The finite-element method is one of the most general numerical techniques for solving PDEs, and therefore a viable option for streamline-scale modeling in porous materials. It has a number of advantages, including its direct link to the original PDEs, adaptability to complex geometries, ability to handle local grid refinement, and ability to handle a variety of physical phenomena. It's main disadvantage is the associated mesh generation step, which becomes an especially intimidating problem in the complex void structures found in porous media.

For many problems, the above-mentioned pros outweigh the cons. Hence, we are investing significant efforts into FEM-based streamline-scale modeling. The top set of pictures shows the behavior of a yield-stress polymer in a single axisymmetric pore throat under increasing stress. Mesh generation is not a problem in this simple geometry, and FEM is a good approach because of the extensive body of research on non-Newtonian flows by the FEM community. To begin moving toward more general streamline-scale models, we have developed a fast, automated, and robust algorithm for meshing arbitrary pore structures. The bottom graphic shows a 3D tetrahedral mesh of the pore space in a simulated sandstone.