Numerical simulation of conservation laws with moving grid nodes

Abstract : In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension. 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.
Type de document :
Pré-publication, Document de travail
37 pages, 7 figures, 5 tables, 63 references. Other author's papers can be downloaded at http://w.. 2017
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https://hal.archives-ouvertes.fr/hal-01223510
Contributeur : Denys Dutykh <>
Soumis le : vendredi 3 février 2017 - 08:50:51
Dernière modification le : dimanche 5 février 2017 - 01:02:10

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Distributed under a Creative Commons Paternité - Pas d'utilisation commerciale - Pas de modification 4.0 International License

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  • HAL Id : hal-01223510, version 4
  • ARXIV : 1511.02771

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Gayaz Khakimzyanov, Denys Dutykh, Dimitrios Mitsotakis, Nina Shokina. Numerical simulation of conservation laws with moving grid nodes. 37 pages, 7 figures, 5 tables, 63 references. Other author's papers can be downloaded at http://w.. 2017. <hal-01223510v4>

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