Advertisement

Conservation Equations in General Curvilinear Coordinate Systems

  • Nikolay Ivanov KolevEmail author
Chapter
  • 1.9k Downloads

Abstract

In 1974 Vivand and Vinokur published their remarkable works on conservation equations of gas dynamics in curvilinear coordinate systems. Since that time there have been many publications on different aspects of this topic. Several providers of computational fluid dynamics tools use the developed strategy for single-phase flows in attempting to extend the algorithm for multi-phase flows. The usually used approach is to write all partial differential equation in convection-diffusion form and to use the already existing transformations and numerical algorithms for single-phase flow. What remains outside the convection-diffusion terms is pooled as a source into the right hand side. The problems with this approach are two: (a) the remaining terms can contain substantial physics represented in differential terms and (b) the realized coupling between the equations is weak. The latter is manifested if one tries to use such codes for processes with strong feedback of the interfacial heat and mass transfer processes on the pressure, e.g. steam explosion, spontaneous flashing etc.

Keywords

Conservation Equation Versus Versus Versus Steam Explosion Mass Conservation Equation Curvilinear Coordinate System 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Kolev, N.I.: Transiente Dreiphasen Dreikomponenten Strömung, Teil 3: 3D-Dreifluid-Diffusionsmodell, KfK 4080 (1986)Google Scholar
  2. Kolev, N.I.: A three field-diffusion model of three-phase, three-component flow for the transient 3D-computer code IVA2/01. Nuclear Technology 78, 95–131 (1987)Google Scholar
  3. Kolev, N.I.: Derivatives for the equation of state of multi-component mixtures for universal multi-component flow models. Nuclear Science and Engineering 108, 74–87 (1991)Google Scholar
  4. Kolev, N.I.: The code IVA4: Modeling of mass conservation in multi-phase multi component flows in heterogeneous porous media. Kerntechnik 237, 4–5 (1994a)Google Scholar
  5. Kolev, N.I.: The code IVA4: Modeling of momentum conservation in multi phase flows in heterogeneous porous media. Kerntechnik 59(6), 249–258 (1994b)MathSciNetGoogle Scholar
  6. Kolev, N.I.: The code IVA4: Second law of thermodynamics for multi phase flows in heterogeneous porous media. Kerntechnik 60(1), 1–39 (1995)Google Scholar
  7. Kolev, N.I.: Comments on the entropy concept. Kerntechnik 62(1), 67–70 (1997)Google Scholar
  8. Kolev, N.I.: On the variety of notation of the energy conservation principle for single phase flow. Kerntechnik 63(3), 145–156 (1998)Google Scholar
  9. Kolev, N.I.: Applied multi-phase flow analysis and its relation to constitutive physics. In: Proc. of the 8th International Symposium on Computational Fluid Dynamics, ISCFD 1999, Bremen, Germany, September 5-10 (1999); Japan Journal for Computational Fluid Dynamics (2000)Google Scholar
  10. Kolev, N.I.: Conservation equations for multi-phase multi-component multi-velocity fields in general curvilinear coordinate systems, Keynote lecture. In: Proceedings of ASME FEDSM 2001, ASME 2001 Fluids Engineering Division Summer Meeting, New Orleans, Louisiana, May 29-June 1 (2001)Google Scholar
  11. Peyret, R. (ed.): Handbook of computational fluid mechanics. Academic Press, London (1996)Google Scholar
  12. Thompson, J.F., Warsi, Z.U.A., Wayne, M.C.: Numerical grid generation. North-Holland, Amsterdam (1985)zbMATHGoogle Scholar
  13. Vinokur, M.: Conservation equations of gas dynamics in curvilinear coordinate systems. J. Comput. Phys. 14, 105–125 (1974)zbMATHMathSciNetCrossRefGoogle Scholar
  14. Vivand, H.: Formes conservatives des equations de la dynamique des gas, Conservative forms of gas dynamics equations. La Recherche Aerospatiale, no 1 (Janvier-Fevrier), 65–68 (1974)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.MöhrendorferstrHerzogenaurachGermany

Personalised recommendations