Preprint Article Version 1 This version is not peer-reviewed

Numerical Simulation of Conservation Laws with Moving Grid Nodes

Version 1 : Received: 25 March 2019 / Approved: 26 March 2019 / Online: 26 March 2019 (10:54:05 CET)

A peer-reviewed article of this Preprint also exists.

Khakimzyanov, G.; Dutykh, D.; Mitsotakis, D.; Shokina, N.Y. Numerical Simulation of Conservation Laws with Moving Grid Nodes: Application to Tsunami Wave Modelling. Geosciences 2019, 9, 197. Khakimzyanov, G.; Dutykh, D.; Mitsotakis, D.; Shokina, N.Y. Numerical Simulation of Conservation Laws with Moving Grid Nodes: Application to Tsunami Wave Modelling. Geosciences 2019, 9, 197.

Journal reference: Geosciences 2019, 9, 197
DOI: 10.3390/geosciences9050197

Abstract

In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension for the sake of simplicity. 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 high solution gradients or any other special features. No interpolation procedure is employed, thus an unnecessary solution smearing is avoided. Thus, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according 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. We believe that the techniques described in our paper can be beneficially used to model tsunami wave propagation and run-up.

Subject Areas

Conservation laws; finite volumes; conservative finite differences; moving grids; adaptivity; advection; shallow water equations; wave run-up

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