Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness - Mengaldo,G; De,Grazia D; Moura,RC; Sherwin,S (Journal of Computational Physics, 2018)
This study focusses on the dispersion and diffusion characteristics of high-order energy-stable flux recon-struction (ESFR) schemes via the spatial eigensolution analysis framework proposed in [1]. The analysis isperformed for five ESFR schemes, where the parameter ‘c’ dictating the properties of the specific schemerecovered is chosen such that it spans the entire class of ESFR methods, also referred to as VCJH schemes,proposed in [2]. In particular, we used five values of ‘c’, two that correspond to its lower and upper boundsand the others that identify three schemes that are linked to common high-order methods, namely theESFR recovering two versions of discontinuous Galerkin methods and one recovering the spectral differencescheme. The performance of each scheme is assessed when using different numerical intercell fluxes (e.g.different levels of upwinding), ranging from “under-” to “over-upwinding”. In contrast to the more commontemporal analysis, the spatial eigensolution analysis framework adopted here allows one to grasp crucialinsights into the diffusion and dispersion properties of FR schemes for problems involving non-periodicboundary conditions, typically found in open-flow problems, including turbulence, unsteady aerodynamicsand aeroacoustics.