Accuracy, stability, and performance comparison between the spectral difference and flux reconstruction schemes

• Published in: Computers & fluids Vol. 221; p. 104922
• Main Authors: Cox, C., Trojak, W., Dzanic, T., Witherden, F.D., Jameson, A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 15.05.2021; Elsevier BV
• Subjects: Aliasing; Computational fluid dynamics; Discontinuous spectral element; Flux; Flux reconstruction; Implicit large eddy simulation; Reconstruction; Spectra; Spectral difference; Stability analysis; 76N15; Flux reconstruction; 65M70; Discontinuous spectral element; 46N35; Spectral difference; Implicit large eddy simulation; 46E39
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2021.104922

•We report the development of a discontinuous spectral element flow solver that includes implementation of both spectral difference and flux reconstruction formulations.•We provide a fair and accurate assessment of spectral difference and flux reconstruction schemes in terms of accuracy, stability, and performance. Additionally, we perform a novel nonlinear stability analysis of the spectral difference scheme.•Through various numerical experiments, we demonstrate the additional stability afforded by the true, baseline spectral difference scheme-without explicit filtering or de-aliasing-due to its inherent feature of staggered flux points.•Ultimately, we show that the spectral difference scheme provides favorable suppression of aliasing errors and improves stability needed for under-resolved simulations of turbulent flows. We report the development of a discontinuous spectral element flow solver that includes the implementation of both spectral difference and flux reconstruction formulations. With this high order framework, we have constructed a foundation upon which to provide a fair and accurate assessment of these two schemes in terms of accuracy, stability, and performance with special attention to the true spectral difference scheme and the modified spectral difference scheme recovered via the flux reconstruction formulation. Building on previous analysis of the spectral difference and flux reconstruction schemes, we provide a novel nonlinear stability analysis of the spectral difference scheme. Through various numerical experiments, we demonstrate the additional stability afforded by the true, baseline spectral difference scheme without explicit filtering or de-aliasing due to its inherent feature of staggered flux points. This arrangement leads to favorable suppression of aliasing errors and improves stability needed for under-resolved simulations of turbulent flows.