A Study of Fifth-Order WENO Reconstruction for Genuinely Two-Dimensional Convection-Pressure Flux Split Riemann Solver
Year: 2024
Author: Shide Tan, Haizhuan Yuan, Lijun Hu
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 6 : pp. 1297–1327
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0299
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 6 : pp. 1297–1327
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Genuinely two-dimensional HLL-CPS solver WENO fifth-order dimension-by-dimension reconstruction.