We present an adaptation of the lattice BGK method for fast convergence of simulations of laminar time-dependent flows. The technique is an extension to the recent accelerated procedures for steady flow computations. Being based on Mach number annealing, the present technique substantially improves the accuracy and computational efficiency of the standard lattice BGK method for such unsteady fl...

We introduce a class of discrete velocity BGK type approximations to multidimensional scalar nonlinearly diiusive conservation laws. We prove the well-posedness of these models, a priori bounds and kinetic entropy inequalities that allow to pass into the limit towards the unique entropy solution recently obtained by Carrillo. Examples of such BGK models are provided.

We consider isentropic gas dynamics equations with unilateral constraint on the density and mass loss. The and pressureless pressure laws are considered. We propose an entropy weak formulation of the system that incorporates the constraint and Lagrange multiplier, for which we prove weak stability and existence of solutions. The nonzero pressure model is approximated by a kinetic BGK relaxation...

A 2D lattice Boltzmann model for inviscid compressible flows was proposed in this paper. Finite volume method was implemented on 2D curvilinear structural grids to solve the lattice BGK-Boltzmann equations. MUSCL scheme was used to perform interpolation. The obtained results agree excellently well with experimental and previous numerical results. AMS subject classifications: 76P05

Motivated by the theory of kinetic models in gas dynamics, we obtain an integral representation of lower semi-continuous functions on Rd, d ≥ 1. We use the representation to study the problem of compactness of a family of the solutions of the discrete time BGK model for the compressible Euler equations.

We consider a one-dimensional, collisionless plasma given by the Vlasov-Poisson system and investigate the stability of periodic steady state solutions known as Bernstein-Greene-Kruskal (BGK) waves. Using information about the induced dispersion operator, we determine sufficient conditions under which BGK waves are linearly unstable under perturbations that share the same period as the equilibr...

We consider a kinetic description of multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the frequency varies not only time and space but also microscopic velocity. In this model, Maxwellians typically used standard BGK operators are replaced by generalization such target functions, defined variational procedure [20]. paper we present numerical metho...