Generic boundary conditions for lattice Boltzmann models and their application to advection and anisotropic dispersion equations
Generic boundary conditions for lattice Boltzmann models and their application to advection and anisotropic dispersion equations
复制标题
DOI：
10.1016/j.advwatres.2005.03.009
复制
发表时间：
2005-11
影响因子：
4.7
通讯作者：
I. Ginzburg
中科院分区：
文献类型：
--
作者：
I. Ginzburg
我们提出了一种“多重反射”方法，用于在任意形状表面的格子玻尔兹曼方法中对狄利克雷和诺依曼时间相关边界条件进行建模。输入群体的多重反射条件表示已知群体解的线性组合。首先为平衡函数的对称和反对称部分建立闭合关系，与问题的性质无关。调整对称部分，为平衡分布指定的标量函数建立二阶和三阶精确狄利克雷边界条件。重点是平流和各向异性色散方程 (AADE) 的两种方法：当扩展的平衡函数的系数与变换的色散张量的系数匹配时的平衡技术，以及当色散张量的系数被构建为与链接型碰撞算子相关的特征值函数的线性组合时的特征值技术。作为一种特殊的局部边界技术，我们对“防反弹”条件进行了分析。通用闭合关系的反对称部分允许指定法向通量条件，而无需反转扩散张量。针对反弹和镜面反射导出法向和切向约束。反弹闭合关系从前导阶处的非物理切向通量限制中释放出来。针对具有指定狄利克雷和诺伊曼边界条件的各向同性/各向异性配置，给出了泊松方程和对流扩散方程的解。
We address a “multi-reflection” approach to model Dirichlet and Neumann time-dependent boundary conditions in lattice Boltzmann methods for arbitrarily shaped surfaces. The multi-reflection condition for an incoming population represents a linear combination of the known population solutions. The closure relations are first established for symmetric and anti-symmetric parts of the equilibrium functions, independently of the nature of the problem. The symmetric part is tuned to build second- and third-order accurate Dirichlet boundary conditions for the scalar function specified by the equilibrium distribution. The focus is on two approaches to advection and anisotropic-dispersion equations (AADE): the equilibrium technique when the coefficients of the expanded equilibrium functions match the coefficients of the transformed dispersion tensor, and the eigenvalue technique when the coefficients of the dispersion tensor are built as linear combinations of the eigenvalue functions associated with the link-type collision operator. As a particular local boundary technique, the “anti-bounce-back” condition is analyzed. The anti-symmetric part of the generic closure relation allows to specify normal flux conditions without inversion of the diffusion tensor. Normal and tangential constraints are derived for bounce-back and specular reflections. The bounce-back closure relation is released from the non-physical tangential flux restriction at leading orders. Solutions for the Poisson equation and for convection–diffusion equations are presented for isotropic/anisotropic configurations with specified Dirichlet and Neumann boundary conditions.