Acta Numerica

Research Article

Tsunami modelling with adaptively refined finite volume methods*

Randall J. LeVequea1, David L. Georgea2 and Marsha J. Bergera3

a1 Department of Applied Mathematics, University of Washington, Seattle, WA 98195-2420, USA E-mail:

a2 US Geological Survey, Cascades Volcano Observatory, Vancouver, WA 98683, USA E-mail:

a3 Courant Institute of Mathematical Sciences, New York University, NY 10012, USA E-mail:


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.

(Online publication April 28 2011)


* Colour online for monochrome figures available at