A general approximate-state Riemann solver for hyperbolic systems of conservation laws with source terms

An approximate‐state Riemann solver for the solution of hyperbolic systems of conservation laws with source terms is proposed. The formulation is developed under the assumption that the solution is made of rarefaction waves. The solution is determined using the Riemann invariants expressed as functi...

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Bibliographic Details
Published in:International journal for numerical methods in fluids 2007-03, Vol.53 (9), p.1509-1540
Main Authors: Lhomme, Julien, Guinot, Vincent
Format: Article
Language:English
Subjects:
Applied sciences
Buildings. Public works
Computational methods in fluid dynamics
Dams and subsidiary installations
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Godunov-type schemes
Hydraulic constructions
Physics
Piping
Riemann solvers
shallow water equations
source terms
water hammer equations
Water supply. Pipings. Water treatment
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Summary:An approximate‐state Riemann solver for the solution of hyperbolic systems of conservation laws with source terms is proposed. The formulation is developed under the assumption that the solution is made of rarefaction waves. The solution is determined using the Riemann invariants expressed as functions of the components of the flux vector. This allows the flux vector to be computed directly at the interfaces between the computational cells. The contribution of the source term is taken into account in the governing equations for the Riemann invariants. An application to the water hammer equations and the shallow water equations shows that an appropriate expression of the pressure force at the interface allows the balance with the source terms to be preserved, thus ensuring consistency with the equations to be solved as well as a correct computation of steady‐state flow configurations. Owing to the particular structure of the variable and flux vectors, the expressions of the fluxes are shown to coincide partly with those given by the HLL/HLLC solver. Computational examples show that the approximate‐state solver yields more accurate solutions than the HLL solver in the presence of discontinuous solutions and arbitrary geometries. Copyright © 2006 John Wiley & Sons, Ltd.
ISSN:0271-2091
1097-0363
DOI:10.1002/fld.1374