A finite volume method for modeling shallow flows with wet-dry fronts on adaptive Cartesian grids
type: Item
instance of: scholarly article
title: A finite volume method for modeling shallow flows with wet-dry fronts on adaptive Cartesian grids
zbMATH Open document ID: 1407.76082
DOI: 10.1155/2014/209562
author: Sheng Bi
author: Yi Liu
author: Lixiang Song
author: Jianzhong Zhou
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: A second-order accurate, Godunov-type upwind finite volume method on dynamic refinement grids is developed in this paper for solving shallow-water equations. The advantage of this grid system is that no data structure is needed to store the neighbor information, since neighbors are directly specified by simple algebraic relationships. The key ingredient of the scheme is the use of the prebalanced shallow-water equations together with a simple but effective method to track the wet/dry fronts. In addition, a second-order spatial accuracy in space and time is achieved using a two-step unsplit MUSCL-Hancock method and a weighted surface-depth gradient method (WSDM) which considers the local Froude number is proposed for water depths reconstruction. The friction terms are solved by a semi-implicit scheme that can effectively prevent computational instability from small depths and does not invert the direction of velocity components. Several benchmark tests and a dam-break flooding simulation over real topography cases are used for model testing and validation. Results show that the proposed model is accurate and robust and has advantages when it is applied to simulate flow with local complex topographic features or flow conditions and thus has bright prospects of field-scale application.
Mathematics Subject Classification ID: 76M12
Mathematics Subject Classification ID: 65M08
Mathematics Subject Classification ID: 76D08
zbMATH DE Number: 7015919
Wikidata QID: Q59063840
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/209562
OpenAlex ID: W2039539538
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description: scientific article; zbMATH DE number 7015919