A recently developed analytical version of the discrete-ordinates method is used to establish a concise and particularly accurate solution to the problem of Couette #ow of a binary gas mixture in a plane channel. The model kinetic equations used to describe the #ow are based on the BGK theory of the linearized Boltzmann equation, and, in addition to the complete distribution functions for the t...

We present an analysis of the accuracy of the lattice Boltzmann BGK (LBGK) method in simulating pulsatile blood flow in a model of the Human Abdominal Aorta. The flow is driven by a systolic pressure cycle. As a benchmark, we consider fully developed pulsatile flow in a straight tube. We compare velocity profiles and shear stress to the analytical Womersley solutions. The accuracy of the bounce...

Recently, a new class of semi-Lagrangian methods for the BGK model of the Boltzmann equation has been introduced [8, 17, 18]. These methods work in a satisfactory way either in rarefied or fluid regime. Moreover, because of the semi-Lagrangian feature, the stability property is not restricted by the CFL condition. These aspects make them very attractive for practical applications. In this paper...

In this paper, we propose a lattice Boltzmann (LB) model to solve the coupled Cahn-HilliardNavier-Stokes equations. Differently from previous efforts, the LB equation for the fluid velocity is decomposed in a space of non-orthogonal central moments where the surface tension force is inserted directly in the equilibrium state. The present scheme is validated against well-consolidated benchmark t...

In this note we consider the development of a domain decomposition scheme directly obtained from the multiscale hybrid scheme described in [7]. The basic idea is to couple macroscopic and microscopic models in all cases in which the macroscopic model does not provide correct results. We will show that it’s possible to view a Boltzmann-Euler domain decomposition method as a subset of the hybrid ...

We investigate the stability of periodic Bernstein-Greene-Kruskal (BGK) waves. It is proved that any such wave is linearly unstable under some perturbation of twice the period. A new method is developed to find a growing mode.

A recently proposed lattice Boltzmann kinetic scheme offers a promising tool for simulating complex 3-D MHD flows. The algorithm is based on the BGK modeling of the collision term. The conventional approach for implementing magnetic behavior in LBM methods is based on one tensor-valued distribution function to present both the fluids variables (density and momentum) and the magnetic field. This...

We develop a family of second-order implicit-explicit (IMEX) schemes for the stiff BGK kinetic equation. The method is asymptotic-preserving (can capture the Euler limit without numerically resolving the small Knudsen number) as well as positivity-preserving — a feature that is not possessed by any of the existing second or high order IMEX schemes. The method is based on the usual IMEX Runge-Ku...

We solve the Boltzmann equation, whose collision term is modeled by hybridization of binary and BGK approximation. The parameter controlling ratio these two mechanisms selected adaptively on every grid cell at time step. This self-adaptation based a heuristic error indicator describing difference between model original term. derived quadratic terms in modeling with linear operators. Our numeric...