Stabilization of High-Order Methods for Unstructured Grids with Local Fourier Spectral Filtering: high-Re Simulations in Coarse

One of the main barriers to wide adoption of high-order numerical methods in industrial applications is the schemes ’ low robustness relative to low-order methods. HiFiLES, an open-source, high-order, Navier-Stokes solver for unstructured grids is not impervious to this problem. Its stability is generally highly dependent on the quality of the grid. This paper describes the implementation of the Local Fourier-spectral (LFS) filters, developed by Asthana and the authors, in HiFiLES, and shows the results of high-Re simulations in coarse, unstructured 2D meshes. The simulations demonstrate the potential for LFS filters to stabilize high-order simulations under extreme conditions: very coarse grids, high-Re, high-Ma, and very low-Ma. We present a formulation of the LFS filters for a general high-order polygon (2D) or polyhedron (3D). LFS filters are uniquely suited to implementation in highly-parallelizable numerical schemes like Flux Reconstruction (FR) because they operate element-wise, use interface information that is already used by the element to advance the solution, and maintain the operational complexity of the underlying scheme –the filtering operation is two element-local matrix multiplications. I