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Computation of Pressure Fields for a Hybrid Particle-Mesh Method

하이브리드 입자-격자 방법에서의 압력장 계산

  • Lee, Seung-Jae (Research Institute of Marine Systems Engineering, Seoul National University) ;
  • Suh, Jung-Chun (Research Institute of Marine Systems Engineering, Seoul National University)
  • 이승재 (서울대학교 해양시스템공학연구소) ;
  • 서정천 (서울대학교 해양시스템공학연구소)
  • Received : 2014.02.20
  • Accepted : 2014.05.27
  • Published : 2014.08.20

Abstract

A hybrid particle-mesh method based on the vorticity-velocity formulation for solving the incompressible Navier-Stokes equations is a combination of the Vortex-In-Cell(VIC) method for convection and the penalization method for diffusion. The key feature of the numerical methods is to determine velocity and vorticity fields around a solid body on a temporary grid, and then the time evolution of the flow is computed by tracing the convection of each vortex element using the Lagrangian approach. Assuming that the vorticity and velocity fields are to be computed in time domain analysis, pressure fields are estimated through a complete set of solutions at present time step. It is possible to obtain vorticity and velocity fields prior to any pressure calculation since the pressure term is eliminated in the vorticity-velocity formulation. Therefore, pressure field is explicitly treated by solving a suitable Poisson equation. In this paper, we propose a simple way to numerically implement the vorticity-velocity-pressure formulation including a penalty term. For validation of the proposed numerical scheme, we illustrate the early development of viscous flows around an impulsive started circular cylinder for Reynolds number of 9500.

Keywords

References

  1. Angot, P. Brunear, C.H. Fabrie, P., 1999. A penalization method to take into account obstacles in incompressible viscous flows. Numerische Mathematik, 81, pp.497-520. https://doi.org/10.1007/s002110050401
  2. Batchelor, G.K., 1967. An introduction to fluid dynamics, Cambridge University Press: Cambridge.
  3. Bouard, R. & Coutanceau, M., 1980. The early stage of development of the wake behind an impulsively started circular cylinder for 40 < Re < 104. Journal of Fluid Mechanics, 101, pp.586-607.
  4. Cottet, G.H. Gallizio, F. Magni, A. & Mortazavi, I., 2010. A vortex immersed boundary method for bluff body flows. Proceedings of 3rd Joint US-European ASME Fluids Enigineering Summer Meeting, Sympoisum on Development and Applications of Immersed Boundary Methods, Montreal, Canada, FEDSM-ICNMM2010-30787.
  5. Lighthill, M.J., 1963. Introduction, boundary layer theory, Laminar boundary layers, edited by J. Rosenhead, Oxford University Press: New York.
  6. Loc, T.P. & Bouard, R., 1985. Numerical solution of the early stage of the unsteady viscous flow around a circular cylinder: a comparison with experimental visualization and measurements. Journal of Fluid Mechanics, 160, pp.93-117. https://doi.org/10.1017/S0022112085003408
  7. Sarpkaya, T., 1989. Computational methods with vortices: the 1988 Freeman scholar Lecture. Journal of Fluids Engineering, 111(1), pp.5-52. https://doi.org/10.1115/1.3243601
  8. Suh, J.C. & Kim, K.S., 1999. A vorticity-velocity formulation for solving the two-dimensional Navier Stokes equations. Fluid Dynamics Research, 25(4), pp.195-216. https://doi.org/10.1016/S0169-5983(99)00020-9