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 byut-u×(∇×u¯)+∇q-νΔu=f,∇·u=0.This is similar to the NS-αα 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 ( Table 3 and Table 4) at less cost ( Table 2) and requires significantly fewer degrees of freedom (Section 1.1) than a comparable NS-αα simulation. The experiments suggest consideration of adding grad–div stabilization and higher accuracy NS-ω¯-deconvolution models as a next logical step. In fact, this combination produced accurate results (see Fig. 10 and Fig. 11) on the coarsest mesh (mesh 1) upon which all other methods, models and variants tested failed.