Title: A smoothing algorithm for the higher-order derivative terms in a nonlinear k-ε turbulence model

Authors: M. A. R. Sharif, Z. Gu

Addresses: Aerospace Engineering and Mechanics Department, The University of Alabama, Box 870280, Tuscaloosa, AL 35487-0280, USA. Aerospace Engineering and Mechanics Department, The University of Alabama, Box 870280, Tuscaloosa, AL 35487-0280, USA

Abstract: The nonlinear k-ε turbulence models are capable of accurately predicting the Reynolds stresses in recirculating flows with strong anisotropy as opposed to standard or linear k-ε model. However, the nonlinear models introduce higher-order derivatives of the mean velocity field and their products in the stress tensor. The inherent oscillations of the higher-order nonlinear difference equations need to be eliminated which can be achieved if the velocity field is smoothed out before calculating the derivatives. Otherwise, the computation procedure quickly becomes unstable. In this study, a new localised smoothing filter for the velocity field, based on the least squares method is proposed and evaluated using the nonlinear k-ε model and the widely used bench mark test case of the backward facing step problem. The smoothing algorithm effectively stabilised the computation of the nonlinear k-ε model with a modest increase in CPU time compared to the standard k-ε model computation.

Keywords: backward-facing step; nonlinear k-ε model; numerical smoothing; turbulence model; turbulent flow.

DOI: 10.1504/PCFD.2002.003215

Progress in Computational Fluid Dynamics, An International Journal, 2002 Vol.2 No.1, pp.45 - 57

Published online: 19 Aug 2003 *

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