Simulation of three-dimensional incompressible flows with a vortex-in-cell method

Impact of a vortex ring on a density interface using a regularized inviscid vortex sheet method

“…This is especially noticeable when simulating vortex rings, as a grid-induced instability with azimuthal wavenumber k ¼ 4 tends to distort an initially circular ring into a square. This was first seen in vortex filament studies of vortex rings [11]. Results from Section 4.1 are presented here in order to demonstrate this distortion in a vortex sheet method.…”

“…(11). The vorticity field is created from the current vortex sheet geometry and element strengths according to…”

“…This vortex-in-cell (VIC) algorithm reduces the cost per time step to OðN þ M log 2 MÞ, where N is the number of vortex elements and M is the number of cells in the grid. Couët [11] demonstrated the first three-dimensional VIC method, which solved for the motion of vortex filaments to study the evolution of vortex rings. Because the solution is computed on a grid, the finest scales of motion are limited to the size of a cell.…”

Vortex particle methods in aeroacoustic calculations

“…Besides this, the initial drawback of high computing cost was readily overcome by the development of the so-called tree-algorithms [3] and its later combination with 0021-9991/$ -see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2008.06.011 cloud-in-cells methods [4,5]. The possibility, thus offered, to use larger number of discretisation points brought into light the fact that the two first-mentioned qualities of vortex methods constituted also the basis for capturing very small vortex structures developing within boundary layers or wakes through instabilities [6].…”

Calculation of forces and moments in vortex methods

“…This severely limits the maximum attainable number of vortices for a realistic flow simulation. There are two methods to surpass this limit: either the use of multiprocessors and multipole expansions as done by Baden [10] and Greengard et al [11], or the use of fast algorithms for the solution of the Poisson equation using a grid fixed in space, as done for instance by Couet et al [12] for three-dimensional mixing layers and van der Vegt [6] for both two-and three-dimensional flows around circular cylinders.…”