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The dynamic model for large-eddy simulation (LES) of turbulent flows requirestest filtering the resolved velocity fields in order to determine modelcoefficients. However, test filtering is costly to perform in large-eddysimulation of complex geometry flows, especially on unstructured grids. Theobjective of this work is to develop and test an approximate but less costlydynamic procedure which does not require test filtering. The proposed method isbased on Taylor series expansions of the resolved velocity fields. Accuracy isgoverned by the derivative schemes used in the calculation and the number ofterms considered in the approximation to the test filtering operator. Theexpansion is developed up to fourth order, and results are tested a prioribased on direct numerical simulation data of forced isotropic turbulence in thecontext of the dynamic Smagorinsky model. The tests compare the dynamicSmagorinsky coefficient obtained from filtering with those obtained fromapplication of the Taylor series expansion. They show that the expansion up tosecond order provides a reasonable approximation to the true dynamiccoefficient (with errors on the order of about 5 % for c_s^2), but thatincluding higher-order terms does not necessarily lead to improvements in theresults due to inherent limitations in accurately evaluating high-orderderivatives. A posteriori tests using the Taylor series approximation in LES offorced isotropic turbulence and channel flow confirm that the Taylor seriesapproximation yields accurate results for the dynamic coefficient. Moreover,the simulations are stable and yield accurate resolved velocity statistics.Comment: submitted to Theoretical and Computational Fluid Dynamics, 20 pages,  11 figure

Dynamic Model for LES Without Test Filtering: Quantifying the Accuracy of Taylor Series Approximations