A Study of Fifth-Order WENO Reconstruction for Genuinely Two-Dimensional Convection-Pressure Flux Split Riemann Solver (Advances in Applied Mathematics and Mechanics, 2024)
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 andshear 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 reconstructionmethod consisting of a number of 1D fifth-order WENO sweeps. To avoid introducingspurious oscillations, each reconstruction is carried out in the corresponding local characteristic fields. Numerical results of several benchmark tests indicate the higher-orderaccuracy and the multidimensionality property of the proposed scheme. Comparedwith the 1D HLLE, HLLC and HLL-CPS schemes, the proposed high-order genuinelytwo-dimensional HLL-CPS solver provides higher resolution for contact discontinuities and presents better robustness against the shock anomalies.