Numerical solution methods for multiphase flow problems


Characteristic Point Mass Conservation Equation Pipe Network Pipe Section Flow Cross Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Addessio FL et al. TRAC-PF1 (February 1984) An advanced best-estimate computer program for pressurised water reactor analysis, NUREG/CR-3567, LA-9844-MSGoogle Scholar
  2. 2.
    Addessio FL et al. (July-August 1985) TRAC-PF1/MOD1 Computer Code and Developmental Assessment, Nuclear Safety, vol 26 no 4 pp 438–454Google Scholar
  3. 3.
    Andersen JGM, Schang JC (1984) A predictor-corrector method for the BWR version of the TRAC computer code, AICHE Symposium Series, Heat Transfer — Niagara Falls, Farukhi NM (ed) 236.80, pp 275–280Google Scholar
  4. 4.
    Amsden AA (1985) KIVA: A computer program for two-and three-dimensional fluid flows with chemical reactions and fuel sprays, LA-10245-MSGoogle Scholar
  5. 5.
    Bohl WR et al. (1988) Multi-phase flow in the advanced fluid dynamics model, ANS Proc. 1988, Nat. Heat Transfer Conf, July 24–July 27, Houston, Texas. HTC-3 pp 61–70Google Scholar
  6. 6.
    Caretto LS, Gosman AD, Patankar SV, Spalding DB (1973) Two calculation procedures for steady, three dimensional flow with recirculation, Proc. 3rd Int. Conf. on Numerical Methods in Fluid Mechanics, Springer, Lecture Notes in Physics, vol 11 no 19 pp 60–68Google Scholar
  7. 7.
    Chow LC, Tien CL (1978) An examination of four differencing schemes for some elliptic-type convection equations, Numerical Heat Transfer, vol 1 pp 87–100Google Scholar
  8. 8.
    Connell SD, Stow P (1986) A discussion and comparison of numerical techniques used to solve the Navier-Stokes and Euler equations, Int. J. for Num. Math. in Eng., vol 6 pp 155–163Google Scholar
  9. 9.
    Courant R, Isacson E, Rees M (1952) On the solution of non-linear hyperbolic differential equations by finite differentials, Commun. Pure Appl. Math., vol 5 p 243Google Scholar
  10. 10.
    Dearing JF (1985) A four-fluid model of PWR degraded cores, Third Int. Top. Meeting on Reactor Thermal Hydraulics, Newport, Rhode Island, Oct.15–18 1985, LA-UR-85-947/ CONF-85/007—3Google Scholar
  11. 11.
    van Doormaal JP, Raithby GD (1984) Enhancement of the SIMPLE method for prediction of incompressible fluid flows, Numerical Heat Transfer, vol 7 pp 147–163Google Scholar
  12. 12.
    Günther C (1988) Monotone Upwind-Verfahren 2. Ordnung zur Loesung der Konvektions-Diffusionsgleichungen, ZAMM. Z. angew. Math. Mech. vol 68 no 5, T383–T384Google Scholar
  13. 13.
    Günther C (August 1988) Vergleich verschiedener Differenzenverfahren zur numerischen Loesungen der 2-d Konvektions-Diffusionsgleichungen anhand eines Beispieles mit bekannter exakter Loesungen, Kernforschungszentrum Karlsruhe, KfK 4439Google Scholar
  14. 14.
    Gushchin VA, Shchennikov VV (1974) A monotonic difference scheme of second order accuracy, Zh. Vychisl. Mat. Mat. Fiz., vol 14 no 3 pp 789–792Google Scholar
  15. 15.
    Haaland SE (1984) Calculation of entrainment rate, initial values, and transverse velocity for the Patankar-Spalding method, Numerical Heat Transfer, vol 7 pp 39–57Google Scholar
  16. 16.
    Harlow FH, Amsden AA (1971) A numerical fluid dynamics calculations method for all flow speeds, J. Comp. Physics, vol 8 pp 197–213CrossRefGoogle Scholar
  17. 17.
