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High-resolution simulations of the flow around an impulsively started cylinder using vortex methods

  • P. Koumoutsakos (a1) (a2) and A. Leonard (a1)
Abstract

The development of a two-dimensional viscous incompressible flow generated from a circular cylinder impulsively started into rectilinear motion is studied computationally. An adaptative numerical scheme, based on vortex methods, is used to integrate the vorticity/velocity formulation of the Navier–Stokes equations for a wide range of Reynolds numbers (Re = 40 to 9500). A novel technique is implemented to resolve diffusion effects and enforce the no-slip boundary condition. The Biot–Savart law is employed to compute the velocities, thus eliminating the need for imposing the far-field boundary conditions. An efficient fast summation algorithm was implemented that allows a large number of computational elements, thus producing unprecedented high-resolution simulations. Results are compared to those from other theoretical, experimental and computational works and the relation between the unsteady vorticity field and the forces experienced by the body is discussed.

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Barnes, J. E. & Hut, P.1986A hierarchical O(NlogN) force-calculation algorithm. Nature324, 446449.

Bouard, R. & Coutanceau, M. 1980 The early stage of development of the wake behind an impulsively started cylinder for 40 [les ] Re [les ] 104. J. Fluid Mech. 101, 583607 (referred to herein as BC).

Christiansen, J. P.1973Vortex methods for flow simulation. J. Comput. Phys.13, 363.

Collins, W. M. & Dennis, S. C. R.1973The initial flow past an impulsively started circular cylinder. Q. J. Mech. Appl. Maths26, 5375 (referred to herein as CD).

Collins, W. M. & Dennis, S. C. R. 1973b Flow past an impulsively started circular cylinder. J. Fluid Mech. 60, 105127 (referred to herein as CD).

Degond, P. & Mas-Gallic, S.1989The weighted particle method for convection—diffusion equations, Part I: The case of an isotropic viscosity, Part II: The anisotropic case. Math. Comput.53, 485526.

Dennis, S. C. R. & Kocabiyik, S.1991An asymptotic matching condition for unsteady boundary-layer flows governed by the Navier—Stokes equations. IMA J. Appl. Maths47, 8198.

Doligaski, T. L., Smith, C. R. & Walker, J. D. A.1994Vortex interactions with walls. Ann. Rev. Fluid Mech.26, 573616.

Greengard, L. & Rokhlin, V.1987A fast algorithm for particle simulations. J. Comput. Phys.73, 325348.

Koumoutsakos, P. & Leonard, A.1993Improved boundary integral method for inviscid boundary condition applications. AIAA J.31, 401404.

Koumoutsakos, P., Leonard, A. & Pepin, F.1994Boundary conditions for viscous vortex methods. J. Comput. Phys.113, 52.

Lecointe, Y. & Piquet, J.1984On the use of several compact methods for the study of the incompressible viscous flow around a circular cylinder. Computers Fluids12, 255280.

Payne, R. B. 1958 Calculation of viscous unsteady flows past a circular cylinder. J. Fluid Mech. 4, 8186.

Smith, P. A. & Stansby, P. K. 1988 Impulsively started flow around a circular cylinder by the vortex method. J. Fluid Mech. 194, 4577 (referred to herein as SS).

Tritton, D. J. 1959 Experiments on the flow past a circular cylinder at low Reynolds numbers. J. Fluid Mech. 6, 547567.

Van Dommelen, L. L. & Shen, S. F.1980The spontaneous generation of the singularity in a separating boundary layer. J. Comput. Phys.38, 125140.

Wang, X. & Dalton, C.1991Numerical solutions for impulsively started and decelerated viscous flow past a circular cylinder. Intl J. Numer. Meth. Fluids12, 383400.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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