Development of an efficient wetting and drying treatment for shallow‐water modeling using the quadrature‐free Runge‐Kutta discontinuous Galerkin method. (28th July 2020)

• Record Type: Journal Article
• Authors: Li, Longxiang; Zhang, Qinghe
• Is Part Of: International journal for numerical methods in fluids. Volume 93:Number 2(2021)
• Page Start: 314
• Page End: 338
• Publication Date: 2020-07-28
• Subjects: quadrature‐free -- Runge‐Kutta discontinuous Galerkin methods -- solitary wave run‐up -- shallow water equations -- well balanced -- wetting and drying method; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4884
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: To develop a robust, well‐balanced and quadrature‐free Runge‐Kutta discontinuous Galerkin (RKDG) shallow water solver, we introduce an efficient wetting and drying (WD) treatment in this paper. The main feature of this WD treatment is the use of vertex‐based linear reconstructed solutions in transition (partially wet) regions and high‐order solutions in smooth wet areas. To preserve the positivity of water depth, we also propose a modified time step size with the quadrature‐free scheme. The advantages of the WD treatment include robustness and the capability to address arbitrary high‐order RKDG methods in wet regions, thus making the quadrature‐free scheme more accurate and applicable to various flooding and drying problems. Two numerical test cases are used to validate the numerical method, and the results indicate that the WD method is accurate and robust for different flow regimes with dry areas. Abstract : We propose an efficient and robust p ‐adaptive wetting and drying treatment for the well‐balanced RKDG method in the shallow water modeling. The new model is able to preserve the well‐balanced property and ensure the positivity of water depth with arbitrary high‐order basis functions.