    Issa RI (1983) Numerical Methods for Two-and Tree-Dimensional Recirculating Flows, in Comp. Methods for Turbulent Transonic and Viscous Flow, Ed. Essers, J.A.: Hemisphere, Springer, pp 183Google Scholar
  18. 18.
    Kelly JM, Kohrt JR (1983) COBRA-TF: Flow blockage heat transfer program, Proc. Eleventh Water Reactor Safety Research Information Meeting, Gaithersburg — Maryland, NUREG/CP-0048, 1 (Oct.24–28 1983) pp 209–232Google Scholar
  19. 19.
    Knight TD Ed. (1984) TRAC-PD2 Independent Assessment, NUREG/CR-3866, LA-10166Google Scholar
  20. 20.
    Kolev NI (October 1986) IVA-2 A Computer Code for Modeling of Three Dimensional, Three-Phase, Three-Component Flow by Means of Three Velocity Fields in Cylindrical Geometry with Arbitrary Internal Structure Including Nuclear Reactor Core, Proc. of the Int. Seminar "Thermal physics 86" held in Rostock, German Democratic Republic, (in Russian)Google Scholar
  21. 21.
    Kolev NI (Aug. 1987) A three field-diffusion model of three-phase, threecomponent flow for the transient 3D-computer code IVA2/001, Nuclear Technology, vol 78 pp 95–131Google Scholar
  22. 22.
    Kolev NI (1990) Derivatives for the state equations of multi-component mixtures for universal multi-component flow models, Nuclear Science and Engineering, vol 108 pp 74–87Google Scholar
  23. 23.
    Kolev N I (Sept. 1991) A three-field model of transient 3D multi-phase, three-component flow for the computer code IVA3, Part 2: Models for the interfacial transport phenomena. Code validation. KfK 4949 Kernforschungszentrum KarlsruheGoogle Scholar
  24. 24.
    Kolev NI, Tomiyama A, Sakaguchi T (Sept. 1991) Modeling of the mechanical interaction between the velocity fields in three phaseflow, Experimental Thermal and Fluid Science, vol 4 no 5 pp 525–545CrossRefGoogle Scholar
  25. 25.
    Kolev NI (1993) Fragmentation and coalescence dynamics in multi-phase flows, Experimental Thermal and Fluid Science, vol 6 pp 211–251CrossRefGoogle Scholar
  26. 26.
    Kolev NI (Apr. 23–27 1994) IVA4 computer code: dynamic fragmentation model for liquid and its aplication to melt water interaction, Proc. ICONE-3, Third International Conf. on Nucl. Engineering, “Nuclear Power and Energy Future”, Kyoto, Japan. Presented at the „Workshop zur Kühlmittel/ Schmelze — Wechselwirkung“, 14–15 Nov. 1994, Cologne, GermanyGoogle Scholar
  27. 27.
    Kolev NI (1994) The code IVA4: Modeling of mass conservation in multi-phase multicomponent flows in heterogeneous porous media, Kerntechnik, vol 59 no 4–5 pp 226–237Google Scholar
  28. 28.
    Kolev NI (1994) The code IVA4: Modeling of momentum conservation in multi-phase flows in heterogeneous porous media, Kerntechnik, vol 59 no 6 pp 249–258Google Scholar
  29. 29.
    Kolev NI (1995) The code IVA4: Second Law of Thermodynamics for Multi-Phase Multi-Component Flows in Heterogeneous Porous Media, Kerntechnik vol 60 no 1 pp 28–39Google Scholar
  30. 30.
    Kolev NI (1995) How accurate can we predict nucleate boiling, Experimental Thermal and Fluid Science, vol 10 pp 370–378CrossRefGoogle Scholar
  31. 31.
    Kolev NI (1995) The code IVA4: Nucleation and flashing model, Kerntechnik vol 60 (1995) no 6, pp 157–164. Also in: Proc. Second Int. Conf. On Multiphase Flow, Apr. 3–7, 1995, Kyoto; 1995 ASME & JSME Fluid Engineering Conference International Symposium on Validation of System Transient Analysis Codes, Aug. 13–18, 1995, Hilton Head (SC) USA; Int. Symposium on Two-Phase Flow Modeling and Experimentation, ERGIFE Place Hotel, Rome, Italy, October 9–11, 1995Google Scholar
  32. 32.
