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High-Order Flux Correction for Viscous Flows on Arbitrary Unstructured Grids

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Abstract

A novel high-order method, termed flux correction, previously formulated for inviscid flows, is extended to viscous flows on arbitrary triangular grids. The correction method involves the addition of truncation error-canceling terms to the second-order linear Galerkin (node-centered finite volume) scheme to produce a third-order inviscid and fourth-order viscous scheme. The correction requires minimal modification of the underlying second-order scheme. As such, the method retains many of the advantages of traditional finite volume schemes, including robust shock capturing, low algorithmic complexity, and solver efficiency. In addition, we extend the scheme to unsteady flows. Verification and validation studies in two dimensions are presented. Significant improvement in accuracy is observed in all cases, with between 30–70 % increase in computational cost over a second-order finite volume method.

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Acknowledgments

Development was performed with the support of the Army Research Office Fluid Dynamics Program directed by Dr. Frederick Ferguson. Material presented in this paper is a product of the Air Vehicles component of the Computational Research and Engineering for Acquisition Tools and Environments (CREATE) Program sponsored by the U.S. Department of Defense HPC Modernization Program Office.

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  1. Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT , 84322, USA

    B. Pincock & A. Katz

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  1. B. Pincock
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  2. A. Katz
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Correspondence to A. Katz.

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Pincock, B., Katz, A. High-Order Flux Correction for Viscous Flows on Arbitrary Unstructured Grids. J Sci Comput 61, 454–476 (2014). https://doi.org/10.1007/s10915-014-9833-1

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