van der Sman R G M
Agrotechnology & Food Sciences, Wageningen University, the Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Aug;74(2 Pt 2):026705. doi: 10.1103/PhysRevE.74.026705. Epub 2006 Aug 18.
In this paper we present lattice Boltzmann (LB) schemes for convection diffusion coupled to fluid flow on two-dimensional rectangular lattices. Via inverse Chapman-Enskog analysis of LB schemes including source terms, we show that for consistency with physics it is required that the moments of the equilibrium distributions equal those of the Maxwell-Boltzmann distribution. These constraints can be satisfied for the rectangular D2Q9 lattice for only fluid flow in the weakly compressible regime. The analysis of source terms shows that fluxes are really defined on the boundaries of the Wigner-Seitz cells, and not on the lattice sites where the densities are defined-which is quite similar to the staggered grid finite-volume schemes. Our theoretical findings are confirmed by numerical solutions of benchmark problems for convection diffusion and natural convection. The lattice Boltzmann scheme shows remarkably good performance for convection diffusion, showing little to non-numerical diffusion or numerical dispersion, even at high grid Peclet numbers.
在本文中，我们提出了用于二维矩形晶格上对流扩散与流体流动耦合的格子玻尔兹曼（LB）格式。通过对包含源项的LB格式进行逆查普曼 - 恩斯科格分析，我们表明，为了与物理过程保持一致，平衡分布的矩必须等于麦克斯韦 - 玻尔兹曼分布的矩。对于仅在弱可压缩 regime 下的流体流动，矩形 D2Q9 晶格可以满足这些约束条件。源项分析表明，通量实际上是在维格纳 - 赛茨元胞的边界上定义的，而不是在定义密度的晶格点上，这与交错网格有限体积格式非常相似。我们的理论发现通过对流扩散和自然对流基准问题的数值解得到了证实。格子玻尔兹曼格式在对流扩散方面表现出非常好的性能，即使在高网格佩克莱数下，数值扩散或数值色散也很小甚至没有。
