We develop and implement a finite volume method based on an almost conservative approach for the hyperbolic non-conservative system of the shear shallow water model. This model is a generalization of the shallow water model to include the effects of shear, which are ignored in the standard shallow water model. The existing path conservative scheme is extended to unstructured grids composed of triangles or quadrilaterals with the solution stored at the cell centers. The high-resolution scheme is based on a local solution reconstruction idea for which a new set of variables based on a Cholesky decomposition of the Reynolds stress tensor (fluctuation of horizontal velocity) is developed, which is found to increase the robustness of the schemes by maintaining positive definiteness property. The scheme is applied to some test problems like 1D dam break, square dam break, roll waves, and radial hydraulic jump.
Keywords: shallow flow, shear flow, non-conservative system
Shashwat Tiwari 1; Boniface Nkonga 2; Praveen Chandrashekar 1; Sergey Gavrilyuk 3
CC-BY 4.0
@article{SMAI-JCM_2024__10__229_0,
author = {Shashwat Tiwari and Boniface Nkonga and Praveen Chandrashekar and Sergey Gavrilyuk},
title = {Finite volume approximations of shear shallow water model on unstructured grids},
journal = {The SMAI Journal of computational mathematics},
pages = {229--261},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {10},
year = {2024},
doi = {10.5802/smai-jcm.112},
language = {en},
url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.112/}
}
TY - JOUR AU - Shashwat Tiwari AU - Boniface Nkonga AU - Praveen Chandrashekar AU - Sergey Gavrilyuk TI - Finite volume approximations of shear shallow water model on unstructured grids JO - The SMAI Journal of computational mathematics PY - 2024 SP - 229 EP - 261 VL - 10 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.112/ DO - 10.5802/smai-jcm.112 LA - en ID - SMAI-JCM_2024__10__229_0 ER -
%0 Journal Article %A Shashwat Tiwari %A Boniface Nkonga %A Praveen Chandrashekar %A Sergey Gavrilyuk %T Finite volume approximations of shear shallow water model on unstructured grids %J The SMAI Journal of computational mathematics %D 2024 %P 229-261 %V 10 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.112/ %R 10.5802/smai-jcm.112 %G en %F SMAI-JCM_2024__10__229_0
Shashwat Tiwari; Boniface Nkonga; Praveen Chandrashekar; Sergey Gavrilyuk. Finite volume approximations of shear shallow water model on unstructured grids. The SMAI Journal of computational mathematics, Volume 10 (2024), pp. 229-261. doi : 10.5802/smai-jcm.112. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.112/
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