Korea-Australia Rheology Journal

The Korean Society of Rheology (한국유변학회)
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Finite element analysis of elastic solid/Stokes flow interaction problem

  • Myung, Jin-Suk (School of Chemical and Biological Engineering, Seoul National University) ;
  • Hwang, Wook-Ryol (School of Mechanical and Aerospace Engineering, Research Center for Aircraft Parts Technology (ReCAPT), Gyeongsang National University) ;
  • Won, Ho-Youn (Hanwha Chemical, Research and Development Center) ;
  • Ahn, Kyung-Hyun (School of Chemical and Biological Engineering, Seoul National University) ;
  • Lee, Seung-Jong (School of Chemical and Biological Engineering, Seoul National University)
  • Published : 2007.12.31
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Abstract

We performed a numerical investigation to find out the optimal choice of the spatial discretization in the distributed-Lagrangian-multiplier/fictitious-domain (DLM/FD) method for the solid/fluid interaction problem. The elastic solid bar attached on the bottom in a pressure-driven channel flow of a Newtonian fluid was selected as a model problem. Our formulation is based on the scheme of Yu (2005) for the interaction between flexible bodies and fluid. A fixed regular rectangular discretization was applied for the description of solid and fluid domain by using the fictitious domain concept. The hydrodynamic interaction between solid and fluid was treated implicitly by the distributed Lagrangian multiplier method. Considering a simplified problem of the Stokes flow and the linearized elasticity, two numerical factors were investigated to clarify their effects and to find the optimum condition: the distribution of Lagrangian multipliers and the solid/fluid interfacial condition. The robustness of this method was verified through the mesh convergence and a pseudo-time step test. We found that the fluid stress in a fictitious solid domain can be neglected and that the Lagrangian multipliers are better to be applied on the entire solid domain. These results will be used to extend our study to systems of elastic particle in the Stokes flow, and of particles in the viscoelastic fluid.

Keywords

References

  1. Allen, M. P. and D. J. Tildesley, 1987, Computer Simulation of Liquids, Oxford University Press, Oxford, UK
  2. Amestoy, P. R. and I. S. Duff, 1989, Vectorization of a Mu1tiprocessor Multifrontal Code, Intern. J Supercomput. Applicat. 3(3), 41-59 https://doi.org/10.1177/109434208900300303
  3. Amestoy, P. R. and I. S. Duff, 1993, Memory Management Issues in Sparse Multifrontal Methods on Multiprocessors, Intern. J Supercomput. Applicat. 7(1), 64-82 https://doi.org/10.1177/109434209300700105
  4. Amestoy, P. R. and C. Puglisi, 2003, An unsymmetrized multifrontal LU factorization, SIAM J Matrix Anal. Applicat. 24(2), 553-569 https://doi.org/10.1137/S0895479800375370
  5. Baaijens, F. P. T., 2001, A fictitious domain/mortar element method for fluid-structure interaction, Int. J Numer. Methods Fluids 35(7), 743-761 https://doi.org/10.1002/1097-0363(20010415)35:7<743::AID-FLD109>3.0.CO;2-A
  6. Donea, J., S. Giuliani and J. P. Halleux, 1981, Arbitrary Lagrangian-Eulerian fmite element method for transient dynamic fluid-structure interactions, Comput. Methods Appl. Mech. Eng. 33(1-3), 689-723 https://doi.org/10.1016/0045-7825(82)90128-1
  7. Glowinski, R., T. W. Pan, T. I. Hesla and D. D. Joseph, 1999, A distributed Lagrange multiplier fictitious domain method for particulate flows, Int. J Multiph. Flow 25(5), 755-794 https://doi.org/10.1016/S0301-9322(98)00048-2
  8. Hu, H. H., 1996, Direct simulation of flows of solid-liquid mixtures, Int. J. Multiph. Flow 22(2), 335-352 https://doi.org/10.1016/0301-9322(95)00068-2
  9. Hughes, T. J. R., 2000, The Finite Element Method: linear static and dynamic finite element analysis, Dover publications, New York, US
  10. Hiitter, M., 1999, Brownian Dynamics Simulation of Stable and of Coagulating Colloids in Aqueous Suspension, PhD Thesis, ETH, ZURICH
  11. Hwang, W. R., M. A. Hulsen and H. E. H. Meijer, 2004, Direct simulation of particle suspensions in sliding bi-periodic frames, J. Comput. Phys. 194(2), 742-772 https://doi.org/10.1016/j.jcp.2003.09.023
  12. Laso, M. and H. C. Ottinger, 1993, Calculation of Viscoelastic Flow Using Molecular-Models - the Connffessit Approach, J. Non-Newtonian Fluid Mech. 47, 1-20 https://doi.org/10.1016/0377-0257(93)80042-A
  13. Trofimov, S. Y., 2003, Thermodynamic consistency in dissipative particle dynamics, PhD Thesis, Technische Universiteit Eindhoven, Eindhoven
  14. Yu, Z., 2005, A DLM/FD method for fluid/flexible-body interactions, J. Com put. Phys. 207(1), 1-27 https://doi.org/10.1016/j.jcp.2004.12.026