Boundary conditions of the lattice Boltzmann method for convection-diffusion equations
Boundary conditions of the lattice Boltzmann method for convection-diffusion equations
复制标题
DOI：
10.1016/j.jcp.2015.07.045
复制
发表时间：
2015-11
期刊：
影响因子：
--
通讯作者：
Juntao Huang;W. Yong
中科院分区：
文献类型：
--
作者：
Juntao Huang;W. Yong
在本文中，我们采用一种渐近分析技术，构造了两个边界格式伴随格子Boltzmann方法的对流扩散方程的一般罗宾边界条件。一种方案是直边界，边界点位于任何距离的晶格节点，并具有二阶精度。另一种是曲线边界格式，只有一阶精度，比现有格式简单得多。与文献中的方案不同，我们的方案只涉及当前格点。这种“单节点”边界格式对于具有复杂几何形状的问题是非常可取的。数值算例验证了这两种格式的有效性。数值结果表明，构造的格式的实用性和很好地支持我们的理论预测。
In this paper, we employ an asymptotic analysis technique and construct two boundary schemes accompanying the lattice Boltzmann method for convection–diffusion equations with general Robin boundary conditions. One scheme is for straight boundaries, with the boundary points locating at any distance from the lattice nodes, and has second-order accuracy. The other is for curved boundaries, has only first-order accuracy and is much simpler than the existing schemes. Unlike those in the literature, our schemes involve only the current lattice node. Such a “single-node” boundary schemes are highly desirable for problems with complex geometries. The two schemes are validated numerically with a number of examples. The numerical results show the utility of the constructed schemes and very well support our theoretical predications.