GMRES Based Numerical Simulation of Multicomponent Multiphase Flow in Porous Media on LuNA Fragmented Programming System

Nurislam Kassymbek, Bazargul Matkerim, Danil V. Lebedev, Timur Imankulov, Darkhan Akhmed-Zaki

2020

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DOI 10.3997/2214-4609.202035201
Data confidence 85 high
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Abstract

Summary Using supercomputers can significantly accelerate the solution of problems when using numerical methods. One of these tasks is forecasting oil and gas production at specific oil and gas fields. Modeling of multicomponent multiphase fluid (oil and gas) flow in porous media (in oil reservoirs) is relevant and at the same time complex problem of hydrodynamic simulation. To solve such problems, various methods and schemes are used, some of whom are iterative methods for solving linear systems. In this paper, we solve the equation system with the Newton-Raphson method, within each iteration of which the algebraic equation system is solved by the generalized minimal residual method (GMRES) with the ILU(0) preconditioner. The application of this problem which is named Newton-ILU(0)-GMRES method is implemented in parallel with MPI and Fragmented Programming (FP) Technology, which is aimed at automation of implementation of numerical applications for multicomputers. As in other numerical methods, in our case is a non-degenerate matrix. Storage of a full matrix with all zero elements leads to huge memory costs. In order to optimize the memory, the format of storage of sparse matrices was chosen – compressed row storage (CSR). Tested the developed MPI parallel application and fragmented program on the MVS-10P supercomputer of the Interdepartmental Supercomputer Center of the Russian Academy of Sciences. The runtime between the MPI parallel program and the fragmented program in the LuNA system is compared and the results were analyzed. The work was supported by Funding Science committee of Ministry of Education and Science of Kazakhstan, grant no. AP05134651.