Numerical Simulation of Conservation Laws with Moving Grid Nodes: Application to Tsunami Wave Modelling
| Autor: | Gayaz Khakimzyanov, Nina Shokina, Denys Dutykh, Dimitrios Mitsotakis |
|---|---|
| Přispěvatelé: | Institute of Computational Technologies, Russian Academy of Sciences [Moscow] (RAS), Laboratoire de Mathématiques (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Victoria University of Wellington, University of Freiburg [Freiburg] |
| Rok vydání: | 2020 |
| Předmět: |
Computer science
advection FOS: Physical sciences Physics - Classical Physics 01 natural sciences moving grids 010305 fluids & plasmas adaptivity Dimension (vector space) Simple (abstract algebra) wave run-up 0103 physical sciences FOS: Mathematics conservative finite differences [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] Mathematics - Numerical Analysis 0101 mathematics finite volumes Conservation law Finite volume method shallow water equations Computer simulation Advection lcsh:QE1-996.5 74S10 (primary) 74J15 74J30 (secondary) Classical Physics (physics.class-ph) Numerical Analysis (math.NA) Computational Physics (physics.comp-ph) Grid [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation 010101 applied mathematics lcsh:Geology Waves and shallow water General Earth and Planetary Sciences conservation laws Algorithm Physics - Computational Physics [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Interpolation |
| Zdroj: | Geosciences, Vol 9, Iss 5, p 197 (2019) Geosciences Geosciences, MDPI, 2019, 9 (5), pp.197. ⟨10.3390/geosciences9050197⟩ Volume 9 Issue 5 |
| ISSN: | 2076-3263 |
| DOI: | 10.26686/wgtn.12501854 |
| Popis: | 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&ndash 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. |
| Databáze: | OpenAIRE |
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