A local dynamic model for large eddy simulation
Abstract
The dynamic model is a method for computing the coefficient C in Smagorinsky's model for the subgridscale stress tensor as a function of position from the information already contained in the resolved velocity field rather than treating it as an adjustable parameter. A variational formulation of the dynamic model is described that removes the inconsistency associated with taking C out of the filtering operation. This model, however, is still unstable due to the negative eddyviscosity. Next, three models are presented that are mathematically consistent as well as numerically stable. The first two are applicable to homogeneous flows and flows with at least one homogeneous direction, respectively, and are, in fact, a rigorous derivation of the ad hoc expressions used by previous authors. The third model in this set can be applied to arbitrary flows, and it is stable because the C it predicts is always positive. Finally, a model involving the subgridscale kinetic energy is presented which attempts to model backscatter. This last model has some desirable theoretical features. However, even though it gives results in LES that are qualitatively correct, it is outperformed by the simpler constrained variational models. It is suggested that one of the constrained variational models should be used for actual LES while theoretical investigation of the kinetic energy approach should be continued in an effort to improve its predictive power and to understand more about backscatter.
 Publication:

Annual Research Briefs, 1992
 Pub Date:
 January 1993
 Bibcode:
 1993arb..nasa....3G
 Keywords:

 Computational Fluid Dynamics;
 Computational Grids;
 Computerized Simulation;
 Dynamic Models;
 Eddy Viscosity;
 Mathematical Models;
 NavierStokes Equation;
 Reynolds Stress;
 Stress Tensors;
 Vortices;
 Backscattering;
 Kinetic Energy;
 Prediction Analysis Techniques;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer