Numerical simulation of wave-induced fluid flow in digitized porous media using a coupled model with Level Set method

In this paper, we develop a unified mathematical model with velocity as the primary variable for modeling the interaction between incompressible fluid and compressible solid. We numerically solve this problem by combining the finite different method with the level set method, which is able to easily capture the dynamic change of the interface between fluid and solid. Additionally, the zero contour of a level set function can represent the interface or boundary smoothly; this smoothness can be taken into account in numerical modeling so as to avoid the staircase boundary in the traditional finite difference method. A modified projection method is developed for solving fluid and solid sub-domain simultaneously. This method is then applied on a digitized 2D section of Berea sandstone. To obtain a level set function of the 2D section, we applied the region-based active contour method to segment the micro-tomography data.