    Kolev NI (1995) IVA4 computer code: The model for film boiling on a sphere in subcooled, saturated and superheated water, Proc. Second Int. Conference On Multiphase Flow, Apr. 3–7 1995, Kyoto, Japan. Presented At The „Workshop zur Kühlmittel/Schmelze — Wechselwirkung“, 14–15 Nov. 1994, Cologne, GermanyGoogle Scholar
  33. 33.
    Kolev NI (1996) Three fluid modeling with dynamic fragmentation and coalescence fiction or daily practice? 7th FARO Experts Group Meeting Ispra, October 15–16, 1996; Proceedings of OECD/CSNI Workshop on Transient thermal-hydraulic and neutronic codes requirements, Annapolis, Md, U.S.A., 5th-8th November 1996; 4th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics, ExHFT 4, Brussels, June 2–6, 1997; ASME Fluids Engineering Conference & Exhibition, The Hyatt Regency Vancouver, Vancouver, British Columbia, CANADA June 22–26, 1997, Invited Paper; Proceedings of 1997 International Seminar on Vapor Explosions and Explosive Eruptions (AMIGO-IMI), May 22–24, Aoba Kinen Kaikan of Tohoku University, Sendai-City, JapanGoogle Scholar
  34. 34.
    Köller A (1980) Anwendung numerischer Lösungsverfahren der Navier-Stokes-Gleichung zur Vermeidung von Wirbeln, Siemens Forsch.-u. Entwickl.-Ber., vol 9 no 2 pp 99–104Google Scholar
  35. 35.
    Latimaer BR, Pollard A (1985) Comparison of pressure-velocity coupling solution algorithms, Num. Heat Transfer, vol 8 pp 635–652Google Scholar
  36. 36.
    Leonard BP (1978) Third-order finite-difference method for steady two-dimensional convection, Num. Meth. in Laminar and Turbulent Flow, pp 807–819Google Scholar
  37. 37.
    Leonard BP, Mokhtari S (1990) Beyond first — order up winding: The ultra — sharp alternative for non — oscillatory Steady — state simulation of convection. Int. J. for Numerical Methods in Engineering, vol 30 pp 729–766Google Scholar
  38. 38.
    Leonard BP (1990) New flash: Upstream parabolic interpolation, Proc. 2nd GAMM Conference on Num. Meth. in Fluid Mechanics, Köln, GermanyGoogle Scholar
  39. 39.
    Liles D, Reed WR (1978) A semi-implicit method for two-phase fluid dynamics, J. of Comp. Physics, vol 26 pp 390–407CrossRefGoogle Scholar
  40. 40.
    Liles D et al (April 1981) TRAC-FD2 An advanced best-estimate computer program for pressurised water reactor loss-of-coolant accident analysis, NUREG/CR-2054, LA-8709 MSGoogle Scholar
  41. 41.
    Liles D, Mahaffy JM (1984) An approach to fluid mechanics calculations on serial and parallel computer architectures in large scale scientific computation, Parter SV (ed) Academic Press, Inc., Orlando, pp 141–159Google Scholar
  42. 42.
    Mahaffy JH, Liles D (April 1979) Applications of implicit numerical methods to problems in two phase flow, NUREG/CR-0763, LA-7770-MSGoogle Scholar
  43. 43.
    Mahaffy JH (1979) A stability-enhancing two-phase method for fluid flow calculations, NUREG/CR-0971, LA-7951-MS or J. of Comp. Physics, vol 46 no 3 (June 1983)Google Scholar
  44. 44.
    Neuberger AW (March 1984) Optimierung eines numerischen Verfahrens zur Berechnung elliptischer Strömungen, DFVLR-FB84-16Google Scholar
  45. 45.
    Patankar SV, Spalding DB (1967) A finite-difference procedure for solving the equations of the two dimensional boundary layer, Int. J. Heat Mass Transfer vol 10 pp 1389–1411CrossRefGoogle Scholar
  46. 46.
