{"title":"A Study of Fifth-Order WENO Reconstruction for Genuinely Two-Dimensional Convection-Pressure Flux Split Riemann Solver","authors":"Shide Tan, Haizhuan Yuan and Lijun Hu","doi":"10.4208/aamm.oa-2022-0299","DOIUrl":null,"url":null,"abstract":". Although the genuinely two-dimensional HLL-CPS solver holds the inherent multidimensionality property and capability of resolving contact discontinuities, the conventional low-order (second-order and below) reconstruction methods still limits its application in the two-dimensional complex flows involving shock waves and shear layers. A fifth-order reconstruction method is proposed for the genuinely two-dimensional HLL-CPS solver. The conserved variable vectors at the midpoints of interfaces are approximated by the fifth-order 1D WENO reconstruction. Meanwhile, variables at the corners are evaluated by a dimension-by-dimension reconstruction method consisting of a number of 1D fifth-order WENO sweeps. To avoid introducing spurious oscillations, each reconstruction is carried out in the corresponding local characteristic fields. Numerical results of several benchmark tests indicate the higher-order accuracy and the multidimensionality property of the proposed scheme. Compared with the 1D HLLE, HLLC and HLL-CPS schemes, the proposed high-order genuinely two-dimensional HLL-CPS solver provides higher resolution for contact discontinuities and presents better robustness against the shock anomalies.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mathematics and Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.4208/aamm.oa-2022-0299","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
. Although the genuinely two-dimensional HLL-CPS solver holds the inherent multidimensionality property and capability of resolving contact discontinuities, the conventional low-order (second-order and below) reconstruction methods still limits its application in the two-dimensional complex flows involving shock waves and shear layers. A fifth-order reconstruction method is proposed for the genuinely two-dimensional HLL-CPS solver. The conserved variable vectors at the midpoints of interfaces are approximated by the fifth-order 1D WENO reconstruction. Meanwhile, variables at the corners are evaluated by a dimension-by-dimension reconstruction method consisting of a number of 1D fifth-order WENO sweeps. To avoid introducing spurious oscillations, each reconstruction is carried out in the corresponding local characteristic fields. Numerical results of several benchmark tests indicate the higher-order accuracy and the multidimensionality property of the proposed scheme. Compared with the 1D HLLE, HLLC and HLL-CPS schemes, the proposed high-order genuinely two-dimensional HLL-CPS solver provides higher resolution for contact discontinuities and presents better robustness against the shock anomalies.
期刊介绍:
Advances in Applied Mathematics and Mechanics (AAMM) provides a fast communication platform among researchers using mathematics as a tool for solving problems in mechanics and engineering, with particular emphasis in the integration of theory and applications. To cover as wide audiences as possible, abstract or axiomatic mathematics is not encouraged. Innovative numerical analysis, numerical methods, and interdisciplinary applications are particularly welcome.