时间分数输运模型在表现记忆效应的二维非均匀介质计算均匀化中的应用
The use of a time-fractional transport model for performing computational homogenisation of 2D heterogeneous media exhibiting memory effects
摘要：
在这项工作中，一个二维的时间分数次扩散模型的发展，以调查的基本输运现象演变的二元介质中的两个子域所占据的均匀材料。我们利用非结构化网格控制体积的方法来验证模型对派生的半解析解的一类两层问题。这种广义的传输模型，然后使用各种二维非均质多孔介质进行计算均匀化。我们的工作的一个关键贡献是扩展经典的均匀化理论，以适应新的框架，并表明，有效的扩散张量可以计算，一旦细胞的问题达到稳态在微观尺度。我们通过一系列著名的测试问题验证了二元介质的理论，然后研究具有表现出分子弛豫（记忆）效应的夹杂物的介质。最后，我们应用广义运输模型来估计从环境扫描电子显微镜（ESEM）图像云杉木材和澳大利亚硬木的细胞结构上的束缚水扩散系数张量。我们的工作的一个亮点是，计算的扩散系数与分子弛豫的非均匀介质是完全不同的经典扩散的情况下，在稳态的记忆效应的材料占主导地位。
英文摘要：
In this work, a two-dimensional time-fractional subdiffusion model is developed to investigate the underlying transport phenomena evolving in a binary medium comprised of two sub-domains occupied by homogeneous material. We utilise an unstructured mesh control volume method to validate the model against a derived semi-analytical solution for a class of two-layered problems. This generalised transport model is then used to perform computational homogenisation on various two-dimensional heterogenous porous media. A key contribution of our work is to extend the classical homogenisation theory to accommodate the new framework and show that the effective diffusivity tensor can be computed once the cell problems reach steady state at the microscopic scale. We verify the theory for binary media via a series of well-known test problems and then investigate media having inclusions that exhibit a molecular relaxation (memory) effect. Finally, we apply the generalised transport model to estimate the bound water diffusivity tensor on cellular structures obtained from environmental scanning electron microscope (ESEM) images for Spruce wood and Australian hardwood. A highlight of our work is that the computed diffusivity for the heterogeneous media with molecular relaxation is quite different from the classical diffusion cases, being dominated at steady-state by the material with memory effects.
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