Vector/parallel implementation of a porous media flow code
Authors: 
R. Ewing, 
P. O'Leary, J. SochackiAuthors Info & Claims
Pages 294 - 303
References
[1]
B.L. Darlow, R.E. Ewing, and M.F. Wheeler, Mixed finite element methods for miscible displacement problems in porous media, Proceedings Sixth SPE Symposium on Reservoir Simulation, New Orleans, 1982, 137- 146; and Soc. Pet. Eng. J. 4 (1984), 391-398.
[2]
J. Douglas, Jr., R.E. Ewing, and M.F. Wheeler, The approximation of the pressure by a mixed method in the simulation of miscible displacement, R.A.LR.O. Analyse Numerique 17 (1983), 17-33.
[3]
J. Douglas, Jr., R.E. Ewing, and M.F. Wheeler, A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media, R.A.LR.O. Analyse Numerique 17 (1983), 249-265.
[4]
J. Douglas, Jr. and T.F. Russell, Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J. Numer. Anal., (to appear).
[5]
R.E. Ewing, Problems arising in the modeling of processes for hydrocarbon recovery, Vol. I, Mathematics of Reservoir Simulation (R.E. Ewing, ed.), Research Frontiers in Applied Mathematics, SIAM, Philadelphia, 1984, 3-34.
[6]
R.E. Ewing, R.D. Lazarov, P. Lu, and P.S. Vassilevski, Preconditioning indefinite systems arising from mixed finite element discretization of second-order elliptic systems, Preconditioned Conjugate Gradient Methods, Lecture Notes in Mathematics 1457 (O. Axelsson and L. Kolotilina eds.), Springer Verlag, Berlin, 1990, 28-43.
[7]
R.E. Ewing and T.F. Russell, Efficient timestepping methods for miscible displacement problems in porous media, SIAM J. Numer. Anal. 19 (1982), 1-66.
[8]
R.E. Ewing, T.F. Russell, and M.F. Wheeler, Simulation of miscible displacement using mixed methods and a modified method of characteristics, SPE 12241, Proceedings Seventh SPE Symposium on Reservoir Simulation, San Francisco, November 15-18, 1983, 71-82; SPE Reprint Series 20 Numerical Simulation II, Society of Petroleum Engineers, Dallas; Soc. Pet. Eng. J., (to appear).
[9]
R.E. Ewing, T.F. Russell, and L.C. Young, An anisotropic coaxse-grid dispersion model for heterogeneity and viscous fingering in five-spot miscible displacement that matches experiments and fine-grid simulations, SPE 18~41, Proceedings, Tenth SPE Symposium on Reservoir Simulation, Houston, Texas, February 6-8, 1989, 447-465.
[10]
R.E. Ewing, J. Shen, and j. Wang, Pointdistributed algorithms for second-order elliptic equations in mixed form, (in preparation).
[11]
R.E. Ewing and M.F. Wheeler, Computational aspects of mixed finite element methods, Numerical Methods for Scientific Computing (R.S. Stepleman, ed.), North Holland Publishing Co., 163-172.
[12]
D.W. Peaceman, Fundamentals of Numerical Reservoir Simulation, Elsevier North- Holland, New York, 1977.
[13]
P,A. Raviart and J.M. Thomas, A mixed finite element method for 2nd order elliptic problems, Mathematical Aspects of the Finite Element Method, Rome 1975, Lecture Notes in Mathematics, Springer-Verlag, Heidelberg, 1977.
[14]
T.F. Russell, Finite elements with characteristics for two-component incompressible miscible displacement, SPE 10500, Proceedings Sixth SPE Symposium on Reservoir Simulation, New Orleans, LA, January 1-February 3, 1982.
[15]
T.F. Russell and M.F. Wheeler, Finite element and finite difference methods for continuous flows in porous media, in The Mathematics of Reservoir Simulation (R.E. Ewing, ed.), Society for Industrial and Applied Mathematics, Philadelphia, 1983, 35-106.
[16]
T.F. Russell, M.F. Wheeler, and C. Ckiang, Large-scale simulation of miscible displacement by mixed and characteristic finite element methods, in Mathematical and Computational Methods in Seismic Exploration and Reservoir Modeling (W.E. Fitzgibbon, ed.), Society of Industrial and Applied Mathematics, Philadelphia, 1986, 85-107.
[17]
M.F. Wheeler and R. Gonzalez, Mixed finite element methods for petroleum reservoir engineering problems, Proceedings of the Sixth International Symposium on Computing Methods in Applied Sciences and Engineering (R. Glowinski and J.L. Lions, eds.), North-Holland, Amsterdam, 1984, 639-658.
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