Implicit Adaptive Mesh Refinement for Dispersive Tsunami Propagation

SIAM Journal on Scientific Computing, Volume 46, Issue 4, Page B554-B578, August 2024.
Abstract. We present an algorithm to solve the dispersive depth-averaged Serre–Green–Naghdi equations using patch-based adaptive mesh refinement. These equations require adding additional higher derivative terms to the nonlinear shallow water equations. This has been implemented as a new component of the open source GeoClaw software that is widely used for modeling tsunamis, storm surge, and related hazards, improving its accuracy on shorter wavelength phenomena. We use a formulation that requires solving an elliptic system of equations at each time step, making the method implicit. The adaptive algorithm allows different time steps on different refinement levels and solves the implicit equations level by level. Computational examples are presented to illustrate the stability and accuracy on a radially symmetric test case and two realistic tsunami modeling problems, including a hypothetical asteroid impact creating a short wavelength tsunami for which dispersive terms are necessary. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/rjleveque/ImplicitAMR-paper and in the supplementary materials (ImplicitAMR-paper.zip [174KB]).