2023/10/24 by Carlos A. Pereira, Brian C. Vermeire, Pereira, Carlos A. +1
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Nuclear reactor physics and engineering #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2310.15870
openalex publication_date 2023/10/24 · openalex created_date 2023/10/26 · openalex updated_date 2026/08/01
We present the hybridization of flux reconstruction methods for advection-diffusion problems. Hybridization introduces a new variable into the problem so that it can be reduced via static condensation. This allows the solution of implicit discretizations to be done more efficiently. We derive an energy statement from a stability analysis considering a range of correction functions on hybridized and embedded flux reconstruction schemes. Then, we establish connections to standard formulations. We devise a post-processing scheme that leverages existing flux reconstruction operators to enhance accuracy for diffusion-dominated problems. Results show that the implicit convergence of these methods for advection-diffusion problems can result in performance benefits of over an order of magnitude. In addition, we observe that the superconvergence property of hybridized methods can be extended to the family of FR schemes for a range of correction functions.