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Paired explicit Runge-Kutta schemes for stiff systems of equations


Paired explicit Runge-Kutta schemes for stiff systems of equations

Vermeire, Brian C. (2019) Paired explicit Runge-Kutta schemes for stiff systems of equations. Journal of Computational Physics . ISSN 00219991 (In Press)

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Official URL: http://dx.doi.org/10.1016/j.jcp.2019.05.014


In this paper we introduce a family of explicit Runge-Kutta methods, referred to as Paired Explicit Runge-Kutta (P-ERK) schemes, that are suitable for the solution of stiff systems of equations. The P-ERK approach allows Runge-Kutta schemes with a large number of derivative evaluations and large region of absolute stability to be used in the stiff parts of a domain, while schemes with relatively few derivative evaluations are used in non-stiff parts to reduce computational cost. Importantly, different P-ERK schemes with different numbers of derivative evaluations can be chosen based on local stiffness requirements and seamlessly paired with one another. We then verify that P-ERK schemes obtain their designed order of accuracy using the Euler equations with arbitrary combinations of schemes. We then demonstrate that P-ERK schemes can achieve speedup factors of approximately five for simulations using the Navier-Stokes equations including laminar and turbulent flow over an SD7003 airfoil. These results demonstrate that P-ERK schemes can significantly accelerate the solution of stiff systems of equations when using an explicit approach, and that they maintain accuracy with respect to conventional Runge-Kutta methods and available reference data.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Mechanical, Industrial and Aerospace Engineering
Item Type:Article
Authors:Vermeire, Brian C.
Journal or Publication:Journal of Computational Physics
Date:7 May 2019
  • Natural Sciences and Engineering Research Council of Canada (NSERC)
  • Calcul Quebec
  • WestGrid
  • Compute Canada via a Resources for Research Groups allocation
Digital Object Identifier (DOI):10.1016/j.jcp.2019.05.014
ID Code:985444
Deposited By: Monique Lane
Deposited On:03 Jun 2019 18:43
Last Modified:07 May 2021 01:00


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