多孔介质中沉淀溶解相场模型的自适应多尺度迭代格式
An adaptive multi-scale iterative scheme for a phase-field model for precipitation and dissolution in porous media
摘要：
矿物在多孔介质中的沉淀和溶解过程可以改变介质在孔隙尺度上的结构。这种变化使得数值模拟成为一项具有挑战性的任务，因为孔的几何形状以先验未知的方式随时间变化。为了处理这些方面，我们在这里采用了双尺度相场模型，并提出了一个强大的方案的解决方案的数值逼近。该方案既考虑了模型中的尺度分离，又考虑了模型的非线性特征。在证明了格式的收敛性后，引入了自适应双尺度策略，提高了仿真效率。数值试验表明，在各向异性和非均匀性的存在下，该方案的效率和精度。
英文摘要：
Mineral precipitation and dissolution processes in a porous medium can alter the structure of the medium at the scale of pores. Such changes make numerical simulations a challenging task as the geometry of the pores changes in time in an apriori unknown manner. To deal with such aspects, we here adopt a two-scale phase-field model, and propose a robust scheme for the numerical approximation of the solution. The scheme takes into account both the scale separation in the model, as well as the non-linear character of the model. After proving the convergence of the scheme, an adaptive two-scale strategy is incorporated, which improves the efficiency of the simulations. Numerical tests are presented, showing the efficiency and accuracy of the scheme in the presence of anisotropies and heterogeneities.
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