We present a numerical analysis of the validity of classical and generalized hy-drodynamics for Lattice Boltzmann Equation (LBE) and Lattice BGK methods in two and three dimensions, as a function of the collision parameters of these models. Our analysis is based on the wave-number dependence of the evolution operator. Good ranges of validity are found for BGK models as long as the relaxation ti...

In this paper we present a novel technique for the simulation of moving boundaries and rigid bodies immersed in rarefied gas using an Eulerian-Lagrangian formulation based on least square method. The is simulated by solving Bhatnagar-Gross-Krook (BGK) model Boltzmann equation dynamics. BGK solved Arbitrary Lagrangian-Eulerian (ALE) method, where grid-points/particles are moved with mean velocit...

In this paper we present a new algorithm based on a Cartesian mesh for the numerical approximation of kinetic models on complex geometry boundary. Due to the high dimensional property, numerical algorithms based on unstructured meshes for a complex geometry are not appropriate. Here we propose to develop an inverse Lax-Wendroff procedure, which was recently introduced for conservation laws [21]...

A rarefied gas flow through a channel with arbitrary cross section is studied based on the BGK model. The discrete velocity and streamline diffusion finite element methods are combined to yield a numerical scheme. For this method we derive stability and optimal error estimates in the L2 norm. The optimality is due to the maximal available regularity of the exact solution for the corresponding h...

We consider the hydrodynamical limit of a kinetic BGK model in one space dimension, to a scalar conservation law with a strict convex flux. In this paper, we provide sharp estimates for the asymptotic limit to shocks, where layers, called Knudsen layers, may appear. The used method is based on the relative entropy. It follows a previous work of Choi and Vasseur [11] where similar sharp estimate...

the purpose of this paper is to investigate the egm method and the behavior of a solid particle suspended in a twodimensional rectangular cavity due to conjugate natural convection. a thermal lattice boltzmann bgk model is implemented to simulate the two dimensional natural convection and the particle phase was modeled using the lagrangian–lagrangian approach where the solid particles are treat...

A simple second order scheme is presented for BGK equation on cartesian grids to simulate rarefied gas flows. An immersed boundary technique is then used since the mesh is body fitted. The asymptotic preserving properties of the BGK equation discretization towards Euler limit are also investigated with emphasis on the boundary conditions as the Knudsen number goes to zero. Reconstruction techni...

Evaporation of a liquid into a vacuum occupying a half space is investigated on the basis ofthe BGK equation for a three-dimensional gas linearized about a drifting Maxwellian distribu-tion. The theory of singular integral equations is used and numerical results are given. ZusammenfassungDie Verdampfung einer Fliissigkeit im Vakuum, die den Halbraum fiillt, wird untersuchtmi...