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An Enhanced Particle Reseeding Algorithm for the Hybrid Particle Level Set Method in Compressible Flows

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Abstract

The hybrid particle level set (HPLS) method improves the mass conservation of level set method by using Lagrangian marker particles in under-resolved regions. In the HPLS method, the value of Lagrangian particles is calculated prior to the level set equation and used to rebuild the embedded interface. Therefore, it is essential to compute Lagrangian particles with reliable means to sustain accuracy of the level-set based interfaces. The particle method preserves exactly the characteristics line, but it cannot automatically handle the union or deletion of characteristics. So reseeding Lagrangian particles (or regulation) are required to be calculated precisely despite the particle deletion near the interface where loss of characteristics information and unintended error or mass loss may occur. Reseeding procedure of the HPLS method is not suitable for compressible flows in which characteristics are often merged or destroyed, or one material is divided into two. In this paper, reseeding procedure of the original HPLS is evaluated and modified based on the geometrical and characteristics information. The numerical results of various complex interface problems involving solids, liquids and gases demonstrate the capability of the new reseeding procedure in the HPLS method.

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References

  1. 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 

  2. Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, Berlin (2003)

    Book  MATH  Google Scholar 

  3. Sussman, M., Smereka, P., Osher, S.: A level set approach for computing solutions to incompressible 2-phase flow. J. Comput. Phys. 114(1), 146–159 (1994)

    Article  MATH  Google Scholar 

  4. Stewart, D.S., Yoo, S., Wescott, B.L.: High-order numerical simulation and modelling of the interaction of energetic and inert materials. Combust. Theor Model. 11(2), 305–332 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Tran, L.B., Udaykumar, H.S.: A particle-level set-based sharp interface cartesian grid method for impact, penetration, and void collapse. J. Comput. Phys. 193(2), 469–510 (2004)

    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(1), 83–116 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Enright, D., Losasso, F., Fedkiw, R.: A fast and accurate semi-Lagrangian particle level set method. Comput. Struct. 83(6–7), 479–490 (2005)

    Article  MathSciNet  Google Scholar 

  8. Kim, K.H., Yoh, J.J.: Shock compression of condensed matter using multimaterial reactive ghost fluid method. J. Math. Phys. 49(4), 043511 (2008)

  9. Yoh, J.J., Kim, K.H.: Shock compression of condensed matter using Eulerian multimaterial method: applications to multidimensional shocks, deflagration, detonation, and laser ablation. J. Appl. Phys. 103(11), 113507 (2008)

  10. Hieber, S.E., Koumoutsakos, P.: A Lagrangian particle level set method. J. Comput. Phys. 210(1), 342–367 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Peng, D.P., Merriman, B., Osher, S., Zhao, H.K., Kang, M.J.: A PDE-based fast local level set method. J. Comput. Phys. 155(2), 410–438 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  12. Min, C.H.: Local level set method in high dimension and codimension. J. Comput. Phys. 200(1), 368–382 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Wang, S.Y., Lim, K.M., Khoo, B.C., Wang, M.Y.: An extended level set method for shape and topology optimization. J. Comput. Phys. 221(1), 395–421 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang, K.H., Zhang, L., Song, H.H., Zhou, W.G.: Active contours with selective local or global segmentation: a new formulation and level set method. Image Vis. Comput. 28(4), 668–676 (2010)

    Article  Google Scholar 

  15. Cockburn, B., Shu, C.W.: The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35(6), 2440–2463 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  16. Arnold, D.N., Brezzi, F., Cockburn, B., Marini, L.D.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39(5), 1749–1779 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  17. Yan, J., Shu, C.W.: A local discontinuous Galerkin method for KdV type equations. SIAM J. Numer. Anal. 40(2), 769–791 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  18. Marchandise, E., Remacle, J.F., Chevaugeon, N.: A quadrature-free discontinuous Galerkin method for the level set equation. J. Comput. Phys. 212(1), 338–357 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Giraldo, F.X., Restelli, M.: A study of spectral element and discontinuous Galerkin methods for the Navier–Stokes equations in nonhydrostatic mesoscale atmospheric modeling: equation sets and test cases. J. Comput. Phys. 227(8), 3849–3877 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  20. Nave, J.C., Rosales, R.R., Seibold, B.: A gradient-augmented level set method with an optimally local, coherent advection scheme. J. Comput. Phys. 229(10), 3802–3827 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  21. Bockmann, A., Vartdal, M.: A gradient augmented level set method for unstructured grids. J. Comput. Phys. 258, 47–72 (2014)

