An Enhanced-Physics-Based Scheme for the NS-α Turbulence Model

We study a new enhanced-physics-based numerical scheme for the NS-alpha turbulence model that conserves both energy and helicity. Although most turbulence models (in the continuous case) conserve only energy, NS-alpha is one of only a very few that also conserve helicity. This is one reason why it is becoming accepted as the most physically accurate turbulence model. However, no numerical scheme for NS-alpha, until now, conserved both energy and helicity, and thus the advantage gained in physical accuracy by modeling with NS-alpha could be lost in a computation. This report presents a finite element numerical scheme, and gives a rigorous analysis of its conservation properties, stability, solution existence, and convergence. A key feature of the analysis is the identification of the discrete energy and energy dissipation norms, and proofs that these norms are equivalent (provided a careful choice of filtering radius) in the discrete space to the usual energy and energy dissipation norms. Numerical experiments are given to demonstrate the effectiveness of the scheme over usual (helicity-ignoring) schemes. A generalization of this scheme to a family of high-order NS-alpha-deconvolution models, which combine the attractive physical properties of NS-alpha with the high accuracy gained by combining a-filtering with van Cittert approximate deconvolution. (C) 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 26: 1530-1555, 2010