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Numerical Simulation of Conservation Laws with Moving Grid Nodes: Application to Tsunami Wave Modelling

journal contribution
posted on 17.06.2020 by Gayaz Khakimzyanov, Denys Dutykh, Dimitrios Mitsotakis, Nina Yu Shokina
In the present article, we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with an appropriate predictor–corrector method to achieve higher resolutions. The underlying finite volume scheme is conservative, and it is accurate up to the second order in space. The main novelty consists in the motion of the grid. This new dynamic aspect can be used to resolve better the areas with large solution gradients or any other special features. No interpolation procedure is employed; thus, unnecessary solution smearing is avoided, and therefore, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according to the choice of the so-called monitor function. Several more or less universal choices of the monitor function are provided. Finally, the performance of the proposed algorithm is illustrated on several examples stemming from the simple linear advection to the simulation of complex shallow water waves. The exact well-balanced property is proven. We believe that the techniques described in our paper can be beneficially used to model tsunami wave propagation and run-up.

Funding

Dimitrios RSL 2019

Numerical Solution of Time-dependent Multi-dimensional Nonlinear Dispersive Wave Equations with Applications to Coastal Hydrodynamics | Funder: ROYAL SOCIETY OF NEW ZEALAND | Grant ID: 14-VUW-123

History

Preferred citation

Khakimzyanov, G., Dutykh, D., Mitsotakis, D. & Shokina, N.Y. (2019). Numerical Simulation of Conservation Laws with Moving Grid Nodes: Application to Tsunami Wave Modelling. Geosciences, 9(5), 1-33. https://doi.org/10.3390/geosciences9050197

Journal title

Geosciences

Volume

9

Issue

5

Publication date

01/01/2019

Pagination

1-33

Publisher

MDPI AG

Publication status

Published

Contribution type

Article

Online publication date

30/04/2019

ISSN

2163-1719

eISSN

2076-3263

Language

en

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