and study its approximation in the sense of Bhatnagar-Gross-Krook (a BGKlike approximation for short). In particular, we aim to describe the conservation law (1.1) as the hydrodynamic limit of the stochastic BGK model, as the microscopic scale ε goes to 0. The literature devoted to the deterministic counterpart, i.e. corresponding to the situation Φ = 0, is quite extensive (see [1], [11], [15],...

This paper reports an application of gas-kinetic BGK scheme to the computation of turbulent compressible convection in the stellar interior. After incorporating the Subgrid Scale (SGS) turbulence model into the BGK scheme, we tested the effects of numerical parameters on the quantitative relationships among the thermodynamic variables, their fluctuations and correlations in a very deep, initial...

We consider a vector kinetic BGK equation leading to isentropic gas dynamics in the relaxation limit. We prove the existence of a weak solution satisfying a kinetic entropy inequality for any initial data with nite energy. Key-words: isentropic gas dynamics { kinetic BGK model { kinetic entropy Mathematics Subject Classi cation: 35L65, 76N15, 35B35, 82C40 Work partially supported by European TM...

We consider a vector kinetic BGK equation leading to isentropic gas dynamics in the relaxation limit. We prove the existence of a weak solution satisfying a kinetic entropy inequality for any initial data with nite energy. Key-words: isentropic gas dynamics { kinetic BGK model { kinetic entropy Mathematics Subject Classi cation: 35L65, 76N15, 35B35, 82C40 Work partially supported by European TM...

in this paper, a viscous flow simulation is presented using the lattice boltzmann equation (lbe). a finite volume approach is adapted to discretize the lbe on a cell-centered, arbitrary shaped, rectangular tessellation. the formulation includes upwind scheme and high order descretization schemes for the flux term and collision operator respectively. a consistent open and solid boundary treatmen...

We consider a scalar conservation law in the quarter plane. This equation is approximated in a continuous kinetic Bhatnagar-Gross-Krook (BGK) model. The convergence of the model towards the unique entropy solution is established in the space of functions of bounded variation, using kinetic entropy inequalities, without special restriction on the flux nor on the equilibrium problem’s data. As an...

Gas-kinetic schemes based on the BGK model are proposed as an alternative evolution model which can cure some of the limitations of current Riemann solvers. To analyse the schemes, simple advection equations are reconstructed and solved using the gas-kinetic BGK model. Results for gas-dynamic application are also presented. The ®nal ̄ux function derived in this model is a combination of a gas-ki...

The derivation of the celebrated Boltzmann equations relies heavily on the assumption that the gas consists of monatomic particles, which is not the case for most of the realistic gases. Efforts to derive Boltzmann type kinetic models soon confront with the difficulty that it is virtually impossible to write the pre and post collision velocities in an explicit form, since polyatomic molecules c...

In this paper, we establish the entropy-entropy production estimate for ES-BGK model, a generalized version of BGK model Boltzmann equation introduced better approximation in Navier-Stokes limit. Our result improves previous entropy [38] that (1) full range Prandtl parameters −1/2≤ν<1 including critical case ν=−1/2 is covered, and (2) sharper bound obtained. An explicit characterization coeffic...

A unidirectional flow of a rarefied gas between two parallel plates driven by a uniform external force is investigated on the basis of kinetic theory with special interest in the behavior in the near continuum regime. The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation and the diffuse reflection boundary condition are employed as the basic system. First, a systematic asymptotic anal...