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**Advances in direct numerical simulations of 3D wall-bounded flows by vortex-in-cell methods.**
*(English)*
Zbl 1047.76092

Summary: 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 [P. Poncet, Phys. Fluids 14, No. 6, 2021–2023 (2002)] to investigate the effect on the wake topology of cylinder rotations, is an extension of the VIC method presented in [G.-H. Cottet et al., J. Comput. Phys. 175, 702–712 (2002; Zbl 1004.76066)] 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 vorticity 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.

### MSC:

76M23 | Vortex methods applied to problems in fluid mechanics |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

### Citations:

Zbl 1004.76066
PDFBibTeX
XMLCite

\textit{G. H. Cottet} and \textit{P. Poncet}, J. Comput. Phys. 193, No. 1, 136--158 (2004; Zbl 1047.76092)

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