A quadtree-adaptive multigrid solver for the Serre-Green-Naghdi equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:302

Article

Popinet, Stephane^1,2 

[1] Univ Paris 06, Sorbonne Univ, UMR 7190, Paris, France

[2] Inst Jean Rond Alembert, CNRS, UMR 7190, Paris, France

关键词: Dispersive wave model;    Quadtree;    Adaptive mesh refinement;    Tsunami;    Well-balanced;    Multigrid elliptic solver;   

DOI  :  10.1016/j.jcp.2015.09.009

来源: Elsevier

【 摘 要 】

The Serre-Green-Naghdi (SGN) equations, also known as the fully-nonlinear Boussinesq wave equations, accurately describe the behaviour of dispersive shoaling water waves. This article presents and validates a novel combination of methods for the numerical approximation of solutions to the SGN equations. The approach preserves the robustness of the original finite-volume Saint-Venant solver, in particular for the treatment of wetting/drying and equilibrium states. The linear system of coupled vector equations governing the dispersive SGN momentum sources is solved simply and efficiently using a generic multigrid solver. This approach generalises automatically to adaptive quadtree meshes. Adaptive mesh refinement is shown to provide orders-of-magnitude gains in speed and memory when applied to the dispersive propagation of waves during the Tohoku tsunami. The source code, test cases and examples are freely available. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free