A new family of weighted one-parameter flux reconstruction schemes. (30th May 2021)

• Record Type: Journal Article
• Authors: Trojak, W.; Witherden, F.D.
• Is Part Of: Computers & fluids. Volume 222(2021)
• Publication Date: 2021-05-30
• Subjects: High order -- Flux reconstruction -- Discontinuous Galerkin -- Energy stable -- Spectral difference; 46E39 -- 46N40 -- 65M60 -- 65T99 -- 76F65; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2021.104918
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: Weighted Sobolev norms are successfully applied to flux reconstruction (FR). This method leads to a novel extension of the set of FR correction functions. Within this set new spectral difference (SD) schemes identified. Numerical experiments are used to identify schemes with improved performance. Abstract: The flux reconstruction (FR) approach offers a flexible framework for describing a range of high-order numerical schemes; including nodal discontinuous Galerkin and spectral difference schemes. This is accomplished through the use of so-called correction functions. In this study we employ a weighted Sobolev norm to define a new extended family of FR correction functions, the stability of which is affirmed through Fourier analysis. Several of the schemes within this family are found to exhibit reduced dissipation and dispersion overshoot. Moreover, many of the new schemes possess higher CFL limits whilst maintaining the expected rate of convergence. Numerical experiments with homogeneous linear convection and Burgers' turbulence are undertaken, and the results observed to be in agreement with the theoretical findings.