Discrete Filtering on Unstructured Grids Based on Least-Squares Gradient Reconstruction
ILLINOIS UNIV AT URBANA CENTER FOR SIMULATION OF ADVANCED ROCKETS
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The equations for Large-Eddy Simulation LES of turbulent flows are formally derived by applying a low-pass filter to the Navier-Stokes equations. In doing so, it is often tacitly assumed that the filtering and differentiation operations commute. This assumption is invalid if the filter width is not uniform as is the case if wall-bounded flows are computed unless special filter operators are constructed, see, e.g, Vasilyev et at. 1998. The goal of the present work is to develop a simpler filtering method than that of Marsden et al. 2000. The new filtering method is based on the following observation The conditions for filtering a function to a given order of commutation error derived by Vasilyev et al. 1998 are formally identical to the conditions for reconstructing the gradient of a function to a given order of truncation error. In other words, the construction of filtering operators may be reinterpreted as the construction of, suitably reformulated, gradient-reconstruction methods. This apparently trivial observation has important consequences because the reconstruction of gradients is central to many flow-solution methods on unstructured grids and is well understood.
- Fluid Mechanics