Abstract A numerical study of the planar gas expansion under pulsed evaporation into background is carried out. The chosen conditions are typical for nanosecond laser deposition thin films and nanostructure synthesis, with saturated pressure at surface 5.4 MPa 50 500 Pa. problem solved based on direct simulation Monte Carlo method solution BGK model kinetic equation. generally good agreement wa...

In this paper we aim to introduce a systematic way to derive relaxation terms for the Boltzmann equation based under minimization problem of the entropy under moments constraints [7], [11]. In particular the moment constraints and corresponding coefficients are linked with the eigenfunctions and eigenvalues of the linearized collision operator through the Chapman-Enskog expansion. Then we deduc...

The lattice Boltzmann Method (LBM) has become a standard tool for estimating porous medium permeabilities from image data and numerically generated packings. We consider implementations of the single-relaxation time BGK scheme for single phase flow as well as a more computationally intensive multi-relaxation time (MRT) scheme. Results demonstrate that a considerable performance increase is achi...

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...

Implicit-explicit (IMEX) Runge-Kutta (RK) schemes are popular high order time discretization methods for solving stiff kinetic equations. As opposed to the compressible Euler limit (leading order asymptotics of the Boltzmann equation as the Knudsen number ε goes to zero), their asymptotic behavior at the Navier-Stokes (NS) level (next order asymptotics) was rarely studied. In this paper, we ana...

This paper presents a discontinuous Galerkin BGK (DGBGK) method for both viscous and inviscid flow simulations under a DG framework with a gas-kinetic flux and WENO limiters. In the DGBGK method, the construction of the flux in the DG method is based on the particle transport and collisional mechanism which not only couples the convective and dissipative terms together, but also includes both d...

Two discretizations of a 9-velocity Boltzmann equation with a BGK collision operator are studied. A Chapman-Enskog expansion of the PDE system predicts that the macroscopic behavior corresponds to the incompressible Navier-Stokes equations with additional terms of order Mach number squared. We introduce a fourth-order scheme and compare results with those of the commonly used lattice Boltzmann ...