    Patankar SV (1978) A numerical method for conduction in composite materials, Flow in Irregular Geometries and Conjugate Heat Transfer, Proc. 6th Int. Heat Transfer Conf., Toronto, vol 3 p 297Google Scholar
  47. 47.
    Patankar SV (1980) Numerical heat transfer and fluid flow, Hemisphere, New YorkGoogle Scholar
  48. 48.
    Patankar SV, Spalding DB (1972) A calculation procedure for heat, mass and momentum transfer in three dimensional parabolic flows, Int. J. Heat Mass Transfer, vol 15 pp 1787–1806CrossRefGoogle Scholar
  49. 49.
    Patankar SV, Rafiinejad D, Spalding DB (1975) Calculation of the three-dimensional boundary layer with solution of all three momentum equations, Computer Methods in Applied Mechanics and Engineering, North-Holland Publ. Company, vol 6 pp 283–292Google Scholar
  50. 50.
    Patankar SV (1975) Numerical prediction of three dimensional flows, in Ed. Lauder B E, Studies in convection, theory, measurement and application, Academic Press, London, vol 1Google Scholar
  51. 51.
    Patankar SV, Basn DK, Alpay S (December 1977) A prediction of the three-dimensional velocity field of a deflected turbulent jet, Transactions of the ASME, Journal of Fluids Engineering, pp 758–767Google Scholar
  52. 52.
    Patankar S V (1981) A calculation procedure for two-dimensional elliptic situations, Numerical Heat Transfer, vol 4 pp 409–425Google Scholar
  53. 53.
    Prakash C (1984) Application of the locally analytic differencing scheme to some test problems for the convection-diffusion equation, Numerical Heat Transfer vol 7 pp 165–182Google Scholar
  54. 54.
    Patel MK, Markatos NC, Cross MS (1985) A critical evaluation of seven discretization schemes for convection-diffusion equations, Int. J. Num. Methods in Fluids, pp 225–244Google Scholar
  55. 55.
    Patel MK, Markatos NC (1986) An evaluation of eight discretization schemes for two-dimensional convection-diffusion equations, Int. J. for Numerical Methods in Fluids, vol 6 pp 129–154CrossRefGoogle Scholar
  56. 56.
    Patel MK, Markatos NC (1986) An evaluation of eight discretization schemes for two-dimensional convection-Diffusion equations, Int. J. for Numerical Methods in Fluids, vol 6 pp 129–154CrossRefGoogle Scholar
  57. 57.
    Prior RJ (June 1979) Computational methods in thermal reactor safety, NUREG/CR-0851, LA-7856-MSGoogle Scholar
  58. 58.
    Pollard A, Aiu LWA (1982) The calculation of some laminar flows using various discretization schemes, Comp. Math. Appl. Mesh. Eng., vol 35 pp 293–313CrossRefGoogle Scholar
  59. 59.
    Rohatgi US (April 1985) Assessment of TRAC codes with dartmouth college countercurrent flow tests, Nuclear Technology vol 69 pp 100–106Google Scholar
  60. 60.
    Roscoe DF (1976) The solution of the three-dimensional Navier-Stokes equations using a new finite difference approach, Int. J. for Num. Math. in Eng., vol 10 pp 1299–1308CrossRefGoogle Scholar
  61. 61.
    Saad Y (1996) Iterative methods for sparse linear systems, PWS Publishing Company, BostonGoogle Scholar
  62. 62.
    Sargis DA, Chan PC (1984) An implicit fractional step method for two-phase flow. Basic Aspects of Two Phase Flow and Heat Transfer, HTD-34 pp 127–136Google Scholar
  63. 63.
    Scarborough JB (1958) Numerical mathematical analysis, 4th ed., John Hopkins Press, BaltimoreGoogle Scholar
  64. 64.
    Spalding DB (1976) The Calculation of Free-Convection Phenomena in Gas-Liquid Mixtures, ICHMT Seminar Dubrovnik (1976), in Turbulent Buoyant Convection. Eds. Afgan N, Spalding DB, Hemisphere, Washington pp 569–586, or HTS Repport 76/11 (1977)Google Scholar
  65. 65.
    Spalding DB (March 1979) Multi-phase flow prediction in power system equipment and components, EPRI Workshop on Basic Two-Phase Flow Modelling in Reactor Safety and Performance, Tampa, FloridaGoogle Scholar
  66. 66.
    Spalding DB (January 1980) Mathematical modeling of fluid mechanics, Heat-Transfer and Chemical — Reaction Processes, A lecture course, Imperial College of Science and Technology, Mech. Eng. Dep., London. HTS Report 80/1Google Scholar
  67. 67.
    Spalding DB (1980) Numerical computation of multi-phase fluid flow and heat transfer, in Recent Advances in Numerical Methods in Fluids, Eds. Taylor C, Morgan K, pp 139–167Google Scholar
  68. 68.
    Spalding DB (June 1981) Development in the IPSA procedure for numerical computation of multi-phase, slip, unequal temperature, etc, Imperial College of Science and Technology, Mech. Eng. Dep., London. HTS Report 81/11Google Scholar
  69. 69.
    Spalding DB (1981) A general purpose computer program for multi-dimensional one-and two-phase flow, Mathematics and Computers in Simulation vol XXIII pp 267–276CrossRefGoogle Scholar
  70. 70.
    Spalding DB (1981) Numerical computation of multiphase flows, A course of 12 lectures with GENMIX 2P, Listing and 5 Appendices, HTS Report 81/8Google Scholar
  71. 71.
    Tanaka R, Nakamura T, Yabe T (2000) Constructing an exactly conservative scheme in a non conservative form, Comput. Phys. Commun., vol 126 pp 232CrossRefGoogle Scholar
  72. 72.
    Tomiyama A (1990) Study on finite difference methods for fluid flow using difference operators and iteration matrices, PhD Thesis, Tokyo Institute of TechnologyGoogle Scholar
  73. 73.
    Thurgood MJ, Cuta JM, Koontz AS, Kelly JM (1983) COBRA/TRAC — A thermal hydraulic code for transient analysis of nuclear reactor vessels and primary coolant systems, NUREG/CR-3046 1–5Google Scholar
  74. 74.
    Vanka SP (1985) Block-implicit calculation of steady turbulent recirculating flows, Int. J. Heat Mass Transfer, vol 28 no 11 pp 2093–2103CrossRefGoogle Scholar
  75. 75.
    Williams KA, Liles DR (1984) Development and assessment of a numerical fluid dynamics model for non-equilibrium steam-water flows with entrained droplets, AICHE Symposium Series, Heat Transfer — Niagara Falls 1984, ed. by Farukhi NM, 236. 80 pp 416–425Google Scholar
  76. 76.
    Yabe T, Takewaki H (Dezember 1986) CIP, A new numerical solver for general non linear hyperbolic equations in multi-dimension, KfK 4154, Kernforschungszentrum KarlsruheGoogle Scholar
  77. 77.
    Yabe T, Xiao F (1993) Description of complex sharp interface during shock wave interaction with liquid drop, Journal of Computational Physics of Japan, vol 62, no 8 pp 2537–2540CrossRefGoogle Scholar
  78. 78.
    Yabe T, Xiao F, Mochizuki H (1995) Simulation technique for dynamic evaporation processes, Nuclear Engineering and Design, vol 155 pp 45–53CrossRefGoogle Scholar
  79. 79.
    Yabe T, Xiao F, Utsumi T (2001) The constrained interpolation profile method for multiphase analysis, Journal of Computational Physics, vol 169 pp 556–593CrossRefGoogle Scholar
  80. 80.
    Ferzinger JH and Paric (2002) Computational methods for fluid dynamics, Springer, 3rd Edition, BerlinGoogle Scholar
  81. 81.
    Xiao F, Ikebata A and Hasegawa T (2004) Multi-fluid simulation by multi integrated moment method, to be published in Computers & StructuresGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Personalised recommendations