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Volume 30, Issue 3
Shallow Water Moment Models for Bedload Transport Problems

José Garres-Díaz, Manuel J. Castro Díaz, Julian Koellermeier & Tomás Morales de Luna

Commun. Comput. Phys., 30 (2021), pp. 903-941.

Published online: 2021-07

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  • Abstract

In this work a simple but accurate shallow model for bedload sediment transport is proposed. The model is based on applying the moment approach to the Shallow Water Exner model, making it possible to recover the vertical structure of the flow. This approach allows us to obtain a better approximation of the fluid velocity close to the bottom, which is the relevant velocity for the sediment transport. A general Shallow Water Exner moment model allowing for polynomial velocity profiles of arbitrary order is obtained. A regularization ensures hyperbolicity and easy computation of the eigenvalues. The system is solved by means of an adapted IFCP scheme proposed here. The improvement of this IFCP type scheme is based on the approximation of the eigenvalue associated to the sediment transport. Numerical tests are presented which deal with large and short time scales. The proposed model allows to obtain the vertical structure of the fluid, which results in a better description on the bedload transport of the sediment layer.

  • AMS Subject Headings

65M08, 35L45, 35Q86, 86-08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-30-903, author = {Garres-Díaz , JoséJ. Castro Díaz , ManuelKoellermeier , Julian and Morales de Luna , Tomás}, title = {Shallow Water Moment Models for Bedload Transport Problems}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {3}, pages = {903--941}, abstract = {

In this work a simple but accurate shallow model for bedload sediment transport is proposed. The model is based on applying the moment approach to the Shallow Water Exner model, making it possible to recover the vertical structure of the flow. This approach allows us to obtain a better approximation of the fluid velocity close to the bottom, which is the relevant velocity for the sediment transport. A general Shallow Water Exner moment model allowing for polynomial velocity profiles of arbitrary order is obtained. A regularization ensures hyperbolicity and easy computation of the eigenvalues. The system is solved by means of an adapted IFCP scheme proposed here. The improvement of this IFCP type scheme is based on the approximation of the eigenvalue associated to the sediment transport. Numerical tests are presented which deal with large and short time scales. The proposed model allows to obtain the vertical structure of the fluid, which results in a better description on the bedload transport of the sediment layer.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0152}, url = {http://global-sci.org/intro/article_detail/cicp/19316.html} }
TY - JOUR T1 - Shallow Water Moment Models for Bedload Transport Problems AU - Garres-Díaz , José AU - J. Castro Díaz , Manuel AU - Koellermeier , Julian AU - Morales de Luna , Tomás JO - Communications in Computational Physics VL - 3 SP - 903 EP - 941 PY - 2021 DA - 2021/07 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2020-0152 UR - https://global-sci.org/intro/article_detail/cicp/19316.html KW - Shallow Water Exner model, moment approach, hyperbolic system, finite volume method, sediment transport. AB -

In this work a simple but accurate shallow model for bedload sediment transport is proposed. The model is based on applying the moment approach to the Shallow Water Exner model, making it possible to recover the vertical structure of the flow. This approach allows us to obtain a better approximation of the fluid velocity close to the bottom, which is the relevant velocity for the sediment transport. A general Shallow Water Exner moment model allowing for polynomial velocity profiles of arbitrary order is obtained. A regularization ensures hyperbolicity and easy computation of the eigenvalues. The system is solved by means of an adapted IFCP scheme proposed here. The improvement of this IFCP type scheme is based on the approximation of the eigenvalue associated to the sediment transport. Numerical tests are presented which deal with large and short time scales. The proposed model allows to obtain the vertical structure of the fluid, which results in a better description on the bedload transport of the sediment layer.

José Garres-Díaz, Manuel J. Castro Díaz, Julian Koellermeier & Tomás Morales de Luna. (2021). Shallow Water Moment Models for Bedload Transport Problems. Communications in Computational Physics. 30 (3). 903-941. doi:10.4208/cicp.OA-2020-0152
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