Publication Cover
Applicable Analysis
An International Journal
Volume 66, 1997 - Issue 1-2
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Original Articles

An accurate numerical algorithm for solving compressible three-phase flows in porous media

Pages 57-88 | Received 01 Jan 1996, Published online: 02 May 2007

References

  • Aziz , K. and Settari , A. “ Petroleum reservoir simulation ” .
  • Bell , J.B. , Trangenetein , J.A. and Schubin , G.R. 1986 . Conservation laws of mixed type describing three-phaue flow in porous media . SIAM, J. Appl. Math , 46 : 1000 – 1017 .
  • Chavent , G. and Jaffre , J. 1986 . “ Mathematical models and finite elemente for reservoir simulation ” . In Studiea in Mathematics and its Applications , Vol. 17 , North-Holland : Cambridge Univ.press .
  • Douglas , J. and Russell , T.F . 1982 . Numerical methods for convection-dominated diffwion . J.Numer.Anal , 19 : 871 – 885 .
  • Godunov , S.K. 1959 . Finite diflerence model for numerical computation of discontinuous solutions of the equations of fluid dynamics . Mat.SB , 47 : 251 – 306 .
  • Harten , A. 1983 . High resolution schemea for hyperbolic conservation laws. . J.Comp.Phys , 49 : 357 – 393 .
  • Harten , A. 1983 . On the symmetric form of systems of wnservation laws with entropy . J.Comp.Phys , : 151 – 164 .
  • Holdon , L. 1990 . On the strict hyperbolicity of Buckley-Leverett equations for three-phase . SIAM J.Appl.Math , 50 ( 3 ) 6 : 667 – 682 .
  • Roe , P.L. 1981 . On the strict hyperbolicity of Buckley-Leverett equations for three-phase flow in porous media . J.comp.Phys , 43 ( 3 ) 6 : 357 – 372 .
  • Russell , T.F. , Wheeler , M.F. and Chiang , C. 1985 . Large-scale simulation of miscible displacement by mixed and characteristic finite element methods . Proceedings,SEG/SIAM/SPE, SIAM . 1985 , anné . Philadelphia .
  • Saad , M. Propriétés de quelques moddm d'dcoulements en milieu poreux . Ph.D. thesia . 1972/73 , anné . Bordeaux 1 University .
  • Schaeffer , D.G. and Schearer , M. 1987 . The clusification of 2 × 2 systems of non-strictly hyperbolic conservation laws with application to oil recovery . Communications in Pure and Applied Mathematics , XL : 141 – 178 .
  • Schearer , M. and Trangenstein , J.A. 1989 . Loss of real characteristics for models of threephase flow in porow media . Transport in poroue media. , 4 : 499 – 525 .
  • Tardy , P. , Quintard , M. and Le Thiez , P. An accurate numerical modeling of three-phase flows in soils contaminated by hydrocarbons . Rapport 42 358 . 1972/73 , anné . Institut Fran¸ais du Petrole .
  • Toumi , I. in press . A wenk formulation of Roe's approximate Riemann solver .
  • Trangenstein , J.A. 1989 . Three-phose flow with gmvity. . Contemporary Mathematics , 100 : 147 – 159 .
  • Van Leer , B. 1977 . Towards the ultimate wnuervative scheme, a new appmch to the numerical correction laws. . J. Comp. Phys. , 23 : 276 – 299 .
  • Vila , J.A. 1988 . Mathematics of Computation . High order schemes and entopy condition for non linear hyperbolic systems of conservations laws , 50 ( 181 ) : 53 – 73 .
  • Vila , J.A. 1990 . Construction of Roe type matrix, a new approch. Application to real gas dynamics. Third international conference on hyperbolic problems . Collége de France . 1990 , anné . pp. 913 – 922 . UPPSALO . fascicule 4, 19p
  • Yee , H.C. 1987 . Construction of explicit and implicit symmetric TVD schemes and their applications. . J. Comp. Phys. , 68 : 151 – 179 .

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