Journal of Scientific Computing

, Volume 46, Issue 2, pp 166–181 | Cite as

Numerical Method for Interaction Among Multi-particle, Fluid and Arbitrary Shape Structure

  • Kensuke YokoiEmail author


We propose a numerical method for handling interaction among multiple particles, fluid and structure of arbitrary shape. The method is based on the level set method, the DEM (discrete element method), the CIP (Cubic Interpolated Propagation) method and the ghost fluid method. In this formulation, interfaces of particles, liquid and structures are represented by the level set functions. Those level set functions are also used to impose fluid boundary condition on structure and particle, and to detect collisions between particle and structure. Numerical results show that this proposed method can robustly simulate those interactions.


Particle-fluid-structure interaction Level set method Discrete element method CIP method 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29, 47 (1979) CrossRefGoogle Scholar
  2. 2.
    Campbell, C.S.: Rapid granular flow. Ann. Rev. Fluid Mech. 22, 57 (1990) CrossRefGoogle Scholar
  3. 3.
    Mustoe, G. (ed.): Eng. Comput. 9(2) (1992). Special Issue Google Scholar
  4. 4.
    Yokoi, K.: Numerical method for interaction between multi-particle and complex structures. Phys. Rev. E 72, 046713 (2005) CrossRefGoogle Scholar
  5. 5.
    Osher, S., Sethian, J.A.: Front propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulation. J. Comput. Phys. 79, 12 (1988) zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Sussman, M., Smereka, P., Osher, S.: A level set approach for capturing solution to incompressible two-phase flow. J. Comput. Phys. 114, 146 (1994) zbMATHCrossRefGoogle Scholar
  7. 7.
    Sethian, J.A.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1999) zbMATHGoogle Scholar
  8. 8.
    Osher, S., Fedkiw, R.: Level Set Methods and Dynamics Implicit Surface. Applied Mathematical Sciences, vol. 153. Springer, Berlin (2003) Google Scholar
  9. 9.
    Fedkiw, R., et al.: A non-oscillatory Eulerian approach to interfaces in multimaterial flows (The Ghost fluid method). J. Comput. Phys. 152, 457 (1999) zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Watanabe, M., Kikinis, R., Westin, C.F.: Lecture Notes in Computer Science, vol. 2489. Springer, Berlin (2002), 405 Google Scholar
  11. 11.
    Yokoi, K.: Numerical method for moving solid object in flows. Phys. Rev. E 67, 045701(R) (2003) CrossRefGoogle Scholar
  12. 12.
    Peskin, C.S.: Numerical analysis of blood flow in the heart. J. Comput. Phys. 25, 220 (1977) zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Xiao, F., et al.: An algorithm for simulating solid objects suspended in stratified flow. Comput. Phys. Commun. 102, 147 (1997) CrossRefGoogle Scholar
  14. 14.
    Xiao, F.: A computational model for suspended large rigid bodies in 3D unsteady viscous flows. J. Comput. Phys. 155, 348 (1999) zbMATHCrossRefGoogle Scholar
  15. 15.
    Tanaka, T., Kawaguchi, T., Tsuji, Y.: Discrete particle simulation of flow patterns in two-dimensional gas fluidized beds. Int. J. Mod. Phys. B 7, 1889 (1993) CrossRefGoogle Scholar
  16. 16.
    Ladd, A.J.C.: Numerical simulations of particulate flow suspensions via a discretized Boltzmann equation. Part II: Numerical results. J. Fluid Mech. 271, 311 (1994) CrossRefMathSciNetGoogle Scholar
  17. 17.
    Feng, Z.G., Michaelides, E.E.: Proteus: a direct forcing method in the simulation of particulate flows. J. Comput. Phys. 202, 20 (2005) zbMATHCrossRefGoogle Scholar
  18. 18.
    Kim, J., Moin, P.: Applications of a fractional step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59, 308 (1985) zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Yabe, T., et al.: A universal solver for hyperbolic equations by cubic-polynomial interpolation II. Two- and three-dimensional solvers. Comput. Phys. Commun. 66, 233 (1991) zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Yabe, T., Xiao, F., Utsumi, T.: The constrained interpolation profile method for multiphase analysis. J. Comput. Phys. 169, 2 (2001) CrossRefMathSciNetGoogle Scholar
  21. 21.
    Tornberg, A.K., Engquist, B.: Numerical approximations of singular source terms in differential equations. J. Comput. Phys. 200(2), 462–488 (2004) zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Engquist, B., Tornberg, A.K., Tsai, R.: Discretization of Dirac delta functions in level set methods. J. Comput. Phys. 207(1), 28–51 (2005) zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Zhao, H.K., Chan, T.F., Merriman, B., Osher, S.: A variational level set approach to multiphase motion. J. Comput. Phys. 127, 179–195 (1996) zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Yokoi, K.: A variational approach to motion of triple junction of gas, liquid and solid. Comput. Phys. Commun. 180, 1145 (2009) zbMATHCrossRefGoogle Scholar
  25. 25.
    Harten, A., Engquist, B., Osher, S., Chakravarthy, S.: Uniformly high-order accurate essentially non-oscillatory schemes III. J. Comput. Phys. 71, 231 (1987) zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Shu, C.W., Osher, S.: Efficient implementation of essentially non-oscillatory shock capturing schemes. J. Comput. Phys. 77, 439 (1988) zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Liu, X.D., Osher, S., Chan, T.: Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115, 200 (1994) zbMATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Jiang, G.S., Shu, C.W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202 (1996) zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Tsitsiklis, J.: Efficient algorithms for globally optimal trajectories. In: Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista, LF, pp. 1368–1373 (1994) Google Scholar
  30. 30.
    Tsitsiklis, J.: Efficient algorithms for globally optimal trajectories. IEEE Trans. Automat. Control 40, 1528 (1995) zbMATHCrossRefMathSciNetGoogle Scholar
  31. 31.
    Adalsteinsson, D., Sethian, J.A.: The fast construction of extension velocities in level set methods. J. Comput. Phys. 148, 2 (1999) zbMATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    Tsai, Y.R.: Rapid and accurate computation of the distance function using grids. J. Comput. Phys. 178, 175 (2001) CrossRefGoogle Scholar
  33. 33.
    Yokoi, K.: Numerical method for complex moving boundary problems in a Cartesian fixed grid. Phys. Rev. E 65, 055701(R) (2002) Google Scholar
  34. 34.
    Zhao, H.K.: Fast sweeping method for eikonal equations. Math. Comput. 74, 603 (2005) zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of CaliforniaLos AngelesUSA
  2. 2.Department of Electronics and Mechanical EngineeringChiba UniversityChibaJapan
  3. 3.School of EngineeringCardiff UniversityCardiffUK

Personalised recommendations