We propose a new ES-BGK model for diatomic gases which allows translational–rotational and translational–vibrational energy exchanges, as given by Landau–Teller Jeans relaxation equations. This is consistent with the general definition of vibrational rotational collision numbers that are also commonly used in DSMC solvers. It proved to satisfy H-theorem give correct transport coefficients, up v...

The lattice Boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered. Although the equation is a derivative of lattice gas automata, it may be interpreted as a Lagrangian finite-difference method for the numerical simulation of the discrete-velocity Boltzmann equation that makes use of a BGK ...

During the past decade gas-kinetic methods based on the BGK simplification of the Boltzmann equation have been employed to compute fluid flow in a finite-difference or finite-volume context. Among the most successful formulations is the finite-volume scheme proposed by Xu [K. Xu, A gas-kinetic BGK scheme for the Navier–Stokes equations and its connection with artificial dissipation and Godunov ...

In this paper, we present an alternative derivation of the entropy production in turbulent flows, based on a formal analogy with the kinetic theory of rarefied gas. This analogy allows for proving that the celebrated k − e model for turbulent flows is nothing more than a set of coupled BGK (Bhatnagar–Gross–Krook)-like equations with a proper forcing. This opens a novel perspective on this model...

A discontinuous Galerkin Method based on a Bhatnagar-Gross-Krook (BGK) formulation is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The idea behind this approach is to combine the robustness of the BGK scheme with the accuracy of the DG methods in an effort to develop a more accurate, efficient, and robust method for numerical simulations of viscous ...

In this paper, based on the BGK equation, Liouville's theorem, and symplecticity preserving property of a Hamiltonian flow, a well-balanced kinetic scheme for the compressible Navier-Stokes equations under external forcing field is developed. In order to construct such a scheme, the physical process of particles transport through a potential barrier at a cell interface will be modeled with pene...

We investigate the nonlinear instability of periodic Bernstein-Greene-Kruskal(BGK) waves. Starting from an exponentially growing mode to the linearized equation, we proved nonlinear instability in the L-norm of the electric field.

In this paper, we propose a new semi-Lagrangian scheme for the polyatomic ellipsoidal BGK model. order to avoid time step restrictions coming from convection term and small Knudsen number, combine approach with an implicit treatment relaxation term. We show how explicitly solve step, thus obtaining efficient stable any number. also derive explicit error estimate on convergence of proposed every...

In this paper, we are concerned with the local-in-time well-posedness of a fluid-kinetic model in which BGK density dependent collision frequency is coupled inhomogeneous Navier–Stokes equation through drag forces. To best knowledge authors, first result on existence smooth solution for particle–fluid nonlinear inter-particle operator time can be prolonged as size initial data gets smaller.