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

作　　者：Bao-Shan Wang Wai Sun Don Alexander Kurganov Yongle Liu 

机构地区：[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

出　　处：《Communications on Applied Mathematics and Computation》2023年第1期295-314,共20页应用数学与计算数学学报（英文）

基　　金：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;by the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design(No.2019B030301001).

摘　　要：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.

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

分 类 号：O24[理学—计算数学]