论文标题
使用Forman的组合差分形式在多维固体中扩散
Diffusion in multi-dimensional solids using Forman's combinatorial differential forms
论文作者
论文摘要
通过定义分析基于标量变量的物理过程所需的运算符，扩展了组合差分形式的配方，用于分析离散复合物的拓扑特性的组合差分形式。所得的描述是内在的，与称为离散外积分的方法不同，因为它不假定存在光滑的向量场并形成离散复合物的外部外部。此外，所提出的公式提供了重要的新建模能力：物理过程可以设置为在复合物中具有不同尺寸的细胞上以不同的方式操作。提出了新方法将新方法应用于热/扩散方程式，以证明其如何捕获微观结构元素对宏观行为的变化效果。所提出的方法适用于一系列物理问题，包括热量，质量和电荷扩散以及流过多孔介质的流动。
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar variables. The resulting description is intrinsic, different from the approach known as Discrete Exterior Calculus, because it does not assume the existence of smooth vector fields and forms extrinsic to the discrete complex. In addition, the proposed formulation provides a significant new modelling capability: physical processes may be set to operate differently on cells with different dimensions within a complex. An application of the new method to the heat/diffusion equation is presented to demonstrate how it captures the effect of changing properties of microstructural elements on the macroscopic behavior. The proposed method is applicable to a range of physical problems, including heat, mass and charge diffusion, and flow through porous media.
