Implicit Adaptive Mesh Refinement for Dispersive Tsunami Propagation

Fuente: arXiv
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Autori principali: Berger, Marsha J., LeVeque, Randall J.
Natura: Preprint
Pubblicazione: 2023
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author Berger, Marsha J.
LeVeque, Randall J.
author_facet Berger, Marsha J.
LeVeque, Randall J.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2307_05816
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Implicit Adaptive Mesh Refinement for Dispersive Tsunami Propagation
Berger, Marsha J.
LeVeque, Randall J.
Numerical Analysis
Atmospheric and Oceanic Physics
65M50, 65M08, 86A15
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.
title Implicit Adaptive Mesh Refinement for Dispersive Tsunami Propagation
topic Numerical Analysis
Atmospheric and Oceanic Physics
65M50, 65M08, 86A15
url https://arxiv.org/abs/2307.05816