A velocity-vorticity method for highly viscous 3D flows with application to digital rock physics

In this article, we present a numerical iterative method for the solution of internal viscous and incompressible flows in real porous three-dimensional bodies at their pore scale. We use penalized formulation problem involving velocity vorticity: an operator splitting allows to split apart diffusion (inherited from Stokes equation) penalization phenomena (which takes into account solid matrix). By means analysis splitting, exhibit coefficient which is actually effective. This deal only with fast-evaluation operators, that say scaling most as O(nlog⁡n) where n number underlying grid points, such straightforward computations finite differences schemes or FFT solver. The implementation solutions are presented, validated on various digital rock physics geometries acquired by micro-tomography, using physical diagnostics. To enforce validation, also permeability estimations several samples. simulation transport passive active scalars finally investigated order perform practical upscaling 1D models Darcy