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A High-Order Central ENO Finite-Volume Scheme for Three-Dimensional Low-Speed Viscous Flows on Unstructured Mesh

Published online by Cambridge University Press:  02 April 2015

Marc R. J. Charest ,
Clinton P. T. Groth  and
Pierre Q. Gauthier
Marc R. J. Charest*
Affiliation:
University of Toronto Institute for Aerospace Studies, 4925 Dufferin Street, Toronto, Ontario, Canada M3H 5T6
Clinton P. T. Groth
Affiliation:
University of Toronto Institute for Aerospace Studies, 4925 Dufferin Street, Toronto, Ontario, Canada M3H 5T6
Pierre Q. Gauthier
Affiliation:
Energy Engineering & Technology, Rolls-Royce Canada Limited, 9245 Côte-de-Liesse, Dorval, Québec, Canada H9P 1A5
*
* Corresponding author. Email addresses:charest@utias.utoronto.ca (M. R. J. Charest), groth@utias.utoronto.ca (C. P. T. Groth), pierre.gauthier@rolls-royce.com (P. Q. Gauthier)
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Abstract

High-order discretization techniques offer the potential to significantly reduce the computational costs necessary to obtain accurate predictions when compared to lower-order methods. However, efficient and universally-applicable high-order discretizations remain somewhat illusive, especially for more arbitrary unstructured meshes and for incompressible/low-speed flows. A novel, high-order, central essentially non-oscillatory (CENO), cell-centered, finite-volume scheme is proposed for the solution of the conservation equations of viscous, incompressible flows on three-dimensional unstructured meshes. Similar to finite element methods, coordinate transformations are used to maintain the scheme’s order of accuracy even when dealing with arbitrarily-shaped cells having non-planar faces. The proposed scheme is applied to the pseudo-compressibility formulation of the steady and unsteady Navier-Stokes equations and the resulting discretized equations are solved with a parallel implicit Newton-Krylov algorithm. For unsteady flows, a dual-time stepping approach is adopted and the resulting temporal derivatives are discretized using the family of high-order backward difference formulas (BDF). The proposed finite-volume scheme for fully unstructured mesh is demonstrated to provide both fast and accurate solutions for steady and unsteady viscous flows.

Keywords

35Q3065Z0565M0865N0876M1276D0576G25Numerical algorithmscomputational fluid dynamicshigh-order methodsincompressible flows

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Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 3 , March 2015 , pp. 615 - 656
Copyright
Copyright © Global-Science Press 2015 

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