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

TL;DR

This paper introduces a robust interior penalty discontinuous Galerkin method combined with a pressure-correction algorithm to accurately simulate 3D incompressible Navier--Stokes flows for permeability estimation in porous media.

Contribution

It develops a novel numerical framework integrating interior penalty discontinuous Galerkin and pressure-correction for realistic permeability calculations.

Findings

Method is accurate for permeability estimation.

Numerically robust and suitable for real rock samples.

Potential to handle complex porous media problems.

Abstract

Permeability estimation of porous media from direct solving Navier--Stokes equation 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 sample. The proposed method is accurate, numerically robust, and exhibits the potential for tackling realistic problems.