Truncated Navier-Stokes equations with the automatic filtering criterion

2011-07-06A Large Eddy Simulation (LES) methodology based on previously developed Truncated Navier Stokes (TNS) approach is proposed. In TNS, the Navier Stokes equations are solved through a sequence of direct numerical simulation runs and a periodical processing of small scales to provide the necessary dissipation. In the simplest case, the processing is accomplished by filtering the turbulent fields with a properly chosen filter. In the previous approach, the period for processing was selected in advance for each case using heuristic arguments validated by trial and error. In this proposed model, the filtering criterion is developed to automate the selection of time instant in simulations when the processing is needed. The criterion is based on the relationship between the energy of the flow field and the energy of the same field filtered with the chosen filter. Numerical experiments were conducted to validate this model by comparing the computed low order statistics in fully developed channel flows at low to moderate friction Reynolds numbers with the benchmark data. An analysis of the preliminary results showed that in wall resolved LES the results are independent of the value of the filtering criterion as long as it falls into the derived guideline range. To achieve an improvement of the model's predictability, Reynolds stress and energy budgets in the simulations performed with this model were analyzed. They led to better understanding of filtering effects on the energy transport and suggested how the filtering can be modified to manipulate the energy content in specific areas of the flow. Such selective filtering procedures improve results in marginally resolved LES and can be applied to transitional flows