A thermohydrodynamic lattice-BGK model for the ideal gas was derived by Alexander et al. in 1993, and generalized by McNamara et al. in the same year. In these works, particular forms for the equilibrium distribution function and the transport coefficients were posited and shown to work, thereby establishing the sufficiency of the model. In this paper, we rederive the model from a minimal set o...

Numerical schemes based on the collisional BGK model have been developed in recent years. In this paper, we investigate the rst-order BGK schemes for the Euler equations. Particular attention is given to nd CFL-like conditions under which the schemes are positivity-preserving (i.e. density and internal energy remain nonnegative). The rst-order BGK schemes are linear combinations of collisionles...

Numerical schemes based on the collisional BGK model have been developed in recent years. In this paper, we investigate the first-order BGK schemes for the Euler equations. Particular attention is given to finding CFL-like conditions under which the schemes are positivity-preserving (i.e. density and internal energy remain nonnegative). The first-order BGK schemes are linear combinations of col...

This paper presents an improved gas-kinetic scheme based on the Bhatnagar– Gross–Krook (BGK) model for the compressible Navier–Stokes equations. The current method extends the previous gas-kinetic Navier–Stokes solver developed by Xu and Prendergast (J. Comput. Phys. 114, 9) by (a) implementing a general nonequilibrium state based on the Chapman–Enskog expansion of the BGK model as the initial ...

An efficient algorithm is presented for determining the unique solvability of certain one-dimensional stationary transport problems. The non-existence of stationary evaporation states withsupersonic drift velocities for one and three dimensional BGK model is recovered. Sommariot~ presentato un algoritmo efficiente per determinare la solubilitfi univoca di alcuni probiemiunid...

We propose a BGK model of the quantum Boltzmann equation for gas mixtures. We also provide sufficient condition that guarantees existence equilibrium coefficients so shares same conservation laws and \begin{document}$ H $\end{document}-theorem with equation. Unlike classical mixtures, local equilibriums m...

Our purpose is to derive a model for charged particles which combines a kinetic description of the fast particles with a fluid description of the slow ones. In a previous paper, a similar model was derived from a kinetic BGK equation that uses a constant relaxation time and does not include the effect of an electric field. In this paper, we consider a more general kinetic equation including an ...

The purpose of the paper is an investigation of compactness properties of a family of solutions of a BGK-type model for near equilibrium kinetic densities for the system of the Euler equations for isentropic flows. 0.