Fifth-Order A-WENO Schemes Based on the Adaptive Diffusion Central-Upwind Rankine-Hugoniot Fluxes

doi:10.1007/s42967-021-00161-2

Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (1): 295-314.doi: 10.1007/s42967-021-00161-2

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Fifth-Order A-WENO Schemes Based on the Adaptive Diffusion Central-Upwind Rankine-Hugoniot Fluxes

Bao-Shan Wang¹, Wai Sun Don¹, Alexander Kurganov², Yongle Liu^3,4

1 School of Mathematical Sciences, Ocean University of China, Qingdao 266100, Shandong, China;
2 Department of Mathematics, SUSTech International Center for Mathematics and Guangdong Provincial Key Laboratory of Computational Science and Material Design, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China;
3 Department of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China;
4 Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China

Received:2021-01-30 Revised:2021-06-21 Online:2023-03-20 Published:2023-03-08
Contact: Alexander Kurganov,E-mail:alexander@sustech.edu.cn;Bao-Shan Wang,E-mail:wbs@stu.ouc.edu.cn;Wai Sun Don,E-mail:donwaisun@outlook.com;Yongle Liu,E-mail:liuyl2017@mail.sustech.edu.cn E-mail:alexander@sustech.edu.cn;wbs@stu.ouc.edu.cn;donwaisun@outlook.com;liuyl2017@mail.sustech.edu.cn
Supported by:
The work of B. S. Wang and W. S. Don was partially supported by the Ocean University of China through grant 201712011. The work of A. Kurganov was supported in part by NSFC grants 11771201 and 1201101343 and by the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design (No. 2019B030301001).

Abstract

Abstract: We construct new fifth-order alternative WENO (A-WENO) schemes for the Euler equations of gas dynamics. The new scheme is based on a new adaptive diffusion centralupwind Rankine-Hugoniot (CURH) numerical flux. The CURH numerical fluxes have been recently proposed in [Garg et al. J Comput Phys 428, 2021] in the context of secondorder semi-discrete finite-volume methods. The proposed adaptive diffusion CURH flux contains a smaller amount of numerical dissipation compared with the adaptive diffusion central numerical flux, which was also developed with the help of the discrete RankineHugoniot conditions and used in the fifth-order A-WENO scheme recently introduced in [Wang et al. SIAM J Sci Comput 42, 2020]. As in that work, we here use the fifth-order characteristic-wise WENO-Z interpolations to evaluate the fifth-order point values required by the numerical fluxes. The resulting one- and two-dimensional schemes are tested on a number of numerical examples, which clearly demonstrate that the new schemes outperform the existing fifth-order A-WENO schemes without compromising the robustness.

Key words: A-WENO schemes, Central-upwind schemes, Discrete Rankine-Hugoniot conditions, Numerical dissipation switch, Local speeds of propagation, Euler equations of gas dynamics

CLC Number:

Bao-Shan Wang, Wai Sun Don, Alexander Kurganov, Yongle Liu. Fifth-Order A-WENO Schemes Based on the Adaptive Diffusion Central-Upwind Rankine-Hugoniot Fluxes[J]. Communications on Applied Mathematics and Computation, 2023, 5(1): 295-314.

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Fifth-Order A-WENO Schemes Based on the Adaptive Diffusion Central-Upwind Rankine-Hugoniot Fluxes

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