WATCH VIDEOThe simulation of multi-phase flow at the pore scale has important applications in hydrocarbon recovery, including the estimation of relative permeabilities and capillary pressure. Accurate simulations with advanced numerical methods, such as discontinuous Galerkin (DG) methods, are computationally demanding, and the feasibility of such simulations often depends on the availability of scalable iterative linear solvers. In this presentation, we show how multigrid methods can accelerate the solution of linear systems in DG discretizations of two-phase flow in complex pore geometries. We discuss the hybrid-parallel implementation of a combined p-multigrid and algebraic multigrid method and evaluate its computational performance in numerical experiments with pore-scale flow simulations in rock samples. We demonstrate speedups of up to 15.4x compared to a Jacobi-preconditioned conjugate gradient solver, resulting in speedups of up to 2.2x for the overall simulation.
