Abstract
This paper describes a way of solving the reservoir simulation pressure equation using multigrid technique. The subroutine MG of four-grid method is presented. The result for 2-D two-phase problem is exactly the same as that of the SOR method and the CPU time is much less than that of the latter one.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Fedorenko, R.P., A relaxation method for solving elliptic difference equation,U.S.S.R. Computational Math, and Math. Phys.,1, 5 (1962), 1092–1096.
Brandt, A., Multi-level adaptive solution to boundary-value problems.,Math. Comp.,31 (1977), 333–390.
Hackbusch, W., Convergence of multi-grid iterations applied to difference equations,Math. Comp.,34 (1980), 425–440.
Studen, K., Multigrid methods: Fundamental algorithms, model problem analysis and applications,Multigrid Methods, Proceedings of the Conference, Koln-Porz (1981).
Aziz, K.,Petroleum Reservoir Simulator, Applied Science Publishers Ltd (1979).
Zhang Hou-qing and Lü Tao, Three-dimensional modelling of bottom water gas reservior and fractional step algorithm,Acta Petrolei Sinica 7, 4 (1986), 83–93. (in Chinese)
Hachbusch, W.,The Multigrid Method, Springer (1985).
Parter, S.V. and D. Kamowitg, A study of multigrid ideas,Science Report of University of Wisconsin-Madison (1984).
Crichlow, H.B.,Modern Reservoir Engineering—A Simulation Approach (1977).
Spalding, D.B.,Numerical Prediction of Flow, Heat Transfer, Turbulence and Combustion, Pergamon Press (1983).
Author information
Authors and Affiliations
Additional information
Communicated by Zhou Guang-jiong
Rights and permissions
About this article
Cite this article
Tian-xiang, C., Tao, L. & Ai-min, L. The multigrid method for reservoir simulation. Appl Math Mech 10, 647–654 (1989). https://doi.org/10.1007/BF02115797
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02115797