Journal of Hydrodynamics

, Volume 18, Issue 1, pp 93–100 | Cite as

Modeling of liquid-solid flows with large number of moving particles by multigrid fictitious boundary method

  • Decheng Wan
  • Stefan Turek
Session B1


An efficient multigrid fictitious boundary method (MFBM) for the detailed simulation of solid-liquid flows with large number of moving particles is presented. The MFBM is based on a multigrid FEM background grid which covers the whole computational domain and can be chosen independently from the particles of arbitrary shape, size and number. An obvious advantage of the MFBM is that it is able to efficiently treat the interaction between the fluid and the moving rigid particles, especially a fixed multigrid mesh is allowed to be used and there is no need to remesh. Two examples of numerical simulations of three big disks plunging into 2000 small particles as well as sedimentation of 5,000 particles in a cavity are provided to show that the presented method is potentially powerful to simulate real particulate flows with large number of moving particles.

Key words

liquid-solid flows multigrid FEM fictitious boundary method 


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  1. [1]
    Hu, H.H., Joseph, D.D. and Crochet, M.J.: Direct simulation of fluid particle motions, Theor. Comp. Fluid Dyn. 3, (1992), 285–306CrossRefGoogle Scholar
  2. [2]
    Hu, H.H., Patankar, N.A. and Zhu, M.Y.: Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian techniques, J. Comput. Phys., 169, (2001), 427MathSciNetCrossRefGoogle Scholar
  3. [3]
    Maury, B.: Characteristics ALE method for the unsteady 3D Navier-Stokes equations with a free surface, Int. J. of Comput. Fluid Dynamics, 6, (1996), 175–188CrossRefGoogle Scholar
  4. [4]
    Glowinski, R., Pan, T.W., Hesla, T.I., Joseph, D.D. and Periaux, J.: A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow, J. Comput. Phy., 169, (2001), 363–426MathSciNetCrossRefGoogle Scholar
  5. [5]
    Glowinski, R.: Numerical methods for fluids (Part 3), Handbook of numerical analysis, Volume IX, Ciarlet, P.G and Lions, J.L., Editors, North-Holland, (2003)Google Scholar
  6. [6]
    Wan, D.C. and Turek, S.: Direct Numerical Simulation of Particulate Flow via Multigrid FEM Techniques and the Fictitious Boundary Method, International Journal for Numerical Method in Fluids, in press. Currently available at DOI: 10.1002/fld.1129CrossRefMathSciNetzbMATHGoogle Scholar
  7. [7]
    Wan, D.C., Turek, S. and Liudmila S. Rivkind: An Efficient Multigrid FEM Solution Technique for Incompressible Flow with Moving Rigid Bodies, Numerical Mathematics and Advanced Applications, Springer-Verlag, Berlin, (2004), 844–853.CrossRefGoogle Scholar

Copyright information

© China Ship Scientific Research Center 2006

Authors and Affiliations

  • Decheng Wan
    • 1
  • Stefan Turek
    • 2
  1. 1.School of Naval Architecture, Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Department of Applied Mathematics, LS IIIUniversity of DortmundDortmundGermany

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