An ES-BGK model for non polytropic gases with a general framework

In this paper, we derive an ellipsoidal statistical BGK model for a polyatomic gas that is based on a general framework introduced in [12]. The distribution function of the polyatomic gas depends on its velocity and a general internal energy function, which can be discrete or continuous. We solve the minimization problem of Boltzmann entropy under suitable moment constraints and determine the transport coefficients (Prandtl number and first and second viscosity) in the hydrodynamic limit. In the end, we obtain an ES-BGK model for a general framework covering in particular the non-polytropic case.