Particles simulation of viscous flow

A New Diffusion Procedure for Vortex Methods

“…A deterministic method to simulate diffusion has been vortices in order to produce the correct amount of diffusion. However, unlike the deterministic particle developed by Raviart [48], Choquin and Huberson [15], and Cottet and Mas-Gallic [20]. They use viscous/inviscid methods [21,23], the maximum distance that the circulation of a vortex can move during a time-step is restricted splitting of the vorticity equation and then solve the diffusion equation exactly using the fundamental solution to a chosen distance of the order of the point spacing.…”

“…First is the derivation of the redistribution equations To find the lower bound to the redistribution radius (16) and the following. We write the difference between mentioned in Section 7, we integrate (41) over the unit the Fourier transform of the redistributed vorticity (13) circle to produce and the exactly diffused vorticity (14) in terms of the viscous scale h v ϭ ͙ ⌬t and the scaled relative positions (15):…”

Vortex Methods

“…An efficient deterministic viscous scheme is presented next: the particle strength exchange (PSE) scheme, see Degond and Mas-Gallic (1989), Choquin and Huberson (1989), and Cottet and Mas-Gallic (1990). One considers kernels such that x…”

Convergence of high-order deterministic particle methods for the convection-diffusion equation

“…The method adopted by Cottet and Mas-Gallic [6] and Choquin and Huberson [3] uses viscous splitting and the discrete convolution of the convected vorticity with the heat kernel. A new method of vorticity exchange was recently proposed by Shankar and van Dommelen [13].…”