New optimization approach to multiphase flow

Journal of Optimization Theory and Applications

Volumn 111, Issue 3, 2001, Pages 473-488

  Kearsley, A J ^a   Cowsar, L C ^b   Glowinski, R ^c   Wheeler, M F ^d   Yotov, I ^e  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b NOKIA RESEARCH CENTER   (United States)

^c University of Houston   (United States)

^d UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^e UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Cell centered finite differences; Mixed methods; Multiphase flow

Indexed keywords

FINITE ELEMENT METHOD; MULTIPHASE FLOW; NEWTON-RAPHSON METHOD; NONLINEAR EQUATIONS; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS;

CELL-CENTERED FINITE DIFFERENCES; COUPLED SYSTEMS; MIXED FINITE ELEMENT METHODS; MIXED METHOD; MULTIPHASE FLOW IN POROUS MEDIAS; OPTIMIZATION APPROACH; OPTIMIZATION FORMULATIONS; SPATIAL DISCRETIZATIONS; TIME DISCRETIZATION; UNCONDITIONALLY STABLE;

POROUS MATERIALS;

EID: 0035527942     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1012689626027     Document Type: Article

References (23)

1. 1. AZIZ, K., and SETTARI, A., Petroleum Reservoir Simulation, Applied Science Publishers, London, England, 1979.
2. 2. CHAVENT, G., and JAFFRE, J., Mathematical Models and Finite Elements for Reservoir Simulation, North-Holland, Amsterdam, Holland, 1986.
3. 3. WHEELER, M. F., ROBERSON, K. R., and CHILAKAPATI, A., Three-Dimensional Bioremediation Modeling in Heterogeneous Porous Media, Mathematical Modeling in Water Resources, Edited by T. F. Russel, R. E. Ewing, C. A. Brebbia, W. G. Gray, and G. F. Pinder, Computational Mechanics Publications, Southampton, England, Vol. 2, pp. 299-315, 1992.
4. 4. KOEBBE, J., A Computationally Efficient Modification of Mixed Finite-Element Methods for Flow Problems with Full Transmissivity Tensors, Numerical Methods for Partial Differential Equations, Vol. 9, pp. 339-355, 1993.
5. 5. CHEN, Z., Expanded Mixed Finite-Element Methods for Linear Second-Order Elliptic Problems, I, Technical Report 1219, Institute for Mathematics and Its Applications, University of Minnesota, 1994.
6. 6. ARBOGAST, T., WHEELER, M. F., and YOTOV, I., Mixed Finite Elements for Elliptic Problems with Tensor Coefficients as Cell-Centered Finite Differences, SIAM Journal on Numerical Analysis, Vol. 34, pp. 828-852, 1997.
7. 7. YOTOV, I., Mixed Finite-Element Methods for Flow in Porous Media, PhD Thesis, Rice University, 1996.
8. 8. RUSSEL, T. F., and WHEELER, M. F., Finite-Element and Finite-Difference Methods for Continuous Flows in Porous Media, Mathematics of Reservoir Simulation, Edited by R. E. Ewing, SIAM, Philadelphia, Pennsylvania, pp. 35-106, 1983.
9. 9. BREZZI, F., and FORTIN, M., Mixed and Hybrid Finite-Element Methods, Springer Verlag, New York, NY, 1991.
10. 10. RAVIART, P. A., and THOMAS, J. M., A Mixed Finite-Element Method for Second-Order Elliptic Problems, Finite-Element Methods, Edited by I. Galligani and E. Magenes, Lecture Notes in Mathematics, Springer Verlag, Berlin, Germany, Vol. 606, pp. 292-315, 1977.
11. 11. ARBOGAST, T., DAWSON, C. N., KEENAN, P. T., WHEELER, M. F., and YOTOV, I., Enhanced Cell-Centered Finite Differences for Elliptic Equations on General Geometry, SIAM Journal on Scientific and Statistical Computing, Vol. 19, pp. 404-425, 1997.
12. 12. MATTAX, C., and DALTON, R., Reservior Simulation, Society of Petroleum Engineers, Monograph Series, Vol. 13, 1990.
13. 13. PEACEMAN, D. W., Interpretation of Well-Block Pressures in Numerical Reservoir Simulation, Society of Petroleum Engineers Journal, pp. 183-194, 1978.
14. 14. DENNIS, J. E., Jr., and SCHNABEL, R. B., Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1983.
15. 15. ANONYMOUS, Part 3 Library: Mathematical Subroutine Library, ATT Bell Laboratories, Murray Hill, New Jersey, 1984.
16. 16. DENNIS, J. E., GAY, D. M., and WELSCH, R. E., An Adaptive Nonlinear Least-Squares Algorithm, ACM Transactions on Mathematical Software, Vol. 7, pp. 348-368, 1981.
17. 17. DENNIS, J. E., GAY, D. M., and WELSCH, R. E., Algorithm 573: NL2SOL, An Adaptive Nonlinear Least-Squares Algorithm, ACM Transactions on Mathematical Software, Vol. 7, pp. 369-383, 1981.
18. 18. GAY, D. M., Computing Optimal Locally Constrained Steps, SIAM Journal on Scientific and Statistical Computing, Vol. 2, pp. 186-197, 1981.
19. 19. BROYDEN, C. G., The Convergence of a Class of Double-Rank Minimization Algorithms, Journal of the Institute of Mathematics and Its Applications, Vol. 6, pp. 76-90, 1970.
20. 20. FLETCHER, R., A New Approach to Variable-Metric Algorithms, Computer Journal, Vol. 13, pp. 317-322, 1970.
21. 21. GOLDFARB, D., A Family of Variable-Metric Methods Derived by Variational Means, Mathematics of Computation, Vol. 30, pp. 23-26, 1970.
22. 22. SHANNO, D. F., Conditioning of Quasi-Newton Methods for Function Minimization, Mathematics of Computation, Vol. 24, pp. 647-657, 1970.
23. 23. GAY, D. M., Algorithm 611: Subroutines for Unconstrained Minimization Using a Model Trust-Region Approach, ACM Transactions on Mathematical Software, Vol. 9, pp. 503-524, 1983.