Boltzmann Type Schemes for Gas Dynamics and the Entropy Property

Abstract

Let H be a convex function. A Boltzmann equation is built following the B.G.K. model, for which H is an entropy. In the fluid limit, the compressible Euler equations are obtained with a convex entropy naturally associated to H. The motivation is to define numerical Boltzmann schemes with finite speed of propagation corresponding to an equilibrium density function with bounded support. The classical scheme, obtained with $H(f) = f\log (f)$, is based on the equilibrium density function $\exp ({{ - |v|^2 } / 2})$, which has infinite support.