Tsunami modelling with adaptively refined finite volume methods

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.

A depth-averaged debris-flow model that includes the effects of evolving dilatancy. II. Numerical predictions and experimental tests

“…D-Claw is an extension of the CLAWPACK software package [34], an open-source project for solving general hyperbolic problems (e.g. [17,[35][36][37]). …”

“…[52,53]), and later specialized for depth-averaged flows across topography, such as tsunamis and overland floods (e.g. [35][36][37]). With patch-based, blockstructured AMR, the domain is discretized on numerous rectangular grids, each associated with a given level, l = 1, .…”

Multi-level Monte Carlo Finite Volume Methods for Uncertainty Quantification in Nonlinear Systems of Balance Laws

“…eg. [26]). Similarly, the bottom topography is measured with sonar equipment and this data collection is prone to uncertainty.…”

Computationally Efficient Tsunami Modelling on Graphics Processing Units (GPU)

“…TUNAMI by Goto et al (1997), MOST by Titov and Synolakis (1995) and COMCOT by Wang and Liu (2006). In recent years, finite volume Godunov-type schemes have also been implemented to solve the SWEs for tsunami modeling and have gradually gained popularity (Popinet, 2011;Leveque et al, 2011). These models boast of their automatic shock-capturing capability, superior conservation property and flexibility for implementation on different types of computational grids for better boundary fitting.…”