Boundary condition at a two-phase interface in the lattice Boltzmann method for the convection-diffusion equation.
Boundary condition at a two-phase interface in the lattice Boltzmann method for the convection-diffusion equation.
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DOI：
10.1103/physreve.90.013303
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发表时间：
2014-07
期刊：
影响因子：
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通讯作者：
H. Yoshida;Takayuki Kobayashi;H. Hayashi;T. Kinjo;H. Washizu;K. Fukuzawa
中科院分区：
文献类型：
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作者：
H. Yoshida;Takayuki Kobayashi;H. Hayashi;T. Kinjo;H. Washizu;K. Fukuzawa
提出了一种求解对流扩散方程的格子Boltzmann方法（LBM）边界格式，该格式正确地实现了具有不同输运性质的两相界面处的内边界条件。通过修改碰撞算子和LBM的流处理过程，克服了传统LBM在瞬态分析中难以满足界面通量连续性的问题。渐近分析的计划进行，以澄清所发挥的作用，在该计划中所涉及的可调参数。其结果是，内部边界条件被证明是满足二阶精度的晶格间隔，如果我们分配适当的值的可调参数。此外，对两个具体问题进行了数值分析，并与问题的解析解进行了比较，数值验证了所提出的方案。
A boundary scheme in the lattice Boltzmann method (LBM) for the convection-diffusion equation, which correctly realizes the internal boundary condition at the interface between two phases with different transport properties, is presented. The difficulty in satisfying the continuity of flux at the interface in a transient analysis, which is inherent in the conventional LBM, is overcome by modifying the collision operator and the streaming process of the LBM. An asymptotic analysis of the scheme is carried out in order to clarify the role played by the adjustable parameters involved in the scheme. As a result, the internal boundary condition is shown to be satisfied with second-order accuracy with respect to the lattice interval, if we assign appropriate values to the adjustable parameters. In addition, two specific problems are numerically analyzed, and comparison with the analytical solutions of the problems numerically validates the proposed scheme.