复杂非均匀介质中扩散的粗尺度模型数值研究
Numerical investigation into coarse-scale models of diffusion in complex heterogeneous media
摘要：
非均匀介质中扩散的计算模型对于具有精细尺度非均匀性的问题来说过于昂贵。解决这个问题的一个常见策略是将域分解为许多不重叠的子域，并均匀化每个子域（均匀化单元）内的空间依赖扩散率。这个过程产生了一个粗略的规模模型近似的原始精细规模模型的解决方案的行为，以减少计算成本。在本文中，我们研究了块非均匀介质中的粗尺度扩散模型，并首次研究了各种因素对粗尺度解精度的影响。我们提出了新的发现与均匀化的错误，以及确认通过数值实验，周期性的边界条件是最好的选择的均匀化细胞，并证明，最小的均匀化细胞，计算上可行的，应在数值模拟中使用。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
