Uperieure S Ormale N Ecole Département De Mathématiques Et Applications Entropy Satisfying Ux Vector Splittings and Kinetic Bgk Models F. Bouchut Entropy Satisfying Ux Vector Splittings and Kinetic Bgk Models Entropy Satisfying Ux Vector Splittings and Kinetic Bgk Models

We establish forward and backward relations between entropy satisfying BGK models such as those introduced previously by the author and the rst order ux vector splitting numerical methods for systems of conservation laws. Classically, to a kinetic BGK model that is compatible with some family of entropies we can associate an entropy ux vector splitting. We prove that the converse is true: any entropy ux vector splitting can be interpreted by a kinetic model, and we obtain an explicit characterization of entropy satisfying ux vector splitting schemes. We deduce a new proof of discrete entropy inequalities under a sharp CFL condition that generalizes the monotonicity criterion in the scalar case. In particular, this gives a stability condition for numerical kinetic methods with noncompact velocity support. A new interpretation of general kinetic schemes is also provided via approximate Riemann solvers. We deduce the construction of nite velocity relaxation systems for gas dynamics.