A desirable feature for LES on unstructured meshes is that the filtering operation used to remove small scale motions from the flow commutes with the differentiation operator. If this commutation requirement is satisfied, the LES equations have the same form as the unfiltered Navier Stokes equations.
Commutation is generally satisfied if the filter has a constant width.
However, in inhomogeneous turbulent flows, the minimum size of eddies that need to be resolved varies throughout the flow. Thus, the filter width should also vary accordingly. Given these challenges, the objective of this work was to develop a generaltheory for constructing discrete variable width commutative filters for LES on unstructured meshes. In this project, a theory for constructing discrete commutative filters for unstructured meshes in two and three dimensions was developed. In addition to commutation, other issues such as control of filter width and filter profile in wavenumber space were also addressed.