An interior penalty discontinuous Galerkin approach for 3D incompressible Navier–Stokes equation for permeability estimation of porous media

Permeability estimation of porous media from directly solving the Navier–Stokes equations has a wide spectrum of applications in petroleum industry. In this paper, we utilize a pressure-correction projection algorithm in conjunction with the interior penalty discontinuous Galerkin scheme for space discretization to build an incompressible Navier–Stokes simulator and to use this simulator to calculate permeability of real rock samples. The proposed method is accurate, numerically robust, and exhibits the potential for tackling realistic problems. •A computational framework is described for computing effective rock properties from simulations at micro-scale.•Robustness of the algorithm is shown for 3D large scale simulations on images of real rock produced by micro-CT scanning.•Validation is done through a series of benchmark problems.