    Article  MathSciNet  Google Scholar 

  22. Lee, C., Dolbow, J., Mucha, P.J.: A narrow-band gradient-augmented level set method for multiphase incompressible flow. J. Comput. Phys. 273, 12–37 (2014)

    Article  MathSciNet  Google Scholar 

  23. Sussman, M., Almgren, A.S., Bell, J.B., Colella, P., Howell, L.H., Welcome, M.L.: An adaptive level set approach for incompressible two-phase flows. J. Comput. Phys. 148(1), 81–124 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. Losasso, F., Fedkiw, R., Osher, S.: Spatially adaptive techniques for level set methods and incompressible flow. Comput. Fluids 35(10), 995–1010 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  25. Popinet, S.: An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228(16), 5838–5866 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. Gibou, F., Min, C., Fedkiw, R.: High resolution sharp computational methods for elliptic and parabolic problems in complex geometries. J. Sci. Comput. 54(2–3), 369–413 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  27. Leung, S.Y., Zhao, H.K.: A grid based particle method for moving interface problems. J. Comput. Phys. 228(8), 2993–3024 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. Sussman, M., Fatemi, E.: An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow. SIAM J. Sci. Comput. 20(4), 1165–1191 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  29. Jiang, G.S., Peng, D.P.: Weighted ENO schemes for Hamilton–Jacobi equations. SIAM J. Sci. Comput. 21(6), 2126–2143 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  30. Wang, Z.Y., Yang, J.M., Stern, F.: An improved particle correction procedure for the particle level set method. J. Comput. Phys. 228(16), 5819–5837 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  31. Kim, K.H., Yoh, J.J.: A particle level-set based Eulerian method for multi-material detonation simulation of high explosive and metal confinements. Proc. Combust. Inst. 34, 2025–2033 (2013)

    Article  Google Scholar 

  32. Zalesak, S.T.: Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys. 31(3), 335–362 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  33. Hu, X.Y., Khoo, B.C.: An interface interaction method for compressible multifluids. J. Comput. Phys. 198(1), 35–64 (2004)

    Article  MATH  Google Scholar 

  34. Bourne, N.K., Field, J.E.: Shock-induced collapse of single cavities in liquids. J. Fluid Mech. 244, 225–240 (1992)

    Article  Google Scholar 

  35. Mali, V.I.: Flow of metals with a hemispherical indentation under action of shock-waves. Combust. Explos. Shock+ 9(2), 241–245 (1973)

    Article  Google Scholar 

  36. Liu, T.G., Khoo, B.C., Yeo, K.S.: The simulation of compressible multi-medium flow II. Applications to 2D underwater shock refraction. Comput. Fluids 30(3), 315–337 (2001)

    Article  Google Scholar 

  37. Ballhaus, W.F., Holt, M.: Interaction between ocean surface and underwater spherical blast waves. Phys. Fluids 17(6), 1068–1079 (1974)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

The financial support of this work came from the grants provided by the Agency for Defense Development and the National Research Foundation of Korea (2012R1A6A3A01017982) contracted through the IAAT at Seoul National University.

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  1. Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul, 151-742, South Korea

    Ki-Hong Kim, Min-cheol Gwak & Jack J. Yoh

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  1. Ki-Hong Kim
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  3. Jack J. Yoh
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Correspondence to Jack J. Yoh.

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Kim, KH., Gwak, Mc. & 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

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  • DOI: https://doi.org/10.1007/s10915-014-9970-6

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