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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

An improved interpolation scheme for finite volume simulations on unstructured meshes


Authors: Samuel K. M. Chenoweth, Julio Soria and Andrew Ooi
Journal: Math. Comp. 82 (2013), 803-830
MSC (2010): Primary 65D05
Published electronically: November 14, 2012
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Abstract: The unstructured bilinear interpolation scheme of Kim and Choi (2000) is claimed to be second order accurate on the basis of empirical results from finite volume simulations of the incompressible Navier-Stokes equations. In this paper, the scheme is analysed theoretically, and is shown to be only first order accurate for function interpolation and zeroth order accurate for spatial derivative approximation, in the general case. A number of special cases exist, however, where higher order accuracy may be obtained