Skip to main content
SpringerLink
Log in

A Local Curvature Based Adaptive Particle Level Set Method

  • Published:
Journal of Scientific Computing Aims and scope Submit manuscript

Abstract

In this work, we propose an adaptive particle reseeding method based on the local curvature for the particle level set method. Unlike the original method, a larger number of particles are placed near the interface with larger curvature to achieve high efficiency. For the interface evolution with stretching or shrinking, particles are added or deleted according to the local curvature, respectively. Besides, we further developed the correction procedure that has the grid independence. Through a rage of test cases, including star-shaped droplet and square in periodic vortex flow, Zalesak’s disk rigid body rotation and LeVeque’s three-dimensional deformation case, it shows that with this adaptive particle level set method, the unphysical oscillation of interface can be suppressed when the interface is extremely stretched. Compared with the original particle level set method, the present method has better area/volume conservation and higher computational efficiency. Numerical cases showed the CPU time is saved by 50–75% without losing accuracy.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Data Availability

The data sets supporting the results of this article are included within the article.

References

  1. Hageman, L. J., Walsh, J. M.: HELP, A multi-material eulerian program for compressible fluid and elastic-plastic flows in two space dimensions and time. Vol 2. Fortran listing of HELP, Tech. rep., Systems, Science and Software, La Jolla, California (1971)

  2. Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988). https://doi.org/10.1016/0021-9991(88)90002-2

    Article  MathSciNet  MATH  Google Scholar 

  3. Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225 (1981). https://doi.org/10.1016/0021-9991(81)90145-5

    Article  MATH  Google Scholar 

  4. Fedkiw, R.P., Aslam, T., Merriman, B., Osher, S.: A non-oscillatory eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 152, 457–492 (1999). https://doi.org/10.1006/jcph.1999.6236

    Article  MathSciNet  MATH  Google Scholar 

  5. Wang, C.W., Liu, T.G., Khoo, B.C.: A real ghost fluid method for the simulation of multimedium compressible flow. SIAM J. Sci. Comput. 28, 278–302 (2006). https://doi.org/10.1137/030601363

    Article  MathSciNet  MATH  Google Scholar 

  6. Enright, D., Fedkiw, R., Ferziger, J., Mitchell, I.: A hybrid particle level set method for improved interface capturing. J. Comput. Phys. 183, 83–116 (2002). https://doi.org/10.1006/jcph.2002.7166

    Article  MathSciNet  MATH  Google Scholar 

  7. Hieber, S.E., Koumoutsakos, P.: A Lagrangian particle level set method. J. Comput. Phys. 210, 342–367 (2005). https://doi.org/10.1016/j.jcp.2005.04.013

    Article  MathSciNet  MATH  Google Scholar 

  8. Kim, K.-H., Gwak, M., Yoh, J.J.: An enhanced particle reseeding algorithm for the hybrid particle level set method in compressible flows. J. Sci. Comput. 65, 431–453 (2015). https://doi.org/10.1007/s10915-014-9970-6

    Article  MathSciNet  MATH  Google Scholar 

  9. Gaudlitz, D., Adams, N.A.: On improving mass-conservation properties of the hybrid particle-level-set method. Comput. Fluids. 37, 1320–1331 (2008). https://doi.org/10.1016/j.compfluid.2007.11.005

    Article  MATH  Google Scholar 

  10. Wang, Z., Yang, J., Stern, F.: An improved particle correction procedure for the particle level set method. J. Comput. Phys. 228, 5819–5837 (2009). https://doi.org/10.1016/j.jcp.2009.04.045

    Article  MathSciNet  MATH  Google Scholar 

  11. Jiang, L., Liu, F., Chen, D.: A fast particle level set method with optimized particle correction procedure for interface capturing. J. Comput. Phys. 299, 804–819 (2015). https://doi.org/10.1016/j.jcp.2015.06.039

    Article  MathSciNet  MATH  Google Scholar 

  12. Ianniello, S., Di Mascio, A.: A self-adaptive oriented particles Level-Set method for tracking interfaces. J. Comput. Phys. 229, 1353–1380 (2010). https://doi.org/10.1016/j.jcp.2009.10.034

    Article  MathSciNet  MATH  Google Scholar 

  13. Vartdal, M., Bøckmann, A.: An oriented particle level set method based on surface coordinates. J. Comput. Phys. 251, 237–250 (2013). https://doi.org/10.1016/j.jcp.2013.05.044

    Article  MathSciNet  MATH  Google Scholar 

  14. Enright, D., Losasso, F., Fedkiw, R.: A fast and accurate semi-Lagrangian particle level set method. Comput. Struct. 83, 479–490 (2005). https://doi.org/10.1016/j.compstruc.2004.04.024

    Article  MathSciNet  Google Scholar 

  15. Zhao, L., Khuc, H., Mao, J., Liu, X., Avital, E.: One-layer particle level set method. Comput. Fluids. 170, 141–156 (2018). https://doi.org/10.1016/j.compfluid.2018.04.009

    Article  MathSciNet  MATH  Google Scholar 

  16. Sussman, M., Smereka, P., Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, 146–159 (1994). https://doi.org/10.1006/jcph.1994.1155

    Article  MATH  Google Scholar 

  17. Scardovelli, R., Zaleski, S.: Analytical relations connecting linear interfaces and volume fractions in rectangular grids. J. Comput. Phys. 164, 228–237 (2000). https://doi.org/10.1006/jcph.2000.6567

    Article  MathSciNet  MATH  Google Scholar 

  18. Jiang, G.-S., Shu, C.-W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228 (1996). https://doi.org/10.1006/jcph.1996.0130

    Article  MathSciNet  MATH  Google Scholar 

  19. Shu, C.-W., Osher, S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes, II. J. Comput. Phys. 83, 32–78 (1989). https://doi.org/10.1016/0021-9991(89)90222-2

    Article  MathSciNet  MATH  Google Scholar 

  20. Chen, X., Yang, V.: Thickness-based adaptive mesh refinement methods for multi-phase flow simulations with thin regions. J. Comput. Phys. 269, 22–39 (2014). https://doi.org/10.1016/j.jcp.2014.02.035

    Article  MathSciNet  MATH  Google Scholar 

  21. LeVeque, R.J.: High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. Anal. 33, 627–665 (1996). https://doi.org/10.1137/0733033

    Article  MathSciNet  MATH  Google Scholar 

Download references

Funding

The research is supported by the National Natural Science Foundation of China (11732003 and U1830139).

Author information

Authors and Affiliations

  1. State Key Lab of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, China

    Cheng Wang, Wanli Wang & Fuyu Zhao

  2. Department of Fluid Mechanics, Northwestern Polytechnical University, Xian, 710072, China

    Shucheng Pan

Authors
  1. Cheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wanli Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shucheng Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fuyu Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cheng Wang.

Ethics declarations

Conflict of interest

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, C., Wang, W., Pan, S. et al. A Local Curvature Based Adaptive Particle Level Set Method. J Sci Comput 91, 3 (2022). https://doi.org/10.1007/s10915-022-01772-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10915-022-01772-4

Keywords

Search

Navigation