A quadtree-adaptive multigrid solver for the Serre-Green-Naghdi equations
Abstract
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.
- Publication:
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Journal of Computational Physics
- Pub Date:
- December 2015
- DOI:
- 10.1016/j.jcp.2015.09.009
- Bibcode:
- 2015JCoPh.302..336P
- Keywords:
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- Dispersive wave model;
- Quadtree;
- Adaptive mesh refinement;
- Tsunami;
- Well-balanced;
- Multigrid elliptic solver