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Original Articles

Numerical algorithms for solving problems of multiphase flows in porous media

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Pages 133-148 | Received 04 Mar 2006, Published online: 14 Oct 2010

References

  • Arbogast , T. 2005 . Analysis of a two‐scale, locally conservative subgrid upscaling for elliptic problems . SIAM J. Numer Anal. , 42 (2) : 576 – 598 .
  • Asher , U. , Ruuth , S. and Wetton , B. 1995 . Implicit‐explicit methods for time dependent PDEt's . SIAM J. Numer Anal. , 32 : 797 – 823 .
  • Balaguer , A. and Conde , C. 2006 . Fourth‐order nonoscillatory upwind and central schemes for hyperbolic conservation laws . SIAM J. Numer Anal. , 43 : 455 – 473 .
  • Bastian , P. 1999 . Numerical Computation of Multiphase Flows in Porous Media , Kiel university . Habilitation Dissertation
  • Bastian , P. , Birken , K. , Lang , S. , Johannsen , K. , Neuss , N. , Rentz‐Reichert , H. and Wieners , C. 1997 . UG: A flexible software toolbox for solving PDE . Computing and Vizualization in Science , 1 : 27 – 40 .
  • Bear , J. 1972 . Dynamics of Fluids in Porous Media , New York : Elsevier .
  • Chavent , G. 1976 . A new formulation of diphasic incompressible flow in porous media . Lecture Notes in Mathematics , 503
  • Chen , Y. , Durlofsky , L.J. , Gerritsen , M. and Wen , X.H. 2003 . A coupled local‐global upscaling approach for simulating flow in highly heterogeneous formations . Advances in Water Resources , 26 : 1041 – 1060 .
  • Chen , Z. , Huan , G. and Li , B. 2004 . Av improved IMPES method for two‐phase flow in porous media . Transport in Porous Media , 54 : 361 – 376 .
  • Èiegis , R. and V&Starikovi;egrave , V. 2002 . Mathematical modelling of wood drying process . Mathematical modelling and analysis , 7 (2) : 177 – 190 .
  • Coats , K.H. 2003 . IMPES stability: selection of stable time steps . SPE Journal , 8 (2) : 181 – 187 .
  • Crandal , M. and Majda , A. 1980 . The method of fractional steps for conservation laws . Numer. Math. , 34 : 285 – 314 .
  • Enquist , B. and Runborg , O. 1996 . Multi‐phase computations in geometrical optics . J. Comput. Appl. Math. , 74 : 175 – 192 .
  • Ewing , R. 1983 . “ Problems arising in the modeling of processes for hydrocarbon recovery ” . In Research Frontiers in Applied Mathematics , Edited by: R&Ewing;lpar , R. volume 1 , 3 – 34 . SIAM .
  • Ewing , R. 1997 . Aspects of upscaling in simulation of flow in porous media . Adv. Water Resources , 20 (5–6) : 349 – 358 .
  • Farmer , C.L. 2002 . Upscaling: a review . Int. Journal Numer. Meth. Fluids , 40 : 63 – 78 .
  • Helmig , R. 1997 . Multiphase Flow and Transport Processes in the Subsurface ‐ A Contribution to the Modelling of Hydrosystems , Springer‐Verlag .
  • Homsy , G.M. 1987 . Viscous fingering in porous media . Ann. Rev. Fluid Mech. , 19 : 271 – 311 .
  • Jiang , G.‐S. and Tadmor , E. 1998 . Nonoscillatory central schemes for multidimensional hyperbolic conservation laws . SIAM J. Sci Comput , 19 (6) : 1892 – 1917 .
  • Jiang , G.S. , Levy , D. , Lin , C.‐T. , Osher , S. and Tadmor , E. 1998 . High‐resolution nonoscillatory central schemes with nonstaggered grids for hyperbolic conservation laws . SIAM J. Numer Anal. , 35 (6) : 2147 – 2168 .
  • Kröner , D. 1996 . Numerical Schemes for Conservation Laws , Wiley und Teubner .
  • Kröner , D. and Ohlberger , M. 2000 . A posteriori error estimates for upwind finite volume schemes in several space dimensions . Math. Comput. , 69 : 25 – 39 .
  • Kurganov , A. , Noelle , S. and Petrova , G. 2001 . Semidiscrete central‐upwind schemes for hyperbolic conservation laws and Hamilton‐Jacobi equations . SIAM J. Sci Comput , 23 (3) : 707 – 740 .
  • Langtangen , H.P. 2002 . Computational Partial Differential Equations. Numerical Methods and Diffpack Programming , Berlin : Springer .
  • LeVeque , R.J. 1991 . Numerical Methods for Conservation Laws , Birkhäuser Verlag .
  • Liu , X.‐D. and Lax , P.D. 1996 . Positive schemes for solving multi‐dimensional hyperbolic systems of conservation laws . CFD Journal , 5 : 1 – 24 .
  • Nessyahu , H. and Tadmor , E. 1990 . Non‐oscillatory central differencing for hyperbolic conservation laws . J. Comput. Phys. , 87 : 408 – 448 .
  • Pruess , K. and Garcia , J.E. 2002 . Multiphase flow dynamics during CO2 disposal into saline aquifers . Environmental Geology , 42 (2–3) : 282 – 295 .
  • Pruess , K. , Oldenburg , C. and Moridis , G. 1999 . TOUGH2 users's guide, version 2.0. Technical report lbnl‐43134, Lawrence Berkeley National Laboratory Berkeley, California
  • Qiu , J. and Shu , C.W. 2002 . On the construction, comparison, and local characteristic decomposition for high‐order central WENO schemes . Journal of Computational Physics , 183 (1) : 187 – 209 .
  • Richtmyer , R.D. and Morton , K.W. 1967 . Difference Methods for Initial Value Problems , New York : Interscience .
  • Saffman , P.G. and Taylor , S.G. 1958 . The penetration of a fluid into a porous medium or Hele‐Shaw cell containing a more viscous liquid . Proc. Roy. Soc. London Series A , 245 : 225 – 257 .
  • Sheldon , J.W. , Zondek , B. and Cardwell , W.T. 1959 . One‐dimensional, incompressible, non‐capillary, two‐phase fluid flow in a porous medium . T. SPE AIME , 216 : 290 – 296 .
  • Stone , H.L. and Garder , A.O. 1961 . Analysis of gas‐cap or dissolved‐gas reservoirs . T. SPE AIME , 222 : 92 – 104 .
  • Whitaker , S. 1977 . Simultaneous heat, mass, and momentum transfer in porous media: A theory of drying . Advances in Heat Transfer , 13 : 119 – 203 .

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