Optimization of a GMRES-Based Parallel Algorithm for Numerical Simulation of Multicomponent Multiphase Flow in Porous Media

Abstract

Summary The actual task of petroleum geophysics is to solve the problem of multicomponent multiphase flow in a porous medium. At the same time, the development of effective parallel algorithms is an urgent task for modeling processes of this type. For these purposes, the authors carried out the following works. The problem of modeling the movement of a multicomponent multiphase liquid in a porous medium was solved. The equations describing fluid movement were linearized by the Newton-Raphson method and the resulting system of linear equations was solved using the generalized minimal residuals method (GMRES) with the Incomplete Lower-Upper factorization (ILU(0)) preconditioner. As a result, the problem was solved by the developed algorithm called Newton-ILU(0)-GMRES. A parallel program using the MPI standard and a fragmented program in the LuNA language for shared memory systems were developed and implemented. After analyzing the results of the previous work, it was decided to optimize the parallel GMRES algorithm, since the parallel program was not effective enough. Bottlenecks were identified, in particular Arnoldi orthogonalization, which negatively affected the effectiveness of the parallel program. An optimized version of the GMRES parallel algorithm was developed and implemented, which avoids the loss of parallel execution efficiency on Arnoldi orthogonalization. The developed program was tested and the results were analyzed. Comparisons were made with the previous version of the developed method.