Dry and wet boundary treatment and improvement of a TVD-MacCormack scheme in shallow water flow

DOI10.1002/FLD.5174MaRDI QIDQ6537460

Zuyin Zou, Haiguang Cheng, Zhanyuan Zhu, Pengshuai Chen, Xiao-Qing Chen, Xiangang Jiang, Huayong Chen

Publication date: 14 May 2024

Published in: International Journal for Numerical Methods in Fluids (Search for Journal in Brave)

zbMATH Keywords

finite difference schemeshallow water equationdry-wet boundaryTVD-MacCormack

Mathematics Subject Classification ID

Fluid mechanics (76-XX) Numerical analysis (65-XX)

Cites Work

• Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography
• A wetting and drying treatment for the Runge-Kutta discontinuous Galerkin solution to the shallow water equations
• Self-adjusting grid methods for one-dimensional hyperbolic conservation laws
• Mathematical balancing of flux gradient and source terms prior to using Roe's approximate Riemann solver.
• Simulation of rapidly varying flow using an efficient TVD–MacCormack scheme
• Riemann problems and the WAF method for solving the two-dimensional shallow water equations
• The improved surface gradient method for flows simulation in variable bed topography channel using TVD-MacCormack scheme
• An efficient and flexible solver for the simulation of the morphodynamics of fast evolving flows on coarse sediment beaches
• The surface gradient method for the treatment of source terms in the shallow-water equations

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