TY - JOUR
T1 - A Study of Fifth-Order WENO Reconstruction for Genuinely Two-Dimensional Convection-Pressure Flux Split Riemann Solver
AU - Tan , Shide
AU - Yuan , Haizhuan
AU - Hu , Lijun
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1297
EP - 1327
PY - 2024
DA - 2024/10
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2022-0299
UR - https://global-sci.org/intro/article_detail/aamm/23469.html
KW - Genuinely two-dimensional HLL-CPS solver, WENO, fifth-order, dimension-by-dimension reconstruction.
AB - <p style="text-align: justify;">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.</p>