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Optimal Runge-Kutta Schemes for Pseudo Time-Stepping with High-Order Unstructured Methods

Title:

Optimal Runge-Kutta Schemes for Pseudo Time-Stepping with High-Order Unstructured Methods

Vermeire, B.C., Loppi, N.A. and Vincent, P.E. (2019) Optimal Runge-Kutta Schemes for Pseudo Time-Stepping with High-Order Unstructured Methods. Journal of Computational Physics . ISSN 00219991 (In Press)

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Official URL: http://dx.doi.org/10.1016/j.jcp.2019.01.003

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.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Mechanical, Industrial and Aerospace Engineering
Item Type:Article
Refereed:Yes
Authors:Vermeire, B.C. and Loppi, N.A. and Vincent, P.E.
Journal or Publication:Journal of Computational Physics
Date:30 January 2019
Funders:
  • Natural Sciences and Engineering Research Council of Canada
  • Engineering and Physical Sciences Research Council
  • Swiss National Supercomputing Centre
  • West-Grid
  • Compute Canada
Digital Object Identifier (DOI):10.1016/j.jcp.2019.01.003
ID Code:984983
Deposited By: MICHAEL BIRON
Deposited On:08 Feb 2019 22:28
Last Modified:08 Feb 2019 22:28

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