A Consistent and Well‐Balanced Hybrid Weighted Essentially Non‐Oscillatory Scheme for Shallow Water Equations on Unstructured Meshes

Abstract

ABSTRACTIn this article, a type of high‐order consistent and well‐balanced hybrid weighted essentially non‐oscillatory (WENO) scheme is proposed for shallow water equations with flat or non‐flat bottom on unstructured triangular meshes. The hybrid scheme presents a new consistent discretization format on the flux and the source term with the goal of obtaining a hybridization of the high‐order WENO scheme and linear scheme. According to the modified multi‐resolution analysis approach, we can select the more robust and accurate WENO reconstruction in the vicinity of discontinuities, and the less expensive linear reconstruction in the smooth regions. As a result, the suggested hybrid WENO scheme can acquire the capacity of saving the computing time cost while maintaining the excellent numerical features of the original WENO scheme. Eventually, some extensive and classical two‐dimensional numerical examples, including a tidal bore of an estuary with an irregular computation area are provided to validate the performance of this hybrid WENO scheme on triangular meshes in terms of accuracy order, exact conservation property, shock‐capturing, good resolution, and computational efficiency.