Stabilization of Finite-Element High-Order Methods with Fourier Spectral Filters: Surviving High-Re, High-Ma flows, and Coarse Grids

Speaker: Manuel R. López Morales, Northrop Grumman
July 14, 2016

Presentation

Abstract

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 presentation describes the implementation of the Local Fourier-spectral (LFS) filters, developed by Asthana and the author, 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 polygonal (2D) or polyhedral (3D) elements.

LFS filters are uniquely suited to implementation in highly-parallelizable numerical schemes like Flux Reconstruction (FR) and Discontinuous Galerkin (DG) because they operate element-wise, use boundary 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.

Biography

Manuel R. López Morales has recently received his Ph.D. from Stanford University, having been Prof. Antony Jameson's mentee and participated in the development and maintenance of HiFiLES. He has been developing multi-physics simulation software at Northrop Grumman for the past year and is a participant in the company's Future Technical Leaders program. His other interests include developing deep learning algorithms and building a solar UAV.

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