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.

多孔介质中的矿物沉淀和溶解过程可能会在孔隙尺度上改变介质的结构。这种变化使数值模拟成为一项艰巨的任务，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，我们在这里采用两尺度相场模型，并提出了一种用于解决方案的数值逼近的鲁棒方案。该方案考虑了模型中的比例分离以及模型的非线性特征。在证明了该方案的收敛性之后，采用了一种自适应两尺度策略，从而提高了仿真效率。进行了数值测试，显示了在存在各向异性和异质性的情况下该方案的效率和准确性。