摘要
•A new algorithm to simulate viscous flow through a three-dimensional Cartesian representation of a porous space is proposed.•The method adds Tikhonov regularization to finite difference techniques to find a solution with enforced fluid incompressibility.•Tests performed using synthetic and real sandstone samples show good agreement with established finite volume technique and experimental/theoretical values.•The new technique is used in conjunction with level set methods to estimate relative permeability curves.