Comparative study of multicomponent Lattice Boltzmann models for binary mixture flows

Two lattice Boltzmann method (LBM) models for binary mixture flows are numerically compared. The first model solves the Navier–Stokes equations within the incompressible limit and considers the mixture as one single fluid. A multi relaxation time (MRT) collision operator tunes the fluid diffusivity independently of the fluid viscosity. The second model emerges from a different theoretical derivation of the kinetic theory, where the governing equations are recovered for each species of the mixture. A source term in the LBM defines the interspecies friction force and couples the species of the mixture. A pure diffusion flow and a 2D plane Poiseuille binary mixture flow verify both models in the incompressible limit where diffusive and viscous transport occurs. The influence of molecular mass ratio, dynamic viscosity ratio, and Schmidt number on species and mixture flow behavior is investigated. The numerical results show good agreement against their respective analytical solutions and capture the deviation between the velocity profiles according to the flow regime. The present numerical study underlines the difference between the models as a function of the flow regimes which was observed from the macroscopic governing equations.

Incompressible limit of Euler equations with damping

<abstract><p>The Cauchy problem for the compressible Euler system with damping is considered in this paper. Based on previous global existence results, we further study the low Mach number limit of the system. By constructing the uniform estimates of the solutions in the well-prepared initial data case, we are able to prove the global convergence of the solutions in the framework of small solutions.</p></abstract>