Lattice Boltzmann model for a class of convection–diffusion equations with variable coefficients

Abstract

a b s t r a c tIn this work, a lattice Boltzmann model for a class of n-dimensional convection-diffusion equations with variable coefficients is proposed through introducing an auxiliary distribution function. The model can exactly recover the convection-diffusion equation without any assumptions. A detailed numerical study on several types of convection-diffusion equations is performed to validate the present model, and the results show that the accuracy of the present model is better than previous models.

Lattice Boltzmann method for general convection-diffusion equations: MRT model and boundary schemes

“…There have been various LB models for CDEs or systems coupling CDEs and flow fields in the literature, e.g., [13,14,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]. Among them, most models are concerned with linear isotropic or anisotropic CDEs [14,17,18,20,29,30,31,32,33,34,35] and those for nonlinear CDEs are relatively few.…”

“…Among them, most models are concerned with linear isotropic or anisotropic CDEs [14,17,18,20,29,30,31,32,33,34,35] and those for nonlinear CDEs are relatively few. In [19], a Bhatnagar-Gross-Krook (BGK) model for general nonlinear CDEs is proposed by designing appropriate equilibrium and source term, and it is further extended to the anisotropic case in [23] and modified in [13,21,22]. Though these models are shown to correctly recover the CDEs through the Chapman-Enskog analysis, there are still some limitations in their implementations.…”

“…As mentioned above, the existing LB models for general nonlinear CDEs [19,23,21,22,24,25,26,27,28] can not be used for some special CDEs due to the assumptions or the integration term in the models. On the other hand, the boundary schemes in [23,35] involve several lattices nodes and can not be applied when there are no enough nodes available.…”

Lattice Boltzmann solution of advection-dominated mass transport problem: a comparison

“…All of the aforementioned works have made attempts to illustrate that their introduced LB methods are appropriate for solving an ordinary solute transport equation. However, insigni cant attention has been paid to the LB solution of advection-dominated transport problems, wherein advection term plays a more signi cant role than dispersion term [20,25,30]. Arti cial numerical oscillations are one of the major limitations in numerical solutions of advectioncontrolled solute transport problems [31,32].…”

“…To the best of our knowledge, no condition has been found to guarantee that the LB solutions are not subject to arti cial over/undershoots [18,23,30,40]. This implies the necessity to assess di erent schemes of the LB method in the description of the advective mass transport problems.…”