Implicit Adaptive Mesh Refinement for Dispersive Tsunami Propagation

TL;DR

This paper introduces an implicit adaptive mesh refinement algorithm for dispersive tsunami modeling using the Serre-Green-Naghdi equations, enhancing accuracy for short wavelength phenomena within the open source GeoClaw software.

Contribution

It develops a novel implicit adaptive mesh refinement method for dispersive shallow water equations, integrated into GeoClaw, improving simulation accuracy for short wavelength tsunamis.

Findings

The method is stable and accurate in test cases.

It effectively models short wavelength tsunami phenomena.

Adaptive refinement improves computational efficiency.

Abstract

We present an algorithm to solve the dispersive depth-averaged Serre-Green-Naghdi (SGN) 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.