Filtering Techniques for Complex Geometry Fluid Flows

We develop a class of lters based upon the numerical solution of high-order elliptic problems in l R d that allow for independent determination of order and cut-oo wave number and that default to classical Fourier-based lters in homogeneous domains. However, because they are based on the solution of a PDE, the present lters are not restricted to applications in tensor-product-based geometries as is generally the case for Fourier-based lters. The discrete representation of the ltered output is constructed from a Krylov space generated in solving a well-conditioned system arising from a low-order PDE.