Vectorial finite-difference-based lattice Boltzmann method: Consistency, boundary schemes and stability analysis

Abstract

In this paper we propose a vectorial finite-difference-based lattice Boltzmann method (FD-LBM), which unifies several different numerical schemes for the incompressible Navier–Stokes equations. By using the Maxwell iteration, we analyze the consistency under the diffusive scaling. In the situation that the widely used bounce-back or “anti-bounce-back” boundary schemes are not applicable, a new boundary scheme is developed to accompany the vectorial method. It is shown that the scheme has second-order accuracy when the boundary is located at the middle of two neighboring lattice nodes. We also prove the numerical stability of the vectorial method on periodic domains and the vectorial method together with the boundary scheme on bounded domains. Several numerical experiments for 2D & 3D flow problems with straight and curved boundaries validate the stability and accuracy of the vectorial LBM with the proposed boundary scheme.