Discrete-Velocity Vector-BGK Models Based Numerical Methods for the Incompressible Navier-Stokes Equations

In this paper, we propose a class of numerical methods based on discretevelocity vector-BGK models for the incompressible Navier-Stokes equations. By analyzing a splitting method with Maxwell iteration, we show that the usual lattice Boltzmann discretization of the vector-BGK models provides a good numerical scheme. Moreover, we establish the stability of the numerical scheme. The stability and secondorder accuracy of the scheme are validated through numerical simulations of the twodimensional Taylor-Green vortex flows. Further numerical tests are conducted to exhibit some potential advantages of the vector-BGK models, which can be regarded as competitive alternatives of the scalar-BGK models.