Multiple-distribution-function lattice Boltzmann method for convection-diffusion-system based incompressible Navier-Stokes equations

TL;DR

This paper introduces a multiple-distribution-function lattice Boltzmann method with multiple-relaxation-time model for simulating incompressible Navier-Stokes equations, enabling direct computation of velocity and pressure and accurate flow property calculations.

Contribution

It develops a novel MDF-LBM framework that accurately recovers Navier-Stokes equations and allows direct calculation of flow variables, with a locally computational scheme for velocity gradients.

Findings

Numerical results agree with analytical and numerical solutions.

The method achieves second-order convergence in space.

The scheme effectively computes velocity gradients and related flow properties.

Abstract

In this paper, a multiple-distribution-function lattice Boltzmann method (MDF-LBM) with multiple-relaxation-time model is proposed for incompressible Navier-Stokes equations (NSEs) which are considered as the coupled convection-diffusion equations (CDEs). Through direct Taylor expansion analysis, we show that the Navier-Stokes equations can be recovered correctly from the present MDF-LBM, and additionally, it is also found that the velocity and pressure can be directly computed through the zero and first-order moments of distribution function. Then in the framework of present MDF-LBM, we develop a locally computational scheme for the velocity gradient where the first-order moment of the non-equilibrium distribution is used, this scheme is also extended to calculate the velocity divergence, strain rate tensor, shear stress and vorticity. Finally, we also conduct some simulations to test the MDF-LBM, and find that the numerical results not only agree with some available analytical and numerical solutions, but also have a second-order convergence rate in space.