We propose an efficient numerical strategy for solving non-linear parabolic problems defined in a heterogeneous porous medium. This scheme is based on the classical homogenization theory and uses a locally mass-conservative formulation at different scales. In addition, we discuss some properties of the proposed non-linear solvers and use an error indicator to perform a local mesh refinement. The main idea is to compute the effective parameters in such a way that the computational complexity is reduced but preserving the accuracy. We illustrate the behavior of the homogenization scheme and of the non-linear solvers by performing two numerical tests. We consider both a quasi-periodic example and a problem involving strong heterogeneities in a non-periodic medium.

我们提出了一种解决非均质多孔介质中定义的非线性抛物线问题的有效数值策略。该方案基于经典的均质化理论，并使用了不同规模的局部质量保守配方。另外，我们讨论了所提出的非线性求解器的一些特性，并使用误差指示器来执行局部网格细化。主要思想是以减少计算复杂度但保留精度的方式来计算有效参数。通过执行两个数值测试，我们说明了均化方案和非线性求解器的行为。我们既考虑准周期示例，也考虑涉及非周期介质中强异质性的问题。