This dissertation concentrates on pore-scale Newtonian fluid flow simulation in three-dimensions. One-component single-phase compressible Navier-Stokes equations are considered as governing equations. Interior penalty discontinuous Galerkin (DG) methods are chosen for numerical discretization. Mass balance equation and momentum balance equations are coupled by fixed-point iteration. The DG methods in this thesis are defined on voxel sets representing the pore space of rock samples at micrometer scale. The methods exhibit optimal convergence and the simulated velocity fields compare well against the ones yielded by analytical solutions for simple geometries. The DG-based simulator also delivers intuitive velocity fields for complex pore geometries.