Skip to main content

A Parallel Strategy for a Level Set Simulation of Droplets Moving in a Liquid Medium

  • Conference paper
High Performance Computing for Computational Science – VECPAR 2010 (VECPAR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6449))

Abstract

The simulation of two-phase flow problems involving two time-dependent spatial regions with different physical properties is computationally hard. The numerical solution of such problems is complicated by the need to represent the movement of the interface. The level set approach is a front-capturing method representing the position of the interface implicitly by the root of a suitably defined function. We describe a parallel adaptive finite element simulation based on the level set approach. For freely sedimenting n-butanol droplets in water, we quantify the parallel performance on a Xeon-based cluster using up to 256 processes.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bertakis, E., Groß, S., Grande, J., Fortmeier, O., Reusken, A., Pfennig, A.: Validated simulation of droplet sedimentation with finite-element and level-set methods. Chemical Engineering Science 65(6), 2037–2051 (2010)

    Article  Google Scholar 

  2. Bey, J.: Simplicial grid refinement: On Freudenthal’s algorithm and the optimal number of congruence classes. J. Numer. Math. 85(1), 1–29 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100(2), 335–354 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fortmeier, O., Henrich, T., Bücker, H.M.: Modeling data distribution for two-phase flow problems by weighted graphs. In: Beigl, M., Cazorla-Almeida, F.J. (eds.) 23rd Workshop on Parallel Sytems and Algorithms, Hannover, Germany, February 12, pp. 31–38. VDE (2010)

    Google Scholar 

  5. Groß, S., Reichelt, V., Reusken, A.: A finite element based level set method for two-phase incompressible flows. Comput. Vis. Sci. 9(4), 239–257 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Groß, S., Reusken, A.: Parallel multilevel tetrahedral grid refinement. SIAM J. Sci. Comput. 26(4), 1261–1288 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Groß, S., Reusken, A.: Finite element discretization error analysis of a surface tension force in two-phase incompressible flows. SIAM J. Numer. Anal. 45(4), 1679–1700 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gross-Hardt, E., Amar, A., Stapf, S., Pfennig, A., Blümich, B.: Flow dynamics inside a single levitated droplet. Ind. Eng. Chem. Res. 1, 416–423 (2006)

    Article  Google Scholar 

  9. Gross-Hardt, E., Slusanschi, E., Bücker, H.M., Pfennig, A., Bischof, C.H.: Practical Shape Optimization of a Levitation Device for Single Droplets. Opt. Eng. 9(2), 179–199 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Herrmann, M.: A parallel Eulerian interface tracking/Lagrangian point particle multi-scale coupling procedure. J. Comput. Phys. 229(3), 745–759 (2010)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  12. Karypis, G., Kumar, V.: A parallel algorithm for multilevel graph partitioning and sparse matrix ordering. J. Parallel Distrib. Comput. 48(1), 71–95 (1998)

    Article  Google Scholar 

  13. Li, J., Renardy, Y.: Numerical study of flows of two immiscible liquids at low reynolds number. SIAM Rev. 42(3), 417–439 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  14. Li, X.L.: Study of three-dimensional Rayleigh–Taylor instability in compressible fluids through level set method and parallel computation. Phys. Fluids A-Fluid 5(8), 1904–1913 (1993)

    Article  MATH  Google Scholar 

  15. Marquardt, W.: Model-based experimental analysis of kinetic phenomena in multi-phase reactive systems. Trans. Inst. Chem. Eng. 83(A6), 561–573 (2005)

    Article  Google Scholar 

  16. Misek, T., Berger, R., Schröter, J.: Standard test systems for liquid extraction, 2nd edn. Europ. Fed. Chem. Eng. Pub. Ser., Inst. Chem. Eng., Warwickshire, vol. 46 (1985)

    Google Scholar 

  17. Osher, S., Sethian, J.A.: Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79(1), 12–49 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  18. Sethian, J.A.: Level Set Methods and Fast Marching Methods—Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, 2nd edn. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  19. Sussman, M.: A parallelized, adaptive algorithm for multiphase flows in general geometries. Comput. Struct. 83(6-7), 435–444 (2005)

    Article  Google Scholar 

  20. Sussman, M., Smereka, P., Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114(1), 146–159 (1994)

    Article  MATH  Google Scholar 

  21. Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S., Jan, Y.J.: A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169(2), 708–759 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  22. Wang, K., Chang, A., Kale, L.V., Dantzig, J.A.: Parallelization of a level set method for simulating dendritic growth. J. Parallel Distrib. Comput. 66(11), 1379–1386 (2006)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fortmeier, O., Bücker, H.M. (2011). A Parallel Strategy for a Level Set Simulation of Droplets Moving in a Liquid Medium. In: Palma, J.M.L.M., Daydé, M., Marques, O., Lopes, J.C. (eds) High Performance Computing for Computational Science – VECPAR 2010. VECPAR 2010. Lecture Notes in Computer Science, vol 6449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19328-6_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-19328-6_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19327-9

  • Online ISBN: 978-3-642-19328-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics