TY - JOUR
T1 - High-Resolution and High-Precision Weighted Essentially Non-Oscillatory Scheme for Compressible Flow Simulations
AU - Tang , Shujiang
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 980
EP - 1008
PY - 2024
DA - 2024/05
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2022-0321
UR - https://global-sci.org/intro/article_detail/aamm/23119.html
KW - WENO scheme, high resolution, optimal accuracy, mapping function, freely adjustable term.
AB - <p style="text-align: justify;">In this paper, a new high-resolution WENO-MIM scheme that can achieve
optimal accuracy at high-order critical points is developed. The nonlinear weight function of the new scheme can be obtained by adding a freely adjustable term with a parameter $λ$ to the mapping function of the WENO-IM scheme. A sufficient condition
shows the shock-capturing ability of WENO-MIM will be enhanced with the increase
of $λ.$ The parameter $λ=467$ obtained from experience can guarantee the new scheme
achieves high resolution. Numerical example results show that the present scheme can
achieve optimal accuracy at high-order critical points and perform significantly better
than other WENO schemes in highly efficient computing of various compressible fluid
problems.</p>