Extracting Spatial Spectra Using Coarse-Graining Based On Implicit Filters

Abstract

Scale analysis based on coarse-graining has been proposed recently as an alternative to Fourier analysis. It requires interpolation to a regular mesh for data from unstructured-mesh models. We propose an alternative coarse-graining method which relies on implicit filters using powers of discrete Laplacians. This method can work on arbitrary (structured or unstructured) meshes and is applicable to the direct output of unstructured-mesh models. Illustrations and detailed discussions are provided for discrete fields placed at vertices of triangular meshes. The case with placement on triangles is also briefly discussed.