A well-known disadvantage of traditional (non-adaptive) CFD algorithms is that they suffer from high numerically induced diffusion. The excessive damping caused by numerical diffusion inhibits the growth of inviscid instabilities observed in typical turbulent flow scenarios, and it leads to the premature dissipation of coherent vortical structures of interest to industrial applications, such as the wake behind airfoils or bluff bodies, or the vortical flow in IC engines. In other words, numerical diffusion tends to "laminarize" otherwise turbulent flow simulations. In contrast, thanks to the Lagrangian nature of the computation, our simulations are virtually free of numerical diffusion. This allows us to model and capture complex turbulent vortical structures with minimal computational effort, as evidenced with the example on this page.
This is a
"simple" but very powerful demonstration of the robustness of It is quite well-known that when a vortex ring is perturbed sinusoidally in the radial direction around the azimuth of the ring, the perturbations will re-orient themselves along the streamwise direction and, given the proper wave-number, will grow inviscidly in that direction. If the CFD algorithm used is too diffusive, streamwise vorticies never develop and the vortex ring laminarizes. In this example, we demonstrate the robustness of our method using the LES of a vortex ring with vortex core to ring radius ratio of 0.45 - thus the term "fat" ring. The vortex core distribution is initially a cubic Gaussian and the ring is perturbed sinusoidally around its azimuth with the most unstable wave-number (=7) and 5% perturbation amplitude. A standard Smagorinsky LES model is used in this case, and the ring propagates by its self-induced velocity in free space at infinite Reynolds number.
The animation at the top of the page depicts
the perspective view of the evolution of selected vortex particles (the
actual computational elements), color coded by the vorticity magnitude
(red being the highest and blue being the lowest values). The
"sticks" depict the direction of the vorticity vectors. The
animation clearly demonstrates the ability of our
Once again, note the development of
streamwise vortices within the ring core ( |