Parallel Non-Conforming Finite Element Technique for Mathematical Simulation of Fluid Flow in Multiscale Porous Media

We consider the three-dimensional steady-state incompressible fluid flow problem in a heterogeneous porous medium using the framework of the Newtonian rheology. The Stokes-Darcy equations are applied as a mathematical model of the mentioned physical process with the Biver-Joseph-Suffman interface conjugation conditions. For spatial approximation of the mathematical model, computational schemes of non-conforming finite element methods based on the discontinuous Galerkin technique are chosen. This approach allows one to use inconsistent macroscale mesh partitions and to satisfy the “inf-sup”-conditions when the Stokes-Darcy problem is solved. We proposed to apply the domain decomposition method based on the modified Schwartz procedure, which allows realizing a parallel computational algorithm. The effectiveness of the developed algorithms is shown by solving the fluid flow problem in the channels and pores of a geological rock. A three-dimensional geometric model of the geological rock is built using the results of computer tomography of cores.