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Evaluation of Fully Implicit Runge Kutta Schemes for Unsteady Flow Calculations

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Abstract

This paper presents the formulation of a dual time stepping procedure to solve the equations of fully implicit Runge–Kutta schemes. In particular the method is applied to Gauss and Radau 2A schemes with either two or three stages. The schemes are tested for unsteady flows over a pitching airfoil modeled by both the Euler and the unsteady Reynolds averaged Navier Stokes equations. It is concluded that the Radau 2A schemes are more robust and less computationally expensive because they require a much smaller number of inner iterations. Moreover these schemes seem to be competitive with alternative implicit schemes.

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Acknowledgements

In recent years the author’s research has benefited greatly from the continuing support of the AFOSR Computational Mathematics Program through grant number FA9550-14-1-0186, under the direction of Dr. Fariba Fahroo and Dr. Jean-Luc Cambier.

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  1. Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, 94305-4035, USA

    Antony Jameson

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  1. Antony Jameson
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Correspondence to Antony Jameson.

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Dedicated to Chi-Wang Shu on the occasion of his 60th birthday.

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Jameson, A. Evaluation of Fully Implicit Runge Kutta Schemes for Unsteady Flow Calculations. J Sci Comput 73, 819–852 (2017). https://doi.org/10.1007/s10915-017-0476-x

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