Tsunami modelling with adaptively refined finite volume methods

Acta Numerica ◽  
2011 ◽  
Vol 20 ◽  
pp. 211-289 ◽  
Author(s):  
Randall J. LeVeque ◽  
David L. George ◽  
Marsha J. Berger
Keyword(s):  
Finite Volume ◽  
Adaptive Mesh Refinement ◽  
Spatial Scales ◽  
Adaptive Mesh ◽  
Finite Volume Methods ◽  
Small Scale ◽  
Tsunami Propagation ◽  
Small Perturbations ◽  
Tsunami Modelling ◽  
Two Space Dimensions

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.

CFD simulations of tsunamis from large scale propagation up to local coastal impacts

2020 ◽  
Author(s):  
Richard Marcer ◽  
Camille Journeau ◽  
Kévin Pons
Keyword(s):  
Adaptive Mesh Refinement ◽  
Large Scale ◽  
Adaptive Mesh ◽  
Navier Stokes ◽  
Water Volume ◽  
Tsunami Propagation ◽  
Tsunami Modelling ◽  
Tsunami Waves ◽  
In Situ Data ◽  
Run Up

<p>This work has been performed within the framework of the TANDEM project (Tsunamis in northern AtlaNtic: Definition of Effects by Modelling) which is dedicated to the appraisal of coastal effects due to tsunami waves on the French coastlines. One of the identified objectives of TANDEM consisted in designing, adapting and validating numerical codes for tsunami hazard assessment, addressing the various stages of a tsunami event: generation, propagation, run-up and coastal inundation.</p><p>PRINCIPIA has been working on the development and qualification of two in-house CFD software’s: a 2D Saint-Venant model (often called NLSW for Non-Linear Shallow Water) using an Adaptive Mesh Refinement (AMR) for simulation of large scale tsunami propagation from the source up to coastal scale, and a 3D Navier-Stokes model dedicated to tsunami coastal impact modelling.</p><p>An overview of the results obtained with both codes aiming at being applicable to tsunami modelling, is presented. The validation process has been done on several academic test cases having experimental data for comparisons, as the breaking of a solitary wave on a reef, the generation of a long wave induced by a vertical bloc (massive cliffs, ice bodies) falling down an underlying water volume, the tsunami generation due to a submarine landslide and the tsunami impact on a coastal city.</p><p>A real case simulation is concerned as well, the devastating 2011 Tohoku event which is compared with in-situ data.</p><p>The work was supported by the Tandem project in the frame of French PIA grant ANR-11-RSNR-00023.</p>

Logically rectangular finite volume methods with adaptive refinement on the sphere

2009 ◽  
Vol 367 (1907) ◽  
pp. 4483-4496 ◽  
Author(s):  
Marsha J. Berger ◽  
Donna A. Calhoun ◽  
Christiane Helzel ◽  
Randall J. LeVeque
Keyword(s):  
Finite Volume ◽  
Shallow Water Equations ◽  
Adaptive Mesh Refinement ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Finite Volume Methods ◽  
Adaptive Refinement ◽  
Two Dimensional ◽  
Equilibrium Solutions ◽  
Courant Number

The logically rectangular finite volume grids for two-dimensional partial differential equations on a sphere and for three-dimensional problems in a spherical shell introduced recently have nearly uniform cell size, avoiding severe Courant number restrictions. We present recent results with adaptive mesh refinement using the G eo C law software and demonstrate well-balanced methods that exactly maintain equilibrium solutions, such as shallow water equations for an ocean at rest over arbitrary bathymetry.

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