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The generalized Riemann problem method for the shallow water equations with bottom topography
Author(s) -
Li Jiequan,
Chen Guoxian
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1471
Subject(s) - discretization , shallow water equations , riemann solver , riemann problem , mathematics , riemann hypothesis , flow (mathematics) , mathematical analysis , midpoint , numerical analysis , interface (matter) , point (geometry) , riemann surface , surface (topology) , geometry , mechanics , physics , finite volume method , bubble , maximum bubble pressure method
Abstract This paper extends the generalized Riemann problem method (GRP) to the system of shallow water equations with bottom topography. The main contribution is that the generalized Riemann problem method ( J. Comput. Phys. 1984; 55 (1):1–32) is used to evaluate the midpoint values of solutions at each cell interface so that the bottom topography effect is included in numerical fluxes, and at the same step the source term is discretized with an interface method in which only mid‐point values are plugged in. This scheme is well balanced between the flux gradient and bottom topography when incorporating the surface gradient method (SGM) ( J. Comput. Phys. 2001; 168 (1):1–25) into data reconstruction step, and it is also suitable for both steady and unsteady flow simulations. We illustrate the accuracy of this scheme by several 1‐D and 2‐D numerical experiments. Copyright © 2005 John Wiley & Sons, Ltd.