Well-Balanced High Order Extensions of Godunov's Method for Semilinear Balance Laws

2008/01/01 by Manuel Castro, Manuel J. Castro, José M. Gallardo +2 · 6 citations
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #Gas Dynamics and Kinetic Theory #Fluid Dynamics and Turbulent Flows

paper · doi:10.1137/060674879

Abstract

This paper is concerned with the development of well-balanced high order numerical schemes for systems of balance laws with a linear flux function, whose coefficients may be variable. First, well-balanced first order numerical schemes are obtained based on the use of exact solvers of Riemann problems that include both the flux and the source terms. Godunov's methods so obtained are extended to higher order schemes by using a technique of reconstruction of states. The main contribution of this paper is to introduce a reconstruction technique that preserves the well-balanced property of Godunov's methods. Some numerical experiments are presented to verify in practice the properties of the developed numerical schemes.

Citations

• Total variation diminishing Runge-Kutta schemes
• A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations

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