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High Order Anchoring and Reinitialization of Level Set Function for Simulating Interface Motion

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Abstract

A second order interface anchoring method has been developed and used with fast sweeping algorithm for reinitialization of a level set function. The algebraic anchoring formulation ensures that the location of the actual interface is preserved, leading to better mass conservation property. It also provides high order accurate algebraic constraint for solving the Eikonal equation on a finite difference grid. Geometric properties of the interface such as surface normal and curvature are subsequently computed from the reinitialized distance function. Various analytical functions for modeling distortion in level set field are considered and accuracy of reinitialization is evaluated using first and second order anchoring schemes. It is also shown that accurate computation of interface curvature requires a high order anchor in addition to a high order fast sweeping method. Mass conservation property of reinitialization is also analyzed by considering test problems from literature including the classic Rider–Kothe single vortex problem. The formulation is suitable for efficient parallelization for both distributed memory and on-node shared memory parallel systems. Scalability and performance of the reinitialization scheme on multiple architectures are demonstrated.

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References

  1. Sussman, M., Ohta, M.: High-order techniques for calculating surface tension forces. In: Figueiredo, I.N., Rodrigues, J.F., Santos, L. (eds.) Free Boundary Problems, pp. 425–434. Birkhäuser Basel, Basel (2007)

    Chapter  Google Scholar 

  2. 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  Google Scholar 

  3. du Chéné, A., Min, C., Gibou, F.: Second-order accurate computation of curvatures in a level set framework using novel high-order reinitialization schemes. J. Sci. Comput. 35(2–3), 114–131 (2008)

    Article  MathSciNet  Google Scholar 

  4. 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  Google Scholar 

  5. Gibou, F., Fedkiw, R., Caflisch, R., Osher, S.: A level set approach for the numerical simulation of dendritic growth. J. Sci. Comput. 19(1–3), 183–199 (2003)

    Article  MathSciNet  Google Scholar 

  6. Shaikh, J., Sharma, A., Bhardwaj, R.: On sharp-interface level-set method for heat and/or mass transfer induced Stefan problem. Int. J. Heat Mass Transf. 96, 458–473 (2016)

    Article  Google Scholar 

  7. Udaykumar, H.S., Mittal, R., Shyy, W.: Computation of solid–liquid phase fronts in the sharp interface limit on fixed grids. J. Comput. Phys. 153(2), 535–574 (1999)

    Article  Google Scholar 

  8. Jin, S., Wang, X., Starr, T.L., Chen, X.: Robust numerical simulation of porosity evolution in chemical vapor infiltration I: two space dimension. J. Comput. Phys. 162(2), 467–482 (2000)

    Article  Google Scholar 

  9. Jin, S., Wang, X.: Robust numerical simulation of porosity evolution in chemical vapor infiltration III: three space dimension. J. Comput. Phys. 186(2), 582–595 (2003)

    Article  Google Scholar 

  10. Gibou, F., Fedkiw, R., Osher, S.: A review of level-set methods and some recent applications. J. Comput. Phys. 353, 82–109 (2018)

    Article  MathSciNet  Google Scholar 

  11. Desjardins, O., Moureau, V., Pitsch, H.: An accurate conservative level set/ghost fluid method for simulating turbulent atomization. J. Comput. Phys. 227(18), 8395–8416 (2008)

    Article  MathSciNet  Google Scholar 

  12. Mittal, R., Dong, H., Bozkurttas, M., Najjar, F.M., Vargas, A., von Loebbecke, A.: A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries. J. Comput. Phys. 227(10), 4825–4852 (2008)

    Article  MathSciNet  Google Scholar 

  13. Bo, W., Liu, X., Glimm, J., Li, X.: A robust front tracking method: verification and application to simulation of the primary breakup of a liquid jet. SIAM J. Sci. Comput. 33(4), 1505–1524 (2011)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  15. Youngs, D.: Time-dependent multi-material flow with large fluid distortion. In: Numerical Methods for Fluid Dynamics, vol. 24, pp. 273–285. Academic Press, Cambridge (1982)

