite volume method, ”carbuncle” shock. AB -

We compare in this paper the properties of Osher flux with O-variant and P-variant (Osher-O flux and Osher-P flux) in finite volume methods for the twodimensional Euler equations and propose an entropy fix technique to improve their robustness. We consider both first-order and second-order reconstructions. For inviscid hypersonic flow past a circular cylinder, we observe different problems for different schemes: A first-order Osher-O scheme on quadrangular grids yields a carbuncle shock, while a first-order Osher-P scheme results in a dislocation shock for high Mach number cases. In addition, a second-order Osher scheme can also yield a carbuncle shock or be unstable. To improve the robustness of these schemes we propose an entropy fix technique, and then present numerical results to show the effectiveness of the proposed method. In addition, the influence of grid aspects ratio, relative shock position to the grid and Mach number on shock stability are tested. Viscous heating problem and double Mach reflection problem are simulated to test the influence of the entropy fix on contact resolution and boundary layer resolution.

Huajun Zhu, Xiaogang Deng, Meiliang Mao, Huayong Liu & Guohua Tu. (2020). Osher Flux with Entropy Fix for Two-Dimensional Euler Equations. Advances in Applied Mathematics and Mechanics. 8 (4). 670-692. doi:10.4208/aamm.2014.m469
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