Traditional Lattice-Boltzmann modelling of advection–diffusion flow is affected by numerical instability if the advective term becomes dominant over the diffusive (i.e., high-Péclet flow). To overcome the problem, two 3D one-way coupled models are proposed. In a traditional model, a Lattice-Boltzmann Navier–Stokes solver is coupled to a Lattice-Boltzmann advection–diffusion model. In a novel model, the Lattice-Boltzmann Navier–Stokes solver is coupled to an explicit finite-difference algorithm for advection–diffusion. The finite-difference algorithm also includes a novel approach to mitigate the numerical diffusivity connected with the upwind differentiation scheme.

The models are validated using two non-trivial benchmarks, which includes discontinuous initial conditions and the case ${\mathrm{Pe}}_{\mathrm{g}}\to \infty$ for the first time, where ${\mathrm{Pe}}_{\mathrm{g}}$ is the grid Péclet number. The evaluation of ${\mathrm{Pe}}_{\mathrm{g}}$ alongside $\mathrm{Pe}$ is discussed. Accuracy, stability and the order of convergence are assessed for a wide range of Péclet numbers. Recommendations are then given as to which model to select depending on the value ${\mathrm{Pe}}_{\mathrm{g}}$—in particular, it is shown that the coupled finite-difference/Lattice-Boltzmann provide stable solutions in the case $\mathrm{Pe}\to \infty$, ${\mathrm{Pe}}_{\mathrm{g}}\to \infty$.

如果平流项对扩散流起主导作用（即高佩克莱流），则传统的对流-扩散流的莱迪思-玻尔兹曼模型将受到数值不稳定性的影响。为了克服该问题，提出了两个3D单向耦合模型。在传统模型中，将Lattice-Boltzmann Navier-Stokes解算器与Lattice-Boltzmann对流扩散模型耦合。在一个新颖的模型中，将Lattice-Boltzmann Navier-Stokes求解器与用于对流扩散的显式有限差分算法耦合。有限差分算法还包括一种新颖的方法，以减轻与迎风微分方案相关的数值扩散率。

使用两个不平凡的基准对模型进行了验证，其中包括不连续的初始条件和工况。 ${\mathrm{PE}}_{\mathrm{G}}\to \infty$ 第一次，在哪里 ${\mathrm{PE}}_{\mathrm{G}}$是网格Péclet号。评价${\mathrm{PE}}_{\mathrm{G}}$ 并排 $\mathrm{PE}$讨论。评估范围广泛的Péclet数的准确性，稳定性和收敛性。然后给出有关根据值选择哪种模型的建议${\mathrm{PE}}_{\mathrm{G}}$-特别是，在这种情况下，耦合的有限差分/格子-玻尔兹曼方程提供了稳定的解决方案 $\mathrm{PE}\to \infty$， ${\mathrm{PE}}_{\mathrm{G}}\to \infty$。