Parallel Numerical Solution of Two-Phase Flow in Porous Media On Non-Orthogonal Geometries: a Performance Study Using Different GPU Architectures

Abstract

A parallel numerical model for two phase flow (water and oil) in porous media on nonorthogonal geometries is solved by using different Graphics Processing Unit (GPU) architectures to carry out a comparison of the performance that can be reached by each of them. The mathematical model is based on the mass conservation transformed equations for water and oil phases, which results in two coupled non-linear partial differential equations (PDEs). The Finite Volume Method (FVM) is used to discretize the set of PDEs that govern this problem and the Newton-Raphson method is utilized to linearize and solve them simultaneously. Solution of the linear equations system is computationally expensive and requires a large amount of time as the number of unknowns increases. We take advantage of the current GPUs computing technology for constructing massive parallel numerical algorithms for modeling multi-phase flow in porous media [1, 2]. The construction of the Jacobian is directly done in the GPU, which reduces the information that needs to be exchanged between the CPU (Central Processing Unit) and the GPU. Libraries that include Krylov methods are used and tested. The numerical results indicate until 12x of speed up over a single CPU by applying the GPU parallelism with the different architectures tested in this study (Kepler, Pascal and Turing). Furthermore, this study also tries to identify which of these architectures is the best option according to our computing needs.