Numerical Assessment of Criteria for Mesh Adaptation in the Finite Volume Solution of Shallow Water Equations

Numerical Assessment of Criteria for Mesh Adaptation in the Finite Volume Solution of Shallow Water Equations

Year:    2020

Author:    Imad Kissami, Mohammed Seaid, Fayssal Benkhaldoun

Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 503–526

Abstract

We present a numerical assessment of a class of criteria for mesh adaptation in the finite volume solution of shallow water flows. The shallow water equations are numerically approximated by a predictor-corrector procedure in unstructured triangular meshes. The numerical fluxes at the interfaces of each triangle are reconstructed in the predictor stage using an upwind scheme along with slope limiters to achieve a second-order accuracy. Treatment of source terms is performed in the corrector stage using a well-balanced technique. Four error indicators using the flow variables are discussed and applied as criteria for the mesh adaptation. Numerical results are presented for two test examples for a circular dam-break flow and dam-break problem over a single building. The presented criteria are found to give accurate results in comparison with similar simulations carried out using uniformly refined fixed meshes. Dynamic grid adaptation and the use of an explicit time integration scheme are found to enhance the computational efficiency of the finite volume solution of shallow water flows. In addition, the obtained results for dam-break problems are considered to be representative, and might be helpful for a fair rating of criteria for mesh adaptation in the finite volume solution of shallow water flows, particularly in long time computations.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2019-0011

Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 503–526

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Shallow water equations finite volume methods mesh adaptation unstructured grids dam-break problems.

Author Details

Imad Kissami

Mohammed Seaid

Fayssal Benkhaldoun