Tsunami modelling with adaptively refined finite volume methods

Randall J. Leveque, David L. George, Marsha Berger

Research output: Contribution to journalArticle

Abstract

Numerical modelling of transoceanic tsunami propagation, together with the detailed modelling of inundation of small-scale coastal regions, poses a number of algorithmic challenges. The depth-averaged shallow water equations can be used to reduce this to a time-dependent problem in two space dimensions, but even so it is crucial to use adaptive mesh refinement in order to efficiently handle the vast differences in spatial scales. This must be done in a 'wellbalanced' manner that accurately captures very small perturbations to the steady state of the ocean at rest. Inundation can be modelled by allowing cells to dynamically change from dry to wet, but this must also be done carefully near refinement boundaries. We discuss these issues in the context of Riemann-solver-based finite volume methods for tsunami modelling. Several examples are presented using the GeoClaw software, and sample codes are available to accompany the paper. The techniques discussed also apply to a variety of other geophysical flows.

Original languageEnglish (US)
Pages (from-to)211-289
Number of pages79
JournalActa Numerica
Volume20
DOIs
StatePublished - Apr 2011

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Tsunami
Tsunamis
Finite volume method
Finite Volume Method
Geophysical Flows
Riemann Solver
Adaptive Mesh Refinement
Shallow Water Equations
Numerical Modeling
Small Perturbations
Modeling
Ocean
Refinement
Propagation
Software
Cell
Water
Context

ASJC Scopus subject areas

  • Mathematics(all)
  • Numerical Analysis

Cite this

Tsunami modelling with adaptively refined finite volume methods. / Leveque, Randall J.; George, David L.; Berger, Marsha.

In: Acta Numerica, Vol. 20, 04.2011, p. 211-289.

Research output: Contribution to journalArticle

Leveque, Randall J. ; George, David L. ; Berger, Marsha. / Tsunami modelling with adaptively refined finite volume methods. In: Acta Numerica. 2011 ; Vol. 20. pp. 211-289.
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