A well-balanced numerical model for depth-averaged two-layer shallow water flows

被引：0
作者：
Xin Liu
Junfeng He
机构：
[1] Numerical Environmental Prediction Section Environment and Climate Change Canada,Department of Civil Engineering
[2] University of Ottawa,College of Big Data and Internet
[3] Shenzhen Technology University,undefined
来源：
Computational and Applied Mathematics | 2021年 / 40卷
关键词：
Two-layer shallow water equations; Finite volume method; Well-balanced; Wetting–drying; Path-conservative approach; 76M12; 65M08; 86-08; 35L65;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this study, a well-balanced and positivity-preserving scheme for the nonconservative two-layer shallow water equations is developed in the framework of the path-conservative finite volume method. Special attention is paid to guaranteeing the well-balanced properties even in the presence of the wet–dry fronts for each layer. To this end, in this study, new numerical discretization and special local reconstruction are proposed. Moreover, the developed scheme also allows to stably compute flows in under-resolved meshes. The results of the numerical experiments illustrate the robustness and good performance of the constructed numerical scheme.
引用
收藏
相关论文
共 45 条
  • [1] Abgrall R(2009)Two-layer shallow water system: a relaxation approach SIAM J Sci Comput 31 1603-1627
  • [2] Karni S(2015)An efficient splitting technique for two-layer shallow-water model Numer Methods Partial Differ Equ 31 1396-1423
  • [3] Berthon C(2013)A well-balanced reconstruction of wet/dry fronts for the shallow water equations J Sci Comput 56 267-290
  • [4] Foucher F(2011)Finite volume evolution Galerkin methods for the shallow water equations with dry beds, Commun Comput Phys 10 371-404
  • [5] Morales T(2008)Why many theories of shock waves are necessary: convergence error in formally path-consistent schemes J Comput Phys 227 8107-8129
  • [6] Bollermann A(1995)Definition and weak stability of nonconservative products Journal de mathématiques pures et appliquées 74 483-548
  • [7] Chen G(2014)High order space-time adaptive ader-weno finite volume schemes for non-conservative hyperbolic systems Comput Methods Appl Mech Eng 268 359-387
  • [8] Kurganov A(2001)Strong stability-preserving high-order time discretization methods SIAM Rev 43 89-112
  • [9] Noelle S(2001)Semi-discrete central-upwind scheme for hyperbolic conservation laws and Hamilton-Jacobi equations SIAM J Sci Comput 23 707-740
  • [10] Bollermann A(2007)A second-order well-balanced positivity preserving central-upwind scheme for the Saint-Venant system Commun Math Sci 5 133-160
12345