A multiscale fractured-porous medium has several hierarchical levels of heterogeneity and consists of a connected network of fractures and of a periodic system of low permeable blocks, each of them also consisting of smaller fractures and smaller blocks. Repeating this procedure n times, we obtain a fractured-porous medium having n scales. The numerical simulation of a fluid flow in such a medium is impossible due to the need to use a very fine numerical grid. To reduce the number of numerical cells, we suggest applying irregular grids based on the technology of quadtrees. We perform numerical simulations of an example of flow in a four-scale medium and compare with the results obtained by using regular grids, as well as with averaged model of the process. We introduced a quantitative criterion that enables us to identify which cells should be refined or not. This gave us the opportunity to formalize the procedure for constructing a quadtree and embed it in the Basilisk platform.

多尺度裂缝-多孔介质具有多个层次的非均质性，由连通的裂缝网络和低渗透区块的周期性系统组成，每个低渗透区块也由较小的裂缝和较小的区块组成。重复这个过程n次，我们得到一个裂隙多孔介质，具有n秤。由于需要使用非常精细的数值网格，因此不可能对这种介质中的流体流动进行数值模拟。为了减少数值单元格的数量，我们建议应用基于四叉树技术的不规则网格。我们对四尺度介质中的流动实例进行数值模拟，并与使用规则网格获得的结果以及过程的平均模型进行比较。我们引入了一个定量标准，使我们能够确定哪些单元格应该被改进。这让我们有机会将构建四叉树的过程正式化并将其嵌入 Basilisk 平台。