Flux-gradient and source-term balancing for certain high resolution shock-capturing schemes

Abstract We present an extension of Marquina’s flux formula, as introduced in Fedkiw et al. [Fedkiw RP, Merriman B, Donat R, Osher S. The penultimate scheme for systems of conservation laws: finite difference ENO with Marquina’s flux splitting. In: Hafez M, editor. Progress in numerical solutions of partial differential equations, Arcachon, France; July 1998], for the shallow water system. We show that the use of two different Jacobians at cell interfaces prevents the scheme from satisfying the exact C -property [Bermudez A, Vazquez ME. Upwind methods for hyperbolic conservation laws with source terms. Comput Fluids 1994;23(8):1049–71] while the approximate C -property is satisfied for high…