An examination of LES filtering within the finite element method

The finite element method (FEM), in combination with large-eddy simulation (LES) techniques, is considered for the study of incompressible turbulent flows. The combination of these methodologies brings together the advantages of each: LES provides a high degree of accuracy with a minimum of empiricism for turbulence modelling, and FEM provides a robust way to simulate flow in very complex domains. It is shown that the LES filtering operator and filter width can be independently chosen with FEM just as with spectral methods because, even though FEM is grid based, it is also a method that provides an unambiguous solution everywhere by employing global basis functions. The assumption that the LES filtering operator commutes with differentiation is shown to be valid with the FEM approach. It is also shown that the error introduced by non-uniform filtering is small so long as the filter width changes smoothly. Copyright © 2002 John Wiley & Sons, Ltd.