论文标题
对复杂异质介质扩散模型的粗略模型的数值研究
Numerical investigation into coarse-scale models of diffusion in complex heterogeneous media
论文作者
论文摘要
对于精细异质性问题，异质培养基中扩散的计算建模非常昂贵。解决此问题的常见策略是将域分解为许多非重叠的子域，并在每个子域内（均质化细胞）中均质化空间依赖性扩散率。该过程产生了一个粗尺度模型，用于以降低的计算成本近似原始细尺度模型的解决方案行为。在本文中，我们研究了块异质介质中的粗尺度扩散模型，并首次研究各种因素对产生的粗尺度溶液的准确性的影响。我们提出了有关与均质化相关的误差的新发现，并通过数值实验确认了周期性边界条件是均质细胞的最佳选择，并证明应在计算上可行的最小均质化细胞应在数值模拟中使用。
Computational modelling of diffusion in heterogeneous media is prohibitively expensive for problems with fine-scale heterogeneities. A common strategy for resolving this issue is to decompose the domain into a number of non-overlapping sub-domains and homogenize the spatially-dependent diffusivity within each sub-domain (homogenization cell). This process yields a coarse-scale model for approximating the solution behaviour of the original fine-scale model at a reduced computational cost. In this paper, we study coarse-scale diffusion models in block heterogeneous media and investigate, for the first time, the effect that various factors have on the accuracy of resulting coarse-scale solutions. We present new findings on the error associated with homogenization as well as confirm via numerical experimentation that periodic boundary conditions are the best choice for the homogenization cell and demonstrate that the smallest homogenization cell that is computationally feasible should be used in numerical simulations.
