On the behaviour of fully-discrete flux reconstruction schemes

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Title: On the behaviour of fully-discrete flux reconstruction schemes
Author(s): Vermeire, BC
Vincent, PE
Item Type: Journal Article
Abstract: In this study we employ von Neumann analyses to investigate the disper- sion, dissipation, group velocity, and error properties of several fully discrete flux reconstruction (FR) schemes. We consider three FR schemes paired with two explicit Runge-Kutta (ERK) schemes and two singly diagonally implicit RK (SDIRK) schemes. Key insights include the dependence of high-wavenumber numerical dissipation, relied upon for implicit large eddy simulation (ILES), on the choice of temporal scheme and time-step size. Also, the wavespeed characteristics of fully-discrete schemes and the relative dominance of temporal and spatial errors as a function of wavenumber and time-step size are investigated. Salient properties from the aforementioned theoretical analysis are then demonstrated in practice using linear advection test cases. Finally, a Burgers turbulence test case is used to demonstrate the importance of the temporal discretisation when using FR schemes for ILES.
Publication Date: 5-Dec-2016
Date of Acceptance: 14-Nov-2016
URI: http://hdl.handle.net/10044/1/42633
DOI: https://dx.doi.org/10.1016/j.cma.2016.11.019
ISSN: 0045-7825
Publisher: Elsevier
Start Page: 1053
End Page: 1079
Journal / Book Title: Computer Methods in Applied Mechanics and Engineering
Volume: 315
Copyright Statement: © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons. org/licenses/by/4.0/).
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Commission of the European Communities
Funder's Grant Number: EP/K027379/1
EP/M50676X/1
635962
Keywords: Science & Technology
Technology
Physical Sciences
Engineering, Multidisciplinary
Mathematics, Interdisciplinary Applications
Mechanics
Engineering
Mathematics
Fully-discrete
High-order
von Neumann
Discontinuous Galerkin
Flux reconstruction
Runge-Kutta
LARGE-EDDY SIMULATION
FINITE-ELEMENT-METHOD
CONSERVATION-LAWS
DISPERSION
TURBULENCE
Applied Mathematics
01 Mathematical Sciences
09 Engineering
Publication Status: Published
Appears in Collections:Faculty of Engineering
Aeronautics



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