  16. Benson, D.J.: Volume of fluid interface reconstruction methods for multi-material problems. Appl. Mech. Rev. 55(2), 151–165 (2002)

    Article  Google Scholar 

  17. Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press. Google-Books-ID: ErpOoynE4dIC (1999)

  18. 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  Google Scholar 

  19. Coquerelle, M., Glockner, S.: A fourth-order accurate curvature computation in a level set framework for two-phase flows subjected to surface tension forces. J. Comput. Phys. 305, 838–876 (2016)

    Article  MathSciNet  Google Scholar 

  20. Trujillo, M.F., Anumolu, L., Ryddner, D.: The distortion of the level set gradient under advection. J. Comput. Phys. 334, 81–101 (2017)

    Article  MathSciNet  Google Scholar 

  21. Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. Nat. Acad. Sci. 93(4), 1591–1595 (1996)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  23. Chopp, D.: Some improvements of the fast marching method. SIAM J. Sci. Comput. 23(1), 230–244 (2001)

    Article  MathSciNet  Google Scholar 

  24. McCaslin, J.O., Desjardins, O.: A localized re-initialization equation for the conservative level set method. J. Comput. Phys. 262, 408–426 (2014)

    Article  MathSciNet  Google Scholar 

  25. Nourgaliev, R., Kadioglu, S., Mousseau, V.: Marker redistancing/level set method for high-fidelity implicit interface tracking. SIAM J. Sci. Comput. 32(1), 320–348 (2010)

    Article  MathSciNet  Google Scholar 

  26. Zhao, H.: A fast sweeping method for Eikonal equations. Math. Comput. 74(250), 603–627 (2005)

    Article  MathSciNet  Google Scholar 

  27. Zhao, H.: Parallel implementations of the fast sweeping method. J. Comput. Math. 25(4), 421–429 (2007)

    MathSciNet  Google Scholar 

  28. Qian, J., Yong-Tao, Z., Zhao, H.: A fast sweeping method for static convex Hamilton–Jacobi equations. J. Sci. Comput. 31, 237–271 (2007)

    Article  MathSciNet  Google Scholar 

  29. Zhang, Y.-T., Zhao, H.-K., Qian, J.: High order fast sweeping methods for static Hamilton–Jacobi equations. J. Sci. Comput. 29(1), 25–56 (2006)

    Article  MathSciNet  Google Scholar 

  30. Zhang, Y.-T., Shu, C.-W.: Chapter 5–ENO and WENO schemes. In: Abgrall, R., Shu, C.-W. (eds.) Handbook of Numerical Methods for Hyperbolic Problems, of Handbook of Numerical Analysis, vol. 17, pp. 103–122. Elsevier, Amsterdam (2016)

    Google Scholar 

  31. 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  Google Scholar 

  32. Bajaj, C.L., Xu, G., Zhang, Q.: Smooth surface constructions via a higher-order level-set method. In: 2007 10th IEEE international conference on computer-aided design and computer graphics, pp. 27–27 (2007)

  33. Edwards, H.C., Trott, C.R., Sunderland, D.: Kokkos: enabling manycore performance portability through polymorphic memory access patterns. J. Parallel Distrib. Comput. 74(12), 3202–3216 (2014)

    Article  Google Scholar 

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Acknowledgements

This research was supported by the High-Performance Computing for Manufacturing Project Program (HPC4Mfg), managed by the U.S. Department of Energy Advanced Manufacturing Office within the Energy Efficiency and Renewable Energy Office. It was performed using resources of the Oak Ridge Leadership Computing Facility and Oak Ridge National Laboratory, which are supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0500OR22725.

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  1. Oak Ridge National Laboratory, 1 Bethel Valley Rd., Oak Ridge, TN, 37831, USA

    Vimal Ramanuj & Ramanan Sankaran

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  1. Vimal Ramanuj
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  2. Ramanan Sankaran
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Correspondence to Vimal Ramanuj.

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Ramanuj, V., Sankaran, R. High Order Anchoring and Reinitialization of Level Set Function for Simulating Interface Motion. J Sci Comput 81, 1963–1986 (2019). https://doi.org/10.1007/s10915-019-01076-0

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