Weak scalability analysis of GPGPU-based iterative solvers in a two-phase pore-scale flow simulator

Abstract

Summary Direct numerical simulation of two-phase flow at the pore scale is computationally challenging due to high requirements on physical fidelity and because of the spatial resolution necessary to accurately represent pore geometries. In this paper, we explore how GPGPU-accelerated iterative linear solvers can help to make these simulations feasible in workflows such as relative permeability estimation. Our target application is a Cahn-Hilliard-Navier-Stokes solver that uses a discontinuous Galerkin discretization in space and an implicit discretization in time. The performance bottleneck of the application is the solution of sparse linear systems in each time step. We evaluate and compare the performance of a CPU-based iterative solver from the Trilinos package and its GPGPU-accelerated counterpart from the AMGX package. In simulations with realistic porous rock geometries, we demonstrate that the weak scalability of the two solvers are comparable. At the same time, the GPGPU-accelerated solvers are approximately forty times faster on our multi-GPGPU compute nodes, resulting in more than a four-fold speedup of the overall simulation. Our results show that GPGPUs can improve parallel efficiency in pore-scale flow simulations, and they can help to make larger simulations feasible.