Adaptive simulations of two-phase flow by discontinuous Galerkin methods

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 1-3, 2006, Pages 404-419

  Klieber, W ^a   Riviere B ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Adaptive time stepping; Discontinuous Galerkin; Error indicators; Five spot; IIPG; NIPG; OBB; SIPG; Slope limiters

Indexed keywords

COMPUTER SIMULATION; ERROR ANALYSIS; GALERKIN METHODS; NUMERICAL METHODS; PRESSURE MEASUREMENT;

ADAPTIVE SIMULATIONS; ADAPTIVE TIME STEPPING; DISCONTINUOUS GALERKIN METHODS; SLOPE LIMITERS;

TWO PHASE FLOW;

COMPUTER SIMULATION; ERROR ANALYSIS; GALERKIN METHODS; NUMERICAL METHODS; PRESSURE MEASUREMENT; TWO PHASE FLOW;

EID: 33846524895     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.05.007     Document Type: Article

References (27)

1. Arnold D.N. An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19 (1982) 742-760
2. P. Bastian, High order discontinuous Galerkin methods for flow and transport in porous media, Challenges in Scientific Computing CISC 2002, vol. 35, 2003.
3. P. Bastian, Discontinuous Galerkin methods for two-phase flow in porous media, Also technical report, 2004-28, IWR (SFB 359), Heidelberg University, submitted for publication.
4. B. Rivière, Numerical study of a discontinuous Galerkin method for incompressible two-phase flow, in: Proceedings of ECCOMAS, 2004.
5. Brooks R.H., and Corey A.T. Hydraulic properties of porous media. Hydrol. Pap. 3 (1964)
6. Chavent G., and Jaffré J. Mathematical Models and Finite Elements for Reservoir Simulation (1986), North-Holland
7. Cockburn B., and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservative laws II: general framework. Math. Comput. 52 (1989) 411-435
8. Cockburn B., and Shu C.-W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35 (1998) 2440-2463
9. Dawson C., Sun S., and Wheeler M.F. Compatible algorithms for coupled flow and transport. Comput. Meth. Appl. Mech. Engrg. 193 (2004) 2565-2580
10. Durlofsky L.J., Engquist B., and Osher S. Triangle based adaptive stencils for the solution of hyperbolic conservation laws. J. Comput. Phys. 98 (1992) 64-73
11. Y. Epshteyn, B. Rivière, Fully implicit discontinuous Galerkin schemes for multiphase flow, Appl. Numer. Math., in press.
12. Ern A., and Proft J. A posteriori discontinuous Galerkin error estimates for transient convection-diffusion equations. Appl. Math. Lett. 18 7 (2005) 833-841
13. O. Eslinger, Discontinuous Galerkin finite element methods applied to two-phase, air-water flow problems, Ph.D. thesis, The University of Texas at Austin, 2005.
14. Helmig R. Multiphase Flow and Transport Processes in the Subsurface (1997), Springer
15. Hoteit H., Ackerer Ph., Mosé R., Erhel J., and Philippe B. New two-dimensional slope limiters for discontinuous Galerkin methods on arbitrary meshes. Int. J. Numer. Meth. Engrg. 61 (2004) 2566-2593
16. Durlofsky L.J. Accuracy of mixed and control volume finite element approximations to Darcy velocity and related quantities. Water Resour. Res. 30 4 (1994) 965-973
17. Nayagum D., Schäfer G., and Mosé R. Modelling two-phase incompressible flow in porous media using mixed hybrid and discontinuous finite elements. Comput. Geosci. 8 1 (2004) 49-73
18. Oden J.T., Babuška I., and Baumann C.E. A discontinuous hp finite element method for diffusion problems. J. Comput. Phys. 146 (1998) 491-519
19. B. Rivière, The dgimpes model in ipars: Discontinuous Galerkin for two-phase flow integrated in a reservoir simulator framework, Technical Report 02-29, Texas Institute for Computational and Applied Mathematics, 2002.
20. Rivière B., and Jenkins E. In pursuit of better models and simulations, oil industry looks to the math sciences. SIAM News January/February (2002)
21. Rivière B., and Wheeler M.F. Discontinuous Galerkin methods for flow and transport problems in porous media. Commun. Numer. Meth. Engrg. 18 (2002) 63-68
22. B. Rivière, M.F. Wheeler, Non conforming methods for transport with nonlinear reaction, in: Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment, 2002.
23. Rivière B., Wheeler M.F., and Girault V. Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I. Comput. Geosci. 3 (1999) 337-360
24. S. Sun, B. Rivière, M.F. Wheeler, A combined mixed finite element and discontinuous Galerkin method for miscible displacement problems porous media, in: Proceedings of International Symposium on Computational and Applied PDEs, 2002, pp. 321-348.
25. Sun S., and Wheeler M.F. Symmetric and non-symmetric discontinuous Galerkin methods for reactive transport in porous media. SIAM J. Numer. Anal. 43 1 (2005) 195-219
26. Sun S., and Wheeler M.F. Symmetric and nonsymmetric discontinuous Galerkin methods for reactive transport in porous media. SIAM J. Numer. Anal. 43 1 (2005) 195-219
27. Wheeler M.F. An elliptic collocation-finite element method with interior penalties. SIAM J. Numer. Anal. 15 1 (1978) 152-161