Vortex-in-cell method combined with a boundary element method for incompressible viscous flow analysis. (English) Zbl 1253.76071

Summary: An immersed boundary vortex-in-cell (VIC) method for simulating the incompressible flow external to two-dimensional and three-dimensional bodies is presented. The vorticity transport equation, which is the governing equation of the VIC method, is represented in a Lagrangian form and solved by the vortex blob representation of the flow field. In the present scheme, the treatment of convection and diffusion is based on the classical fractional step algorithm. The rotational component of the velocity is obtained by solving Poisson’s equation using an FFT method on a regular Cartesian grid, and the solenoidal component is determined from solving an integral equation using the panel method for the convection term, and the diffusion term is implemented by a particle strength exchange scheme. Both the no-slip and no-through flow conditions associated with the surface boundary condition are satisfied by diffusing vortex sheet and distributing singularities on the body, respectively. The present method is distinguished from other methods by the use of the panel method for the enforcement of the no-through flow condition. The panel method completes making use of the immersed boundary nature inherent in the VIC method and can be also adopted for the calculation of the pressure field. The overall process is parallelized using message passing interface to manage the extensive computational load in the three-dimensional flow simulations.


76M15 Boundary element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76Z05 Physiological flows
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[1] Cottet G-H 3D Vortex Methods: achievements and challenges Proceedings of the First International Conference on Vortex Methods 1999 123 134
[2] Chorin, Numerical study of slightly viscous flow, Journal of Fluid Mechanics 57 pp 785– (1973)
[3] Greengard, The core spreading vortex method approximates the wrong equation, Journal of Computational Physics 61 pp 345– (1985) · Zbl 0587.76039
[4] Ogami, Viscous flow simulation using the discrete vortex model-the diffusion velocity method, Computers & Fluids 19 pp 433– (1991) · Zbl 0733.76047
[5] Ploumhans, Vortex methods for direct numerical simulation of three dimensional bluff body flows: application to the sphere at Re=300, 500, and 1000, Journal of Computational Physics 178 pp 427– (2002) · Zbl 1045.76030
[6] Cottet, Advances in direct numerical simulations of 3D wall-bounded flows by Vortex-in-Cell methods, Journal of Computational Physics 193 pp 136– (2004) · Zbl 1047.76092
[7] Lee KJ An immersed boundary vortex in cell method combined with a panel method for incompressible viscous flow analysis Thesis (PhD) 2009
[8] Kim, A combined vortex and panel method for numerical simulations of viscous flows: a comparative study of a vortex particle method and a finite volume method, International Journal for Numerical Methods in Fluids 49 pp 1087– (2005) · Zbl 1284.76268
[9] Suh, Analytic evaluation of the surface integral in the singularity methods, Transactions of the Society of Naval Architects of Korea 29 pp 14– (1992)
[10] Bar-Lev, Initial flow field over an impulsively started circular cylinder, Journal of Fluid Mechanics 72 pp 625– (1975) · Zbl 0317.76018
[11] Ploumhans, Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry, Journal of Computational Physics 165 pp 354– (2000) · Zbl 1006.76068
[12] Bouard, The early stage development of the wake behind an impulsively started cylinder for 40 < Re < 104, Journal of Fluid Mechanics 101 pp 583– (1980)
[13] Taneda, Studies on wake vortices (III). Experimental investigation of the wake behind a sphere at low Reynolds number, Reports of Research Institute of Applied Mechanics 4 pp 99– (1956)
[14] Johnson, Flow past a sphere up to a Reynolds number of 300, Journal of Fluid Mechanics 378 pp 19– (1999)
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