Dynamic turbulence model for large Eddy Simulations without test-filtering: Quantifying the accuracy of Taylor Series approximations

S. Chester, F. Charlette, and C. Meneveau
Department of Mechanical Engineering
Johns Hopkins University
Baltimore MD 21218

ABSTRACT: The dynamic model for Large Eddy Simulation (LES) of turbulent flows requires test-filtering the resolved velocity fields in order to determine model coefficients. However, test filtering is costly to perform in large eddy simulation of complex geometry flows, especially on unstructured grids. The objective of this work is to develop and test an approxiante but less costly dynamic procedure which does not require test-filtering. The proposed method is based on Taylor-series expansions of the resolved velocity fields. Accuracy is governed by the derivative schemes used in the calculation and the number of terms considered in the approximation to the test-filtering operator. The expansion is developed up to fourth order, and results are tested a priori based on DNS data of forced isotropic turbulence in the context of the dynamic Smagorinsky model. The tests compare the dynamic Smagorinsky coefficient obtained from filtering with those obtained from application of the Taylor-series expansion. They show that the expansion up to second order provides a reasonable approximation to the true dynamic coefficient (with errors on the order of about 5% for cs^2), but that including higher-order terms does not necessarily lead to improvements in the results due to inherent limitations in accurately evaluating high-order derivatives. A posteriori tests using the Taylor series approximation in LES of forced isotropic turbulence and channel flow confirm that the Taylor-series approximation yields accurate results for the dynamic coefficient. Moreover, the simulations are stable and yield accurate resolved velocity statistics.

Theor. & Comput. Fluid Dyn., (2001) 15, p. 165-181.

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