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Volume 3, Issue 4
Mathematical Development and Verification of a Finite Volume Model for Morphodynamic Flow Applications

Fayssal Benkhaldoun, Mohammed Seaïd & Slah Sahmim

Adv. Appl. Math. Mech., 3 (2011), pp. 470-492.

Published online: 2011-03

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  • Abstract

The accuracy and efficiency of a class of finite volume methods are investigated for numerical solution of morphodynamic problems in one space dimension. The governing equations consist of two components, namely a hydraulic part described by the shallow water equations and a sediment part described by the Exner equation. Based on different formulations of the morphodynamic equations, we propose a family of three finite volume methods. The numerical fluxes are reconstructed using a modified Roe's scheme that incorporates, in its reconstruction, the sign of the Jacobian matrix in the morphodynamic system. A well-balanced discretization is used for the treatment of the source terms. The method is well-balanced, non-oscillatory and suitable for both slow and rapid interactions between hydraulic flow and sediment transport. The obtained results for several morphodynamic problems are considered to be representative, and might be helpful for a fair rating of finite volume solution schemes, particularly in long time computations.

  • Keywords

Morphodynamic model, shallow water equations, sediment transport, finite volume method, well-balanced discretization.

  • AMS Subject Headings

65M08, 76B15, 76M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-3-470, author = {Benkhaldoun , FayssalSeaïd , Mohammed and Sahmim , Slah}, title = {Mathematical Development and Verification of a Finite Volume Model for Morphodynamic Flow Applications}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2011}, volume = {3}, number = {4}, pages = {470--492}, abstract = {

The accuracy and efficiency of a class of finite volume methods are investigated for numerical solution of morphodynamic problems in one space dimension. The governing equations consist of two components, namely a hydraulic part described by the shallow water equations and a sediment part described by the Exner equation. Based on different formulations of the morphodynamic equations, we propose a family of three finite volume methods. The numerical fluxes are reconstructed using a modified Roe's scheme that incorporates, in its reconstruction, the sign of the Jacobian matrix in the morphodynamic system. A well-balanced discretization is used for the treatment of the source terms. The method is well-balanced, non-oscillatory and suitable for both slow and rapid interactions between hydraulic flow and sediment transport. The obtained results for several morphodynamic problems are considered to be representative, and might be helpful for a fair rating of finite volume solution schemes, particularly in long time computations.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1056}, url = {http://global-sci.org/intro/article_detail/aamm/179.html} }
TY - JOUR T1 - Mathematical Development and Verification of a Finite Volume Model for Morphodynamic Flow Applications AU - Benkhaldoun , Fayssal AU - Seaïd , Mohammed AU - Sahmim , Slah JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 470 EP - 492 PY - 2011 DA - 2011/03 SN - 3 DO - http://doi.org/10.4208/aamm.10-m1056 UR - https://global-sci.org/intro/article_detail/aamm/179.html KW - Morphodynamic model, shallow water equations, sediment transport, finite volume method, well-balanced discretization. AB -

The accuracy and efficiency of a class of finite volume methods are investigated for numerical solution of morphodynamic problems in one space dimension. The governing equations consist of two components, namely a hydraulic part described by the shallow water equations and a sediment part described by the Exner equation. Based on different formulations of the morphodynamic equations, we propose a family of three finite volume methods. The numerical fluxes are reconstructed using a modified Roe's scheme that incorporates, in its reconstruction, the sign of the Jacobian matrix in the morphodynamic system. A well-balanced discretization is used for the treatment of the source terms. The method is well-balanced, non-oscillatory and suitable for both slow and rapid interactions between hydraulic flow and sediment transport. The obtained results for several morphodynamic problems are considered to be representative, and might be helpful for a fair rating of finite volume solution schemes, particularly in long time computations.

Fayssal Benkhaldoun, Mohammed Seaïd & Slah Sahmim. (1970). Mathematical Development and Verification of a Finite Volume Model for Morphodynamic Flow Applications. Advances in Applied Mathematics and Mechanics. 3 (4). 470-492. doi:10.4208/aamm.10-m1056
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