A discontinuous galerkin method for gravity-driven viscous fingering instabilities in porous media

Journal of Computational Physics

Volumn 233, Issue 1, 2013, Pages 373-399

  Scovazzi, G ^a   Gerstenberger, A ^b   Collis, S S ^b  

^a Duke University   (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Discontinuous Galerkin method; Gravity driven flows; Porous media flows; Viscous fingering

Indexed keywords

GALERKIN METHODS; HYDROGEOLOGY; POROUS MATERIALS;

CARBON SEQUESTRATION; DISCONTINOUS GALERKIN METHODS; FINGERING INSTABILITIES; GRAVITY DRIVEN FLOW; KEY FEATURE; NEW APPROACHES; POROUS MEDIUM; POROUS MEDIUM FLOW; SEQUESTRATION PROCESS; VISCOUS FINGERING;

AQUIFERS;

EID: 85027940324     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.09.003     Document Type: Article

References (37)

1. D.N. Arnold, F. Brezzi, B. Cockburn, L.D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM Journal on Numerical Analysis 39 (2002) 1749-1779.
2. F. Brezzi, L.D. Marini, E. Süli, Discontinuous Galerkin methods for first-order hyperbolic problems, Mathematical Models and Methods in Applied Sciences 14 (2004) 1893-1903.
3. B. Cockburn, C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems, SIAM Journal on Numerical Analysis 35 (1998) 2440-2463.
4. J. Douglas, D. Frìas, N. Henderson, F. Pereira, Simulation of single-phase multicomponent flow problems in gas reservoirs by Eulerian-Lagrangian techniques, Transport in Porous Media 50 (2002) 307-342.
5. J. Droniou, R. Eymard, T. Gallouët, R. Herbin, A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods, Mathematical Models and Methods in Applied Sciences 20 (2010) 1-31.
6. J.P. Ennis-King, I. Preston, L. Paterson, Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions, SPE Journal 17 (2005) 349-356.
7. A. Ern, I. Mozolevski, Discontinuous Galerkin method for two-component liquid-gas porous media flows, Computational Geosciences 16 (2012) 677-690.
8. A. Ern, I. Mozolevski, L. Schuh, Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures, Computer Methods in Applied Mechanics and Engineering 199 (2010) 1491-1501.
9. A. Ern, A.F. Stephansen, P. Zunino, A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally vanishing and anisotrpic diffusivity, IMA Journal on Numerical Analysis 29 (2009) 235-256.
10. V. Girault, S. Sun, M.F. Wheeler, I. Yotov, Coupling discontinuous Galerkin and mixed finite element discretizations using mortar finite elements, SIAM Journal on Numerical Analysis 46 (2008) 949-979.
11. J. Gounot, J.P. Caltagirone, Stabilitë et convection naturelle au sein d'une couche poreuse non homogëne, International Journal of Heat and Mass Transfer 32 (1989) 1131-1140.
12. J.J. Hidalgo, J. Carrera, Effect of dispersion on the onset of convection during CO2 sequestration, Journal of Fluid Mechanics 640 (2009) 441-452.
13. J.J. Hidalgo, J. Carrera, A. Medina, Role of salt sources in density-dependent flow, Water Resources Research 45 (2009) W05503.
14. H. Hoteit, A. Firoozabadi, Multicomponent fluid flow by discontinuous Galerkin and mixed methods in unfractured and fractured media, Advances in Water Resources 41 (2005) W11412.
15. K. Johannsen, On the validity of the Boussinesq approximation for the Elder problem, Computational Geosciences 7 (2003) 169-182.
16. J. Douglas Jr., T. Dupont, Interior penalty procedures for elliptic and parabolic Galerkin methods, Lecture Notes in Physics, vol. 58, Springer-Verlag, Berlin, 1976.
17. A. Landman, R. Schotting, Heat and brine transport in porous media: the Oberbeck-Boussinesq approximation revisited, Transport in Porous Media 70 (2007) 355-373.
18. R. Liu, M.F. Wheeler, C.N. Dawson, R.H. Dean, Modeling of convection-dominated thermoporomechanics problems using incomplete interior penalty Galerkin method, Computer Methods in Applied Mechanics and Engineering 198 (2009) 912-919.
19. R. Liu, M.F. Wheeler, C.N. Dawson, R.H. Dean, On a coupled discontinuous/continuous Galerkin framework and an adaptive penalty scheme for poroelasticity problems, Computer Methods in Applied Mechanics and Engineering 198 (2009) 3499-3510.
20. G.S.H. Pau, A.S. Almgren, J.B. Bell, M.J. Lijewski, A parallel second-order adaptive mesh algorithm for incompressible flow in porous media, Phil. Trans. R. Soc. A 367 (2009) 4633-4654.
21. G.S.H. Pau, J.B. Bell, K. Pruess, A.S. Almgren, M.J. Lijewski, K. Zhang, C. Yang, Y. Gu, High-resolution simulation and characterization of density-driven flow in CO2 storage in saline aquifers, Advances in Water Resources 33 (2010) 443-455.
22. P.J. Phillips, M.F. Wheeler, A coupling of mixed and discontinuous Galerkin finite-element methods for poroelasticity, Computational Geosciences 12 (2008) 417-435.
23. A. Riaz, M. Hesse, H.A. Tchelepi, F.M. Orr, Onset of convection in a gravitationally unstable diffusive boundary layer in porous media, Journal of Fluid Mechanics 548 (2006) 87-111.
24. G.R. Richter, The discontinuous Galerkin method with diffusion, Mathematics of Computation 58 (1992) 631-643.
25. B. Rivière, M.F. Wheeler, Discontinuous Galerkin methods for flow and transport problems in porous media, Communications in Numerical Methods in Engineering 18 (2002) 63-68.
26. B. Rivière, M.F. Wheeler, K. Banas, Part II. Discontinuous Galerkin method applied to a single phase flow in porous media, Computational Geosciences 4 (2000) 337-349.
27. B. Rivière, M.F. Wheeler, V. Girault, Elliptic collocation-finite element method with interior penalties, SIAM Journal on Numerical Analysis 15 (1978) 152-161.
28. B. Rivière, M.F. Wheeler, V. Girault, Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I, Computational Geosciences 3 (1999) 337-360.
29. B. Rivière, M.F. Wheeler, V. Girault, A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems, SIAM Journal on Numerical Analysis 39 (2001) 902-931.
30. C. Siefert, R. Tuminaro, A. Gerstenberger, G. Scovazzi, S.S. Collis, Algebraic Multigrid techniques for Discontinuous Galerkin Methods with varying polynomial order. Computational Geosciences, submitted for publication.
31. S. Sun, M.F. Wheeler, Anisotropic and dynamic mesh adaptation for discontinuous Galerkin methods applied to reactive transport, Computer Methods in Applied Mechanics and Engineering 195 (2006) 3382-3405.
32. S. Sun, M.F. Wheeler, Local problem-based a posteriori error estimators for discontinuous Galerkin approximations of reactive transport, Computers and Mathematics with Applications 52 (2006) 637-650.
33. S. Sun, M.F. Wheeler, Discontinuous Galerkin methods for simulating bioreactive transport of viruses in porous media, Advances in Water Resources 30 (2007) 1696-1710.
34. S. Sun, M.F. Wheeler, Local problem-based a posteriori error estimators for discontinuous Galerkin approximations of reactive transport, Computational Geosciences 11 (2007) 87-101.
35. S.Y. Sun, M.F. Wheeler, Symmetric and nonsymmetric discontinuous Galerkin methods for reactive transport in porous media, SIAM Journal on Numerical Analysis 43 (2005) 195-219.
36. S.Y. Sun, M.F. Wheeler, A posteriori error estimation and dynamic adaptivity for symmetric discontinuous Galerkin approximations of reactive transport problems, Computer Methods in Applied Mechanics and Engineering 195 (2006) 632-652.
37. X. Xu, S. Chen, D. Zhang, Convective stability analysis of the long-term storage of carbon dioxide in deep saline aquifers, Advances in Water Resources 29 (2006) 397-407.