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

Wang，Bao Shan1; Don，Wai Sun1; Kurganov，Alexander2; Liu，Yongle3,4

2023-03-01

10.1007/s42967-021-00161-2

Communications on Applied Mathematics and Computation   Impact Factor & Quartile

2096-6385

2661-8893

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 central-upwind 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 second-order 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 Rankine-Hugoniot 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.

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

ESCI

English

Corresponding

WOS:000713527800001

2-s2.0-85132435631

Scopus

1.School of Mathematical Sciences,Ocean University of China,Qingdao,Shandong,266100,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,Guangdong,518055,China
3.Department of Mathematics,Harbin Institute of Technology,Harbin,Heilongjiang,150001,China
4.Department of Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China

Wang，Bao Shan,Don，Wai Sun,Kurganov，Alexander,et al. 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.

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

Wang，Bao Shan,et al."Fifth-Order A-WENO Schemes Based on the Adaptive Diffusion Central-Upwind Rankine-Hugoniot Fluxes".Communications on Applied Mathematics and Computation 5.1(2023):295-314.