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A lattice Boltzmann model for coupled diffusion

机译：耦合扩散的格子玻尔兹曼模型

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摘要

Diffusion coupling between different chemical components can have significant effects on the distribution of chemical species and can affect the physico-chemical properties of their supporting medium. The coupling can arise from local electric charge conservation for ions or from bound components forming compounds. We present a new lattice Boltzmann model to account for the diffusive coupling between different chemical species. In this model each coupling is added as an extra relaxation term in the collision operator. The model is tested on a simple diffusion problem with two coupled components and is in excellent agreement with the results obtained through a finite difference method. Our model is observed to be numerically very stable and unconditional stability is shown for a class of diffusion matrices. We further develop the model to account for advection and show an example of application to flow in porous media in two dimensions and an example of convection due to salinity differences. We show that our model with advection loses the unconditional stability, but offers a straight-forward approach to complicated two-dimensional advection and coupled diffusion problems.
机译：不同化学成分之间的扩散耦合可能会对化学物质的分布产生重大影响，并可能影响其支持介质的物理化学性质。这种耦合可能是由于离子的局部电荷守恒或形成化合物的结合成分引起的。我们提出了一个新的格子Boltzmann模型来说明不同化学物种之间的扩散耦合。在该模型中，每个耦合都作为额外的松弛项添加到碰撞算子中。该模型在具有两个耦合组件的简单扩散问题上进行了测试，与通过有限差分法获得的结果非常吻合。我们的模型在数值上非常稳定，并且针对一类扩散矩阵显示了无条件稳定性。我们进一步开发了用于解释对流的模型，并显示了二维应用在多孔介质中流动的示例以及因盐度差异而产生的对流的示例。我们表明，带有对流的模型失去了无条件的稳定性，但是为复杂的二维对流和耦合扩散问题提供了一种直接的方法。

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