Time-dependent subgrid scales in residual-based large eddy simulation of turbulent channel flow

The present study investigates the effect of taking into account the time dependency of the fine (subgrid) scales in a residual-based variational multiscale approach for large eddy simulation. The residual-based variational multiscale method with time-dependent (dynamic) subgrid scales is presented, and the impact of the time dependency is studied for the well-known test case of turbulent channel flow. Results are presented from computations for various values of the Reynolds number, namely Re τ = 180 , Re τ = 395 and Re τ = 590 , and several time-step sizes. A generalized- α time-integration scheme is employed. Results from our numerical experiments with dynamic subgrid scales are compared to results obtained with an approximation not explicitly taking the time-dependency of the subgrid scales into account. For all Re τ values and time-step sizes under consideration, results for resolved quantities computed by both approaches are very similar. This statement applies to both, mean streamwise velocity and root-mean-square velocity fluctuations. However, it provides a model for the subgrid-scales not depending on the time-step size and enabling a more robust representation of unresolved scales. Thus we conclude that the time-dependent subgrid-scale approximation is not capable of producing more accurate results for this type of flow if the time-step size is chosen within an optimal range. However, we expect it to be more advantageous for more complex problems, since our results indicate that it provides a more reliable representation of unresolved scales.