A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes

作     者：Moussa Ziggaf Imad Kissami Mohamed Boubekeur Fayssal Benkhaldoun 

作者机构：ENSAOLMCSComplexe UniversitaireB.P.66960000 OujdaMorocco MSDAMohammed VI Polytechnic UniversityLot 66043150 Ben GuerirMorocco Universit´eéSorbonne Paris NordLAGACNRSUMR 7539F-93430VilletaneuseFrance 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2023年第15卷第5期

页      面：1335-1378页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the HPC Project Alkhwarizmi department MSDA-UM6P 

主　　题：Shallow water model method of characteristics FVC scheme finite volume method well-balanced scheme 

摘      要：This paper aims to present a new well-balanced,accurate and fast finite volume scheme on unstructured grids to solve hyperbolic conservation *** is a scheme that combines both finite volume approach and characteristic *** this study,we consider a shallow water system with Coriolis effect and bottom friction stresses where this new Finite Volume Characteristics(FVC)scheme has been *** physical and mathematical properties of the system,including the C-property,have been well ***,we developed this approach by preserving the advantages of the finite volume discretization such as conservation property and the method of characteristics,in order to avoid Riemann solvers and to enhance the accuracy without any complexity of the MUSCL ***,a discretization was applied to the bottom source term that leads to a well-balanced scheme satisfying the steady-state condition of still water.A semi-implicit treatment will also be presented in this study to avoid stability problems due to source ***,the proposed finite volume method is verified on several benchmark tests and shows good agreement with analytical solutions and experimental results;moreover,it gives a noteworthy accuracy and rapidity improvement compared to the original approaches.