Improvements of weighted essentially non-oscillatory schemes for high-resolution compressible flow simulation: A review

The weighted essentially non-oscillatory (WENO) scheme is a high-resolution, non-oscillatory shock-capturing method. It is renowned for its exceptional performance in handling discontinuous solutions in compressible flow simulations. However, as accuracy requirements and problem complexity continue to increase, the WENO scheme has revealed certain limitations, prompting extensive improvement studies by researchers. This paper reviews the improvements of the WENO scheme for numerical simulation of compressible flows, focusing on two aspects: nonlinear weights calculation and spatial reconstruction methods. It highlights the underlying concepts and implementation processes of various improved schemes. Their evolution trends, practical applicability, and limitations are discussed. Finally, suggestions for future work are given.