Advances in direct numerical simulations of 3D wall-bounded flows by Vortex-in-Cell methods

  • Authors:

  • G.-H. Cottet;P. Poncet

  • Affiliations:

  • LMC IMAG, Université Joseph Fourier, BP 53, 38041 Grenoble, Cedex 9, France;Laboratoire MIP, INSA, 135 avenue de Rangueil, 31077 Toulouse, Cedex 4, France

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2004

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Abstract

This paper is devoted to the design of Vortex-In-Cell (VIC) methods for the direct numerical simulations of wall-bounded flows. A first method using body-fitted grid is presented in the particular case of a cylinder wake. This method, which has been used in [Phys. Fluids 14(6) (2002) 2021] to investigate the effect on the wake topology of cylinder rotations, is an extension of the VIC method presented in [J. Comput. Phys. 175 (2002) 702] for periodic geometries. Features of the method that are specific to wall-bounded geometries - interpolation operators, field calculations and vorticity flux formulas to enforce no-slip boundary conditions - are described in details. The accuracy of the method in the calculation of the body forces is investigated by comparisons with experiments and benchmark calculations. A second class of methods is in the spirit of the immersed boundary methods. The paper in particular shows that the no-slip conditions are very naturally handled by the vorficity flux formulas, independently of the relative locations of the particles and the body. Numerical experiments on the test-case of a ring impinging on a cylinder suggest that the method is second-order accurate.