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

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Abstract

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.

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References

  1. Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29, 47 (1979)

    Article  Google Scholar 

  2. Campbell, C.S.: Rapid granular flow. Ann. Rev. Fluid Mech. 22, 57 (1990)

    Article  Google Scholar 

  3. Mustoe, G. (ed.): Eng. Comput. 9(2) (1992). Special Issue

  4. Yokoi, K.: Numerical method for interaction between multi-particle and complex structures. Phys. Rev. E 72, 046713 (2005)

    Article  Google Scholar 

  5. Osher, S., Sethian, J.A.: Front propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulation. J. Comput. Phys. 79, 12 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  7. Sethian, J.A.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  8. Osher, S., Fedkiw, R.: Level Set Methods and Dynamics Implicit Surface. Applied Mathematical Sciences, vol. 153. Springer, Berlin (2003)

    Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  10. Watanabe, M., Kikinis, R., Westin, C.F.: Lecture Notes in Computer Science, vol. 2489. Springer, Berlin (2002), 405

    Google Scholar 

  11. Yokoi, K.: Numerical method for moving solid object in flows. Phys. Rev. E 67, 045701(R) (2003)

    Article  Google Scholar 

  12. Peskin, C.S.: Numerical analysis of blood flow in the heart. J. Comput. Phys. 25, 220 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  13. Xiao, F., et al.: An algorithm for simulating solid objects suspended in stratified flow. Comput. Phys. Commun. 102, 147 (1997)

    Article  Google Scholar 

  14. Xiao, F.: A computational model for suspended large rigid bodies in 3D unsteady viscous flows. J. Comput. Phys. 155, 348 (1999)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  17. Feng, Z.G., Michaelides, E.E.: Proteus: a direct forcing method in the simulation of particulate flows. J. Comput. Phys. 202, 20 (2005)

    Article  MATH  Google Scholar 

  18. Kim, J., Moin, P.: Applications of a fractional step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59, 308 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  20. Yabe, T., Xiao, F., Utsumi, T.: The constrained interpolation profile method for multiphase analysis. J. Comput. Phys. 169, 2 (2001)

    Article  MathSciNet  Google Scholar 

  21. Tornberg, A.K., Engquist, B.: Numerical approximations of singular source terms in differential equations. J. Comput. Phys. 200(2), 462–488 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  24. Yokoi, K.: A variational approach to motion of triple junction of gas, liquid and solid. Comput. Phys. Commun. 180, 1145 (2009)

    Article  MATH  Google Scholar 

  25. Harten, A., Engquist, B., Osher, S., Chakravarthy, S.: Uniformly high-order accurate essentially non-oscillatory schemes III. J. Comput. Phys. 71, 231 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  26. Shu, C.W., Osher, S.: Efficient implementation of essentially non-oscillatory shock capturing schemes. J. Comput. Phys. 77, 439 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  27. Liu, X.D., Osher, S., Chan, T.: Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115, 200 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  28. Jiang, G.S., Shu, C.W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  30. Tsitsiklis, J.: Efficient algorithms for globally optimal trajectories. IEEE Trans. Automat. Control 40, 1528 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  31. Adalsteinsson, D., Sethian, J.A.: The fast construction of extension velocities in level set methods. J. Comput. Phys. 148, 2 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  32. Tsai, Y.R.: Rapid and accurate computation of the distance function using grids. J. Comput. Phys. 178, 175 (2001)

    Article  Google Scholar 

  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. Zhao, H.K.: Fast sweeping method for eikonal equations. Math. Comput. 74, 603 (2005)

    MATH  Google Scholar 

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Correspondence to Kensuke Yokoi.

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Yokoi, K. Numerical Method for Interaction Among Multi-particle, Fluid and Arbitrary Shape Structure. J Sci Comput 46, 166–181 (2011). https://doi.org/10.1007/s10915-010-9385-y

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  • DOI: https://doi.org/10.1007/s10915-010-9385-y

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