Elimination of adaptive grid interface errors in the discrete cell centered pressure equation

Journal of Computational Physics

Volumn 126, Issue 2, 1996, Pages 356-372

  Edwards, Michael G ^a  

^a The University of Texas at Austin   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ERRORS;

ADAPTIVE GRIDS; DISCRETE CELLS; DISCRETIZATIONS; FINITE-VOLUME; GRID INTERFACES; H-ADAPTIVE; PRESSURE EQUATIONS; RESERVOIR-SIMULATION; TRUNCATION ERRORS; VOLUME CORRECTION;

TWO PHASE FLOW;

EID: 0030191275     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1996.0143     Document Type: Article

References (25)

1. 1. P. Quandalle and P. Besset, "Reduction of Grid Effects Due to Local SubGridding in Simulations Using a Composite Grid," SPE 13527, 1985, in Reservoir Simulation Symposium, Dallas, TX, February 10-13, p. 295.
2. 2. M. G. Edwards, "A Dynamically Adaptive Godunov Scheme for Reservoir Simulation on Large Aspect Ratio Grids," in Proceedings, Conference on Numerical Methods for Fluid Dynamics, Reading Univ., UK, April 7-10, edited by K. W. Morton and M. J. Baines.
3. 3. P. A. Forsyth and P. H. Sammon, "Local Mesh Refinement and Modelling of Faults and Pinchouts," SPE 13534, in Reservoir Simulation Symposium, Dallas, TX, February 10-13, 1985, p. 267.
4. 4. D. U. von Rosenberg, "Local Mesh Refinement for Finite Difference Methods," SPE 10974, 1982 (unpublished).
5. 5. Z. E. Heinemann, "Using Local Grid Refinement in a Multiple-Application Reservoir Simulator," SPE 12255, 1983 (unpublished).
6. 6. D. K. Han, D. L. Han, C. Z. Yan, and L. T. Peng, "A More Flexible Approach of Dynamic Local Grid Refinement for Reservoir Modeling," SPE 16014, 1987 (unpublished).
7. 7. M. L. Wasserman "Local Grid Refinement for Three Dimensional Simulators," SPE 16013, 1987 (unpublished).
8. 8. G. H. Schmidt and F. J. Jacobs, J. Comput. Phys. 77, 140 (1988).
9. 9. E. C. Nacul and K. Aziz, "Efficient Use of Domain Decomposition and Local Grid Refinement in Reservoir Simulation," SPE 20740, 1990 (1990).
10. 10. W. A. Mulder and R. H. J. GmeligMeyling, "Numerical Simulation of Two-Phase Flow Using Locally Refined Grids in Three-Space Dimensions," SPE 21230, 1991 (unpublished).
11. 11. F. X. Deimbacher and Z. E. Heinemann, "Time Dependent Incorporation of Locally Irregular Grids in Large Reservoir Simulation Models," SPE 25260, in Twelfth SPE Reservoir Simulation Symposium, New Orleans, LA, Feb 28-March 3, 1993.
12. 12. M. G. Edwards, "A Dynamically Adaptive Higher Order Godunov Scheme For Reservoir Simulation In Two Dimensions," in 3rd European Conference on the Mathematics of Oil Recovery, Delft University 17-19 June 1992, edited by M. A. Christie, F. V. Da Silva, C. L. Farmer, O. Guillon, Z. E. Heinmann, P. Lemonnier, J. M. M. Regtien, and E. van Spronson, p. 239.
13. 13. M. G. Edwards and M. A. Christie, "Dynamically Adaptive Godunov Schemes With Renormalization for Reservoir Simulation," SPE 25268, in Twelfth SPE Reservoir Simulation Symposium, New Orleans, LA, Feb. 28-Mar. 3, 1993, p. 413.
14. 14. M. G. Edwards, to appear.
15. 15. M. G. Edwards, "A Flux Continuous Approximation of the Pressure Equation for h-Adaptive Grids," in MAFELAP, The Mathematics of Finite Elements and Applications. Brunel, April 93, edited by J. R. Whiteman (Wiley, New York, 1993).
16. 16. L. Demkowicz and J. T. Oden, TICOM Report 88-02, Univ. of Texas, Austin, TX, 1988 (unpublished).
17. 17. K. Aziz and A. Settari, "Petroleum Reservoir Simulation," Elsevier Applied Science, New York.
18. 18. P. Wesseling, "Linear Multigrid Methods" in Multigrid Methods, Frontiers in Applied Mathematics, edited by S. F. McCormick (SIAM, Philadelphia, 1987).
19. 19. H. O. Kreiss, T. A. Manteuffel, B. Swartz, B. Wendroff, and A. B. White, Math. Comput. 47, 537 (1986).
20. 20. A. Weiser and M. F. Wheeler SIAM J. Numer. Anal. 25, 351 (1988).
21. 21. P. A. Forsyth and P. H. Sammon, Appl. Numer. Math. 4, 377 (1988).
22. 22. I. Yotov, M. F. Wheeler, and T. Arbogast, private communication.
23. 23. M. G. Edwards, in preparation.
24. 24. J. B. Bell, P. Colella, and J. A. Trangenstein, J. Comput. Phys. 82, 362 (1989).
25. 25. E. B. Becker, G. F. Carey, and J. T. Oden, Finite Elements an Introduction, Vol. 1 (Prentice-Hall, Englewood Cliffs, NJ, 1981).