  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 approximate 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 direct numerical simulation 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 c_s^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.
