Lattice Boltzmann model for the convection-diffusion equation

Abstract

We propose a lattice Boltzmann (LB) model for the convection-diffusion equation (CDE) and show that the CDE can be recovered correctly from the model by the Chapman-Enskog analysis. The most striking feature of the present LB model is that it enables the collision process to be implemented locally, making it possible to retain the advantage of the lattice Boltzmann method in the study of the heat and mass transfer in complex geometries. A local scheme for computing the heat and mass fluxes is then proposed to replace conventional nonlocal finite-difference schemes. We further validate the present model and the local scheme for computing the flux against analytical solutions to several classical problems, and we show that both the model for the CDE and the computational scheme for the flux have a second-order convergence rate in space. It is also demonstrated the present model is more accurate than existing LB models for the CDE.

Linking simulations and experiments for the multiscale tracking of thermally induced martensitic phase transformation in NiTi SMA

“…The Lattice Boltzmann method (LBM) has received extensive attention as a numerical tool in the field of transport phenomena [47][48][49][50][51]. It offers easy application to arbitrary geometry and complex boundaries, significant flexibility such as handling of surface interactions, handling multicomponent systems, domain scalability, and algorithmic parallelizability, which are difficult to invoke through commonly available models based on discretization of the governing differential equations.…”

“…In two dimensions (2-D), transport can be described by the lattice Boltzmann equation expressed as [47,50,51] …”

Acceleration of Macrosegregation Simulation Based on Lattice Boltzmann Method

“…(3) and (4). 26) Therefore, the NS-based model explained in section 2 can be fully recast into the LBM framework. However, our particular attention in this study is directed at the acceleration of the computation of fluid flow.…”

Lattice Boltzmann method for binary fluids based on mass-conserving quasi-incompressible phase-field theory

“…where f i (x, t) and g i (x, t) are the distribution functions for the hydrodynamics and order parameter fields, respectively, c i is the discrete velocity in the ith direction, δt is the time step, τ f and τ g are dimensionless relaxation times related to the shear viscosity and mobility, respectively, F i and G i are the distribution functions for the force term, and G i is used for eliminating the extra term in the CH equation [34]. The local equilibrium distribution functions f eq i (x, t) and g eq i (x, t) are respectively defined as…”