Skew-selfadjoint form for systems of conservation laws

Hyperbolic systems of conservation laws augumented with an entropy inequality are studied. It is shown that such systems can be written in a (quasilinear) skew-selfadjoint form. Centered differencing of such a form under the smooth regime ends up with a systematic recipe for constructing quasiconservative schemes where the global entropy conservation is recovered. Employing the above formulation in bounded regions under the nonsmooth regime as well, a local entropy decay estimate is also concluded. Examples of the shallow-water and the full gasdynamics equations are explicitly treated.