WELL-BALANCED HIGH ORDER EXTENSIONS OF GODUNOV'SMETHOD FOR SEMILINEAR BALANCE LAWS

摘要

This paper is concerned with the development of well-balanced high order numericalschemes 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 ofRiemann problems that include both the flux and the source terms. Godunov's methods so obtainedare extended to higher order schemes by using a technique of reconstruction of states. The maincontribution of this paper is to introduce a reconstruction technique that preserves the well-balancedproperty of Godunov's methods. Some numerical experiments are presented to verify in practice theproperties of the developed numerical schemes.