Li, Wenjun; Chen, Zhangxin; Ewing, Richard E.; Huan, Guanren; Li, Baoyan Comparison of the GMRES and ORTHOMIN for the black oil model in porous media. (English) Zbl 1067.76069 Int. J. Numer. Methods Fluids 48, No. 5, 501-519 (2005). Summary: This paper deals with the application of GMRES algorithm to a three-dimensional, three-phase black oil model used in petroleum reservoir simulation. Comparisons between the GMRES and ORTHOMIN algorithms in terms of storage and total flops per restart step are given. Numerical results show that the GMRES is faster than the ORTHOMIN for large-scale simulation problems. The GMRES uses only as much as 63% of the CPU time of the ORTHOMIN for some of the problems tested. MSC: 76M20 Finite difference methods applied to problems in fluid mechanics 76S05 Flows in porous media; filtration; seepage 65F10 Iterative numerical methods for linear systems 86A05 Hydrology, hydrography, oceanography 76-04 Software, source code, etc. for problems pertaining to fluid mechanics Keywords:ILU preconditioner PDFBibTeX XMLCite \textit{W. Li} et al., Int. J. Numer. Methods Fluids 48, No. 5, 501--519 (2005; Zbl 1067.76069) Full Text: DOI References: [1] ORTHOMIN, an iterative method for solving sparse sets of simultaneous linear equations. Proceedings of the Fourth Symposium on Reservoir Simulations, Society of Petroleum Engineers of AIME, 1976; 149-157. [2] Saad, SIAM Journal on Science, Statistics and Computation 7 pp 856– (1986) [3] Choquet, International Journal for Numerical Methods in Fluids 23 pp 177– (1996) [4] Saad, SIAM Journal on Science, Statistics and Computation 14 pp 461– (1993) [5] Matrix Computations. Johns Hopkins University Press: Baltimore, London, 1983. · Zbl 0559.65011 [6] Dynamics of Fluids in Porous Media. Dover: New York, 1972. · Zbl 1191.76001 [7] Chen, SIAM Journal on Numerical Analysis 38 pp 489– (2000) [8] Li, Advances in Water Resources 27 pp 99– (2004) [9] Interpretation of well-block pressures in numerical reservoir simulation. SPE 6893, 52nd Annual Fall Technical Conference and Exhibition, Denver, 1977. [10] Control volume function approximation method for the black oil model. Proceedings of the 2nd Meeting on Reservoir Simulation, Universidad Argentina de la Empresa, Buenos Aires, Argentina, 5-6 November 2002, CD-ROM. [11] SGI, Origin 2000 and Onyx2 performance tuning and optimization guide. SGI Document Number 007-3430-003. [12] Odeh, Journal of Petroleum Technology January pp 13– (1981) [13] Weinstein, Journal of Petroleum Technology March pp 345– (1986) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.