Optimal Runge-Kutta schemes for pseudo time-stepping with high-order unstructured methods

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Title: Optimal Runge-Kutta schemes for pseudo time-stepping with high-order unstructured methods
Authors: Vermeire, B
Loppi, N
Vincent, P
Item Type: Journal Article
Abstract: In this study we generate optimal Runge-Kutta (RK) schemes for converging the Artificial Compressibility Method (ACM) using dual time-stepping with high-order unstructured spatial discretizations. We present optimal RK schemes with between s = 2 and s = 7 stages for Spectral Difference (SD) and Discontinuous Galerkin (DG) discretizations obtained using the Flux Reconstruction (FR) approach with solution polynomial degrees of k = 1 to k = 8. These schemes are optimal in the context of linear advection with predicted speedup factors in excess of 1.80× relative to a classical RK4,4 scheme. Speedup factors of between 1.89× and 2.11× are then observed for incompressible Implicit Large Eddy Simulation (ILES) of turbulent flow over an SD7003 airfoil. Finally, we demonstrate the utility of the schemes for incompressible ILES of a turbulent jet, achieving good agreement with experimental data. The results demonstrate that the optimized RK schemes are suitable for simulating turbulent flows and can achieve significant speedup factors when converging the ACM using dual time-stepping with high-order unstructured spatial discretizations.
Issue Date: 15-Apr-2019
Date of Acceptance: 4-Jan-2019
URI: http://hdl.handle.net/10044/1/65502
ISSN: 0021-9991
Publisher: Elsevier
Journal / Book Title: Journal of Computational Physics
Copyright Statement: This paper is embargoed until 12 months after publication
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/K027379/1
Keywords: 01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Applied Mathematics
Publication Status: Accepted
Appears in Collections:Faculty of Engineering
Aeronautics



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