Skip to main content

A Conservative Coupling of Level-Set, Volume-of-Fluid and Other Conserved Quantities

  • 1166 Accesses

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 77)

Abstract

A conservative level-set volume-of-fluid synchronization strategy including coupling to other conserved quantities such as mass or momentum is presented. The scheme avoids mass loss/gain of fluidic structures in zero Mach number two-phase flow while keeping the interface between the two fluid phases sharp. Local level-set correction and a consistent discretization error control using information from the energy equation based divergence constraint allow for application of the presented method to both constant and variable density zero Mach number two-phase flow with or without interfacial mass transport.

Keywords

  • Grid Cell
  • Cartesian Grid
  • Correction Flux
  • Interface Representation
  • Phase Indicator

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-05684-5_45
  • Chapter length: 9 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   129.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-05684-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book
USD   179.99
Price excludes VAT (USA)
Fig. 1
Fig. 2

References

  1. Bourlioux, A.: A coupled level-set volume-of-fluid algorithm for tracking material interfaces. In: 3rd Annual Conference of the CFD Society in Cananda (1995)

    Google Scholar 

  2. Chorin, A.J.: Numerical solution of the Navier-Stokes equations. Math. Comput. 22, 745–762 (1968)

    CrossRef  MATH  MathSciNet  Google Scholar 

  3. Courant, R., Friedrichs, K., Lewy, H.: Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 100, 32–74 (1928). [in German]

    CrossRef  MATH  MathSciNet  Google Scholar 

  4. Fedkiw, R., Aslam, T., Merriman, B., Osher, S.: A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 152(2), 457–492 (1999)

    CrossRef  MATH  MathSciNet  Google Scholar 

  5. Gottlieb, S., Shu, C.W., Tadmor, E.: Strong stability-preserving high-order time discretization methods. SIAM Rev. 43(1), 89–112 (2001)

    CrossRef  MATH  MathSciNet  Google Scholar 

  6. Hartmann, D.: A level-set based method for premixed combustion in compressible flow. Ph.D. thesis, Fakultät für Machinenwesen, Rheinisch-Westfälische Technische Hochschule Aachen, Germany (2010)

    Google Scholar 

  7. Hirt, C., Nichols, B.: Volume of fluid (vof) method for the dynamics of free boundaries. J. Comput. Phys. 39(1), 201–225 (1981)

    CrossRef  MATH  Google Scholar 

  8. Klein, R.: Asymptotics, structure, and integration of sound-proof atmospheric flow equations. Theor. Comput. Fluid Dyn. 23(3), 161–195 (2009)

    CrossRef  MATH  Google Scholar 

  9. Le Chenadec, V., Pitsch, H.: A 3d unsplit forward/backward volume-of-fluid approach and coupling to the level set method. J. Comput. Phys. 233, 10–33 (2013)

    CrossRef  MathSciNet  Google Scholar 

  10. Osher, S.J., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988)

    CrossRef  MATH  MathSciNet  Google Scholar 

  11. Schneider, T.: Verfolgung von Flammenfronten und Phasengrenzen in schwachkompressiblen Strömungen. Ph.D. thesis, Fakultät für Machinenwesen, Rheinisch-Westfälische Technische Hochschule Aachen, Germany (2000). [in German]

    Google Scholar 

  12. Schneider, T., Klein, R.: Overcoming mass losses in level-set-based interface tracking schemes. In: 2nd International Conference on Finite Volume for Complexe Application. Editions Hermes (1999)

    Google Scholar 

  13. Smiljanovski, V., Moser, V., Klein, R.: A capturing-tracking hybrid scheme for deflagration discontinuities. Combust. Theor. Model. 1(2), 183–215 (1997)

    CrossRef  MATH  Google Scholar 

  14. Sussman, M., Puckett, E.G.: A coupled level set and volume-of-fluid method for computing 3d and axisymmetric incompressible two-phase flows. J. Comput. Phys. 162, 301–337 (2000)

    CrossRef  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Matthias Waidmann .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Waidmann, M., Gerber, S., Oevermann, M., Klein, R. (2014). A Conservative Coupling of Level-Set, Volume-of-Fluid and Other Conserved Quantities. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_45

Download citation