Volume 12, Issue 2
Numerical Assessment of Criteria for Mesh Adaptation in the Finite Volume Solution of Shallow Water Equations

Imad Kissami, Mohammed Seaid & Fayssal Benkhaldoun

Adv. Appl. Math. Mech., 12 (2020), pp. 503-526.

Published online: 2020-01

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M08, 35L53, 76B15, 74J40, 76B07

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

imad.kissami@um6p.ma (Imad Kissami)

m.seaid@durham.ac.uk (Mohammed Seaid)

fayssal@math.univ-paris13.fr (Fayssal Benkhaldoun)

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  • RIS
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@Article{AAMM-12-503, author = {Kissami , Imad and Seaid , Mohammed and Benkhaldoun , Fayssal }, title = {Numerical Assessment of Criteria for Mesh Adaptation in the Finite Volume Solution of Shallow Water Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {2}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0011}, url = {http://global-sci.org/intro/article_detail/aamm/13631.html} }
TY - JOUR T1 - Numerical Assessment of Criteria for Mesh Adaptation in the Finite Volume Solution of Shallow Water Equations AU - Kissami , Imad AU - Seaid , Mohammed AU - Benkhaldoun , Fayssal JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 503 EP - 526 PY - 2020 DA - 2020/01 SN - 12 DO - http://dor.org/10.4208/aamm.OA-2019-0011 UR - https://global-sci.org/intro/article_detail/aamm/13631.html KW - Shallow water equations, finite volume methods, mesh adaptation, unstructured grids, dam-break problems. AB -

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.

Imad Kissami, Mohammed Seaid & Fayssal Benkhaldoun. (2020). Numerical Assessment of Criteria for Mesh Adaptation in the Finite Volume Solution of Shallow Water Equations. Advances in Applied Mathematics and Mechanics. 12 (2). 503-526. doi:10.4208/aamm.OA-2019-0011
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