On the definition of discrete hydrodynamic variables
On the definition of discrete hydrodynamic variables
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DOI：
10.1063/1.3247586
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发表时间：
2009-10-28
影响因子：
4.4
通讯作者：
Zuniga, Ignacio
中科院分区：
文献类型：
--
作者：
Espanol, Pep;Zuniga, Ignacio
离散流体动力学变量的 Green-Kubo 公式不仅涉及流体传输系数的信息，还涉及控制离散变量演化的微分算子的离散版本的信息。这给出了流体动力学中的离散化程序和用于获得分子流体的流体动力学行为的粗粒度程序之间的密切联系。我们观察到，用 Voronoi 单元对离散流体动力学变量进行自然定义会导致 Green-Kubo 公式发散，从而使完整的粗粒度策略变得毫无用处。为了理解这个微妙的问题，在本文中，我们考虑非相互作用布朗粒子的粗粒化。该问题的离散流体动力学变量是 Voronoi 单元内的粒子数量。由于模型的简单性，我们发现了相关函数奇异行为的起源。我们基于行为正常的 Delaunay 单元的概念提供了另一种定义，建议使用 Delaunay 结构在离散流体动力学水平上对分子流体进行粗粒化。 (C) 2009 年美国物理研究所。 [号码：10.1063/1.3247586]
The Green-Kubo formula for discrete hydrodynamic variables involves information about not only the fluid transport coefficients but also about discrete versions of the differential operators that govern the evolution of the discrete variables. This gives an intimate connection between discretization procedures in fluid dynamics and coarse-graining procedures used to obtain hydrodynamic behavior of molecular fluids. We observed that a natural definition of discrete hydrodynamic variables in terms of Voronoi cells leads to a Green-Kubo formula which is divergent, rendering the full coarse-graining strategy useless. In order to understand this subtle issue, in the present paper we consider the coarse graining of noninteracting Brownian particles. The discrete hydrodynamic variable for this problem is the number of particles within Voronoi cells. Thanks to the simplicity of the model we spot the origin of the singular behavior of the correlation functions. We offer an alternative definition, based on the concept of a Delaunay cell that behaves properly, suggesting the use of the Delaunay construction for the coarse graining of molecular fluids at the discrete hydrodynamic level. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3247586]