三维非均质材料输运的计算分析
Computational analysis of transport in three-dimensional heterogeneous materials
摘要：
多孔和非均质材料存在于从复合材料、膜、化学反应器和其他工程材料到生物物质和天然地下结构的许多应用中。在这项工作中，我们提出了一个综合的方法来生成，研究和高档随机和周期性多孔结构中的输运方程。几何形状生成基于随机算法或弹道沉积。特别是，提出了一种新的算法来产生随机包装的椭球体与随机取向和可调的孔隙率和连通性。多孔结构，然后使用局部细化的笛卡尔为基础的或非结构化的战略。因此，运输方程求解的准周期性边界条件的有限体积制剂，以简化尺度放大问题，通过解决简单的封闭问题与线性对流扩散反应算子的均匀化的经典理论相一致。现有的仿真代码扩展了新的发展和集成，以产生一个完全开源的仿真管道。然后介绍了这些计算方法的一些有趣的三维应用程序的展示。首先，研究了周期性排列球的收敛性质和输运色散性质。然后，传热问题被认为是在管道与层的沉积颗粒的不同高度，并在非均质各向异性材料。
英文摘要：
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated approach to generate, study and upscale transport equations in random and periodic porous structures. The geometry generation is based on random algorithms or ballistic deposition. In particular, a new algorithm is proposed to generate random packings of ellipsoids with random orientation and tunable porosity and connectivity. The porous structure is then meshed using locally refined Cartesian-based or unstructured strategies. Transport equations are thus solved in a finite-volume formulation with quasi-periodic boundary conditions to simplify the upscaling problem by solving simple closure problems consistent with the classical theory of homogenisation for linear advection-diffusion-reaction operators. Existing simulation codes are extended with novel developments and integrated to produce a fully open-source simulation pipeline. A showcase of a few interesting three-dimensional applications of these computational approaches is then presented. Firstly, convergence properties and the transport and dispersion properties of a periodic arrangement of spheres are studied. Then, heat transfer problems are considered in a pipe with layers of deposited particles of different heights, and in heterogeneous anisotropic materials.
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