Numerical Analysis and Computational Comparisons of the NS-alpha and NS-omega regularizations

We study stability, accuracy and efficiency of algorithms for a new regularization of the NSE, the NS-ω model (in which the vorticity term, ω = ∇× u, is averaged) given by ut − u× (∇× u) +∇q − ν∆u = f,∇ · u = 0. This is similar to the NS-alpha model (in which the nonlinear term is u × ∇ × u), but the small difference opens attractive algorithmic possibilities. We give tests both confirming the predicted rates of convergence and exhibiting some shared limitations of both models. The experiments also show the discrete NS-ω simulation has greater accuracy at much less cost than a comparable NS-α simulation. The experiments suggest consideration of higher accuracy NS-ω-deconvolution models as a next logical step.