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Steepest Descent Optimisation of Runge-Kutta Coefficients for Second Order Implicit Finite Volume CFD Codes

Misev, Cyril and Hills, Nicholas (2018) Steepest Descent Optimisation of Runge-Kutta Coefficients for Second Order Implicit Finite Volume CFD Codes Journal of Computational Physics, 354. pp. 576-592.

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One of the key research topics in the computational fluid dynamics community is to improve the computational efficiency of steady-state finite volume codes. Real-world use cases require the solution to the Navier-Stokes equations for a wide range of Mach numbers, Reynolds numbers and mesh cell aspect ratios. This introduces stiffness in the discretised equations and therefore a slowdown in convergence. The community has pursued in particular two avenues to speed up the convergence of the corresponding error modes: Optimisation of Runge-Kutta coefficients for explicit Runge-Kutta schemes; and the introduction of implicit preconditioners, with a limited investigation of Runge-Kutta coefficients suitable to those implicit preconditioners. After proposing improvements to the implicit preconditioner, the present work proposes an optimisation procedure allowing the optimisation of the Runge-Kutta coefficients specifically for the implicit preconditioner. Employed on a realistic use case, the Runge-Kutta coefficients extracted with this method show a 20%−38% reduction of the number of iterations needed for convergence compared to Runge-Kutta coefficients recommended in the literature for comparable schemes and with the same computational cost per iteration.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mechanical Engineering Sciences
Authors :
Date : 1 February 2018
Funders : EU Clean Sky programme, Rolls-Royce plc
DOI : 10.1016/
Copyright Disclaimer : Copyright © 2017 Rolls-Royce plc. Published by Elsevier Inc. All rights reserved.
Uncontrolled Keywords : implicit CFD; Runge-Kutta; Min-Max; Steepest descent; Jameson-Schmidt-Turkel scheme
Depositing User : Clive Harris
Date Deposited : 17 Oct 2017 10:27
Last Modified : 26 Jul 2019 13:09

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