Young–Laplace equation-based algorithms for simulating capillary-driven flow have been used in porous media research for more than two decades. However, the lack of a uniform mathematical description hinders a wider application of these algorithms, as well as impede their comparison. After conducting a detailed review of the most important publications in the area, we propose a unified algorithm. This resulting framework is capable of handling four distinct physical situations: drainage and imbibition with either compressible or incompressible displacement fluid. Additionally, there is no restriction regarding the geometry or the initial fluid distribution used. The proposed algorithm can simulate variable or mixed wettability, even for imbibition, which has not already been described in the literature. Finally, at the end of the manuscript, we provide an efficient open-source C + + code for the proposed unified algorithm and also many examples of its use.

用于模拟毛细管驱动流动的基于杨-拉普拉斯方程的算法已在多孔介质研究中使用了二十多年。然而，缺乏统一的数学描述阻碍了这些算法的更广泛应用，也阻碍了它们的比较。在对该领域最重要的出版物进行详细审查后，我们提出了一个统一的算法。由此产生的框架能够处理四种不同的物理情况：用可压缩或不可压缩的置换液进行排水和吸入。此外，对于所使用的几何形状或初始流体分布没有限制。所提出的算法可以模拟可变或混合润湿性，甚至可以模拟吸吸，这在文献中尚未描述。最后，在手稿的最后，我们为所提出的统一算法提供了高效的开源C++代码以及许多其使用示例。