GMRES based numerical simulation and parallel implementation of multicomponent multiphase flow in porous media

• Main Authors: Saltanbek T. Mukhambetzhanov, Danil V. Lebedev, Nurislam M. Kassymbek, Timur S. Imankulov, Bazargul Matkerim, Darkhan Zh. Akhmed-Zaki
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2020-01-01
• Series: Cogent Engineering
• Subjects: multicomponent multiphase flow; newton-raphson method; gmres; mpi technology
• Online Access: http://dx.doi.org/10.1080/23311916.2020.1785189

This article considered the numerical simulation of multicomponent multiphase flow in porous media. The resulting system of nonlinear equations linearized by the Newton-Raphson method and solved with the iterative Generalized minimal residual method (GMRES) algorithm. To achieve better convergence, we used the ILU(0) preconditioner to the GMRES algorithm. As a result, we used a completely implicit scheme called the Newton-ILU0-GMRES algorithm to solve the problem of interest. Based on the obtained sequential algorithm, we implemented a parallel algorithm using Message Passing Interface (MPI) technology. Additionally, we made comparisons between the parallel program of the presented algorithm and the parallel program using the ready-made Portable Extensible Toolkit for Scientific Computation (PETSc) library. We developed an MPI parallel algorithm and tested it on the MVS-10P supercomputer of the Interdepartmental Supercomputer Center of the Russian Academy of Sciences.