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A discontinuous Galerkin method for two‐dimensional shallow water flows
Author(s) -
Lai W.,
Khan A.A.
Publication year - 2011
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/fld.2721
Subject(s) - riemann solver , compressibility , hydraulic jump , mechanics , shallow water equations , discontinuous galerkin method , geometry , flux limiter , computer simulation , geology , dam break , mathematics , flow (mathematics) , numerical analysis , geotechnical engineering , mathematical analysis , physics , engineering , finite volume method , finite element method , structural engineering , theology , flood myth , philosophy
SUMMARY A numerical scheme is developed for two‐dimensional, depth‐averaged, shallow water flows based on the DG method. In the shallow water equations, the pressure force term and the bed slope term are combined to eliminate numerical imbalance. The HLLC approximate Riemann solver is employed to calculate the numerical flux for the DG scheme. A slope limiting procedure used for compressible flows is adapted for modeling incompressible two‐dimensional flows. A simple treatment for modeling flow over initially dry bed is presented. To validate the scheme, numerical tests are conducted to simulate hydraulic jump, partial dam break, circular dam break, wetting and drying in parabolic bowl, and a real world dam break in the Toce River. Numerical results show that this scheme can accurately model shock waves, wetting and drying, and flows in the channel with varying geometry and bed topography found in natural channels. Copyright © 2011 John Wiley & Sons, Ltd.