Robust well-balanced method with flow resistance terms for accurate wetting and drying modeling in shallow water simulations

Abstract

Hydrodynamic simulations in shallow water environments require careful consideration of the Wetting and Drying (WD) processes, which poses challenges to accurately modeling moving boundaries. This study introduces a novel method called the flow resistance method (FRM), which builds upon the foundation of the Negative-Depth Method (NDM) to tackle the intricacies of the moving boundary problem. Inspired by the Navier-Stokes/Brinkman (NSB) model from porous media theory, FRM incorporates a continuous function related to additional flow resistance that is proportional to the flow velocity. This approach facilitates a seamless transition between the exposed bed and fluid area wherein the additional flow resistance becomes 0 within the fluid area and approaches infinity in the exposed bed. Consequently, FRM adeptly and implicitly manages the moving boundary problem, causing a rapid decay of flow velocity to 0 in the exposed bed. In order to test the performance of FRM, four typical numerical experiments were conducted, along with an examination of a real-life case. Accuracy, robustness, and computational efficiency were assessed as key performance indicators. The simulations demonstrate that FRM adeptly tracks the moving water front, yielding precise results. Furthermore, when compared to established methods such as the Element Removal Method (ERM) and NDM, FRM exhibits broader applicability and achieves significant enhancements in the key performance indicators. These findings underscore the promising potential and broad applications of FRM in the field.