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**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.

### MSC:

76M15 | Boundary element methods applied to problems in fluid mechanics |

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

76Z05 | Physiological flows |

### Keywords:

vortex-in-cell method; immersed boundary technique; boundary element method; bluff body; incompressible fluid; viscous flow; particle method; incompressible flow; marine hydrodynamics; parallelization
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\textit{Y.-C. Kim} et al., Int. J. Numer. Methods Fluids 69, No. 10, 1567--1583 (2012; Zbl 1253.76071)

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### References:

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