Tsunami modelling with adaptively refined finite volume methods
Acta Numerica
By: R.J. LeVeque, D.L. George, and M.J. Berger
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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. ?? 2011 Cambridge University Press.
Suggested Citation
LeVeque, R., George, D., and Berger, M., 2011, Tsunami modelling with adaptively refined finite volume methods: Acta Numerica, v. 20, p. 211-289, https://doi.org/10.1017/S0962492911000043.
| Publication type | Article |
|---|---|
| Publication Subtype | Journal Article |
| Title | Tsunami modelling with adaptively refined finite volume methods |
| Series title | Acta Numerica |
| DOI | 10.1017/S0962492911000043 |
| Volume | 20 |
| Publication Date | April 28, 2011 |
| Year Published | 2011 |
| Language | English |
| Larger Work Type | Article |
| Larger Work Subtype | Journal Article |
| Larger Work Title | Acta Numerica |
| First page | 211 |
| Last page | 289 |