Direct forcing/fictitious domain-Level set method for two-phase flow-structure interaction

이상 유동에서의 유체-구조 연성해석을 위한 Direct Forcing/Ficititious Domain-Level Set Method

Jeon, Chung-Ho;Yoon, Hyun-Sik;Jung, Jae-Hwan

  • Received : 2010.12.31
  • Accepted : 2011.08.16
  • Published : 2011.08.31


In the present paper, a direct forcing/fictitious domain (DF/FD) level set method is proposed to simulate the FSI (fluid-solid interaction) in two-phase flow. The main idea is to combine the direct-forcing/fictitious domain (DF/FD) method with the level set method in the Cartesian coordinates. The DF/FD method is a non-Lagrange-multiplier version of a distributed Lagrange multiplier/fictitious domain (DLM/FD) method. This method does not sacrifice the accuracy and robustness by employing a discrete ${\delta}$ (Dirac delta) function to transfer quantities between the Eulerian nodes and Lagrangian points explicitly as the immersed boundary method. The advantages of this approach are the simple concept, easy implementation, and utilization of the original governing equation without modification. Simulations of various water-entry problems have been conducted to validate the capability and accuracy of the present method in solving the FSI in two-phase flow. Consequently, the present results are found to be in good agreement with those of previous studies.


Immersed Boundary Method;Direct Forcing/Fictitious Domain (DF/FD);Level-Set Method;Free Surface;Two-phase Flow;Fluid Structure Interaction


  1. Azcueta, R.(2001). Computation of Turbulent Free-surface Flows around Ships and Floating bodies, Ph D. Thesis, Technical University Hamburg-Harburg.
  2. Chuang, S.L.(1967). "Experiments on Slamming of Wedge-shaped Bodies", Journal of Ship Research, Vol 11-3.
  3. Chung, J.Y., Chung, J.O., Kang, H.D., Kwon, S.H.(2007). "A Novel Experimental Technique in Slamming.", In: Proceedings of the 22nd International Workshop on Water Waves and Floating Bodies, Croatia, pp 41-44.
  4. Glowinski, R., Pana, T. W., Heslab, T. I., Josephb, D. D. and Périauxc, J.(2001). "A Fictitious Domain approach to the Direct Numerical Simulation of Incompressible Viscous Flow past Moving Rigid Bodies: Application to Particulate Flow", J. Comp. Phys., Vol 169, pp 363-426.
  5. Hirt, C.W. and Nichols, B.D.(1981). "Volume of Fluid (VOF) Methods for the Dynamics of Free Boundaries.", Journal of Computational Physics, Vol 39, pp 201-225.
  6. Hofler, K. and Schwarzer, S. (2001). "Navier-Stokes Simulation with Constraint Forces: Finite-Difference Method for Particleladen Flows and Complex Geometries.", Phys. Rev. E61-6, pp 7146-7160.
  7. Kim, J. and Moin, P. (1985). "Application of a Fractional Step Method to Incompressible Navier-Stokes Equations", J. Comp. Physics Vol 59, pp 308-323.
  8. Kang, M., Fedkiw, R.P. and Liu X.D.(2000). "A Boundary Condition Capturing Method for Multiphase Uncompressible Flow.", Journal of Scientic Computing, Vol 15, pp 323-360.
  9. Lee, B.H., Park, J.C., Kim, M.H., Jung, S.J., Ryu, M.C. and Kim, Y.S. (2010). "Numerical Simulation of Impact Loads using a Particle Method", Ocean Engineering, Vol 37, pp 164-173.
  10. Liu, X.D., Fedkiw, R.P. and Kang M. (2000). "A Boundary Condition Capturing Method for Poisson's Equation on Irregular Domains.", J. Comp. Phys., Vol 160, pp 151-178.
  11. Noh, W.F. and Woodward, P. (1976). "SLIC (Simple Line Interface Calculation).", In Lecture Notes in Physics, Vol 59, Springer-Verlag: New York, pp 330-340.
  12. Osher, S. and Sethian, J.A. (1988). "Fronts Propagating with Curvature-Dependent Speed : Algorithms based on Hamilton-Jacobi Formulations.", J. Comp. Phys., Vol 79, pp 12-49.
  13. Osher, S. and Fedkiw, R.P. (2002). Level Set Method and Dynamic Implicit Surfaces, Springer: Berlin.
  14. Peskin, C.S. (1972). "Flow Patterns around Heart Valves: a Numerical Method.", J. Comput. Phys. Vol 10, pp 252-271.
  15. Peterson, R., Wyman, D., and Frank C. (1997). "Drop Tests to Support Water-Impact and Planing Boat Dynamics Theory", CSS Technical Report, Coastal Systems Station, Panama City, USA. TR-9.
  16. Roma, A., Peskin, C. and Berger, M. (1999). "An Adaptive Version of the immersed Boundary Method", J. Comput. Phys., Vol 153, pp 509-534.
  17. Shu, C. and Osher, S. (1989). "Efficient Implementation of essentially Non Oscillatory Shock Capturing Schemes II", J. Comput. Phys., Vol 83, pp 32-78.
  18. Sussman, M., Smereka, P. and Osher, S. (1994). "A Level Set Approach for Computing Solutions to Incompressible Two-phase Flow.", J. Comp. Phys., Vol 114, pp 146-159.
  19. Sussman, M., Fatemi, E., Smereka, P. and Osher, S. (1997). "An Improved Level Set Method for Incompressible Two-Phase Flows", Computers and Fluids, Vol 27, pp 663-680.
  20. Uhlmann, M. (2005). "An immersed Boundary Method with Direct Forcing for the Simulation of Particulate Flows", J. Comp. Phys., Vol 209, pp 448-476.
  21. Youngs, D.L. (1982). "Time-dependent Multi-material ow with Large uid Distortion.", In Numerical Methods for Fluid Dynamics, Morton K.W., Baines M.J.(eds), Academic: New York, pp 273-285.
  22. Yu, Z. and Shao, X. (2007). "A Direct-forcing Fictitious Domain Method for Particulate Flows.", J. Comput. Phys Vol 227, pp 292-314.
  23. Yue, W. Lin, C.L. and Patel, V.C. (2003). "Numerical Simulation of Unsteady Multidimensional Free Surface Motions by Level Set Method", Int. J. Numer. Meth. Fluids, Vol 42, pp 853-884.
  24. Xu, L., Troesch, A.W. and Peterson R. (1999). "Asymmetric Hydrodynamic Impact and Dynamic Response of Vessels.", J. Offshore Mechanics and Arctic Engineering, Vol 121, pp 83-89..


Supported by : 한국연구재단