格子Boltzmann模拟中的因式分解对称性
Factorization symmetry in lattice Boltzmann simulations
摘要：
基于乘积的对称性，建立了格子玻尔兹曼方法的非微扰代数理论。它包括三个步骤：（i）通过对高阶高斯矩施加限制性扩展的匹配条件导出一维空间中的容许格，（ii）在二维和三维空间中的乘积格上以封闭形式解析地找到的特殊准平衡分布函数，并且证明了准平衡矩的因式分解，和（iii）代数修剪方法的基础上的一对一的关系组离散的速度和时刻。区分了构造格子玻尔兹曼平衡的两种途径。目前的理论包括以前已知的限制和特殊情况下的晶格，并使自动推导晶格玻尔兹曼模型从二维表，通过找到一个多项式的根和解决一些线性系统。
英文摘要：
A non-perturbative algebraic theory of lattice Boltzmann method is developed based on a symmetry of a product. It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which imposes restricted extension of higher-order Gaussian moments, (ii) Special quasi-equilibrium distribution function found analytically in closed form on the product-lattice in two and three spatial dimensions, and which proves factorization of quasi-equilibrium moments, and (iii) Algebraic method of pruning based on a one-into-one relation between groups of discrete velocities and moments. Two routes of constructing lattice Boltzmann equilibria are distinguished. Present theory includes previously known limiting and special cases of lattices, and enables automated derivation of lattice Boltzmann models from two-dimensional tables, by finding roots of one polynomial and solving a few linear systems.
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