In this paper, by introducing a different distribution function and starting from the Boltzmann equation as well as the Maxwell-Boltzmann distribution, we obtain a Boltzmann Bhatnagar-Gross-Krook (BGK) equation for thermal flows with viscous heat dissipation in the incompressible limit. The continuous thermal BGK model is then discretized over both time and phase space to form a lattice BGK mod...

In this paper, a gas-kinetic Bhatnagar-Gross-Krook (BGK) model is constructed for the Rayleigh-Bénard thermal convection in the incompressible flow limit, where the flow field and temperature field are described by two coupled BGK models. Since the collision times in the corresponding BGK models can be different, the Prandtl number can be changed to any value instead of a fixed Pr=1 in the orig...

In this paper, a gas-kinetic BGK model is constructed for the Rayleigh-Bénard thermal convection in the incompressible flow limit, where the flow field and temperature field are described by two coupled BGK models. Since the collision times and pseudo-temperature in the corresponding BGK models can be different, the Prandtl number can be changed to any value instead of a fixed Pr = 1 in the ori...

The Bhatnagar–Gross–Krook BGK model approximates the collision term of the Boltzmann equation by a single relaxation process from a nonequilibrium state to an equilibrium state. From the BGK model, the Navier–Stokes, Burnett, and Super-Burnett equations can be derived. However, the success of these derived macroscopic equations in the description of highly nonequilibrium flow is limited. In ord...

A linearization is developed for Mieussens’s discrete velocity model (see, e.g., [L. Mieussens, Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries, J. Comput. Phys. 162 (2000) 429–466]) for kinetic equations. The basic idea is to use a linearized expression of the reference distribution function in the kinetic equation, instead of ...

The BGK and BGKC (Bhatnagar, Gross, Krook, and Cercignani) collision-term models for the Boltzmann equation are compared to the more rigorous variable-hard-sphere (VHS) collision-term model of Bird. The BGKC model is based on the well-known BGK model but uses an ellipsoidal statistical (ES) distribution instead of a Maxwellian distribution so as to incorporate both viscous effects and heat cond...

We present new numerical models for computing transitional or rarefied gas flows as described by the Boltzmann-BGK and BGK-ES equations. We first propose a new discrete-velocity model, based on the entropy minimization principle. This model satisfies the conservation laws and the entropy dissipation. Moreover, the problem of conservation and entropy for axisymmetric flows is investigated. We fi...

This Brief Communication is about the study of diatomic gas shock structure based on the nonequilibrium gas-kinetic Bhatnagar–Gross–Krook (BGK) model, where an additional rotational energy relaxation equation is added. The BGK Navier–Stokes flow solver is extended to solve the nonequilibrium gas kinetic model. The numerical solutions are compared with the experiment measurements and direct simu...

A thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single distribution function and features an adjustable Prandtl number. Numerical simulations show that using a moderate discrete velocity set, this model can accurately rec...