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Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshes
Author(s) -
Anastasiou K.,
Chan C. T.
Publication year - 1997
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19970615)24:11<1225::aid-fld540>3.0.co;2-d
Subject(s) - inviscid flow , finite volume method , shallow water equations , polygon mesh , solver , roe solver , mathematics , riemann solver , upwind scheme , flow (mathematics) , geometry , mechanics , mathematical analysis , mathematical optimization , physics , discretization
A 2D, depth‐integrated, free surface flow solver for the shallow water equations is developed and tested. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov‐type second‐order upwind finite volume formulation, whereby the inviscid fluxes of the system of equations are obtained using Roe's flux function. The eigensystem of the 2D shallow water equations is derived and is used for the construction of Roe's matrix on an unstructured mesh. The viscous terms of the shallow water equations are computed using a finite volume formulation which is second‐order‐accurate. Verification of the solution technique for the inviscid form of the governing equations as well as for the full system of equations is carried out by comparing the model output with documented published results and very good agreement is obtained. A numerical experiment is also conducted in order to evaluate the performance of the solution technique as applied to linear convection problems. The presented results show that the solution technique is robust. © 1997 John Wiley & Sons, Ltd.