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A steady-state capturing method for hyperbolic systems with geometrical source terms

Published online by Cambridge University Press:  15 April 2002

Shi Jin
Shi Jin*
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA. (jin@math.wisc.edu)
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Abstract

We propose a simple numerical method for capturing thesteady state solution of hyperbolic systems with geometricalsource terms. We usethe interface value, rather than the cell-averages, for the source terms that balance the nonlinear convectionat the cell interface, allowing the numerical capturing of the steadystate with a formal high order accuracy. This method applies to Godunovor Roe type upwind methods butrequires no modification of the Riemann solver. Numerical experiments on scalar conservationlaws and the one dimensional shallow water equationsshow much better resolution of the steady state than the conventionalmethod, with almost no new numerical complexity.

Keywords

Hyperbolic systemssource termssteady statesolutionshallow water equationsshock capturing methods.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 4 , July 2001 , pp. 631 - 645
Copyright
© EDP Sciences, SMAI, 2001

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