@article {Caselles200916,
	title = {Flux-gradient and source-term balancing for certain high resolution shock-capturing schemes},
	journal = {Computers \& Fluids},
	volume = {38},
	year = {2009},
	month = {0/2009},
	pages = {16 - 36},
	abstract = {<p>We present an extension of Marquina{\textquoteright}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{\textquoteright}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 [Berm{\'u}dez A, V{\'a}zquez ME. Upwind methods for hyperbolic conservation laws with source terms. Comput Fluids 1994;23(8):1049{\textendash}71] while the approximate C-property is satisfied for higher order versions of the scheme. The use of a single Jacobian in Marquina{\textquoteright}s flux splitting formula leads to a numerical scheme satisfying the exact C-property, hence we propose a combined technique that uses Marquina{\textquoteright}s two sided decomposition when the two adjacent states are not close and a single decomposition otherwise. Finally, we propose a special treatment at wet/dry fronts and situations of dry bed generation.</p>},
	issn = {0045-7930},
	doi = {10.1016/j.compfluid.2007.07.023},
	author = {Caselles, Vicent and Donat, Rosa and Haro, G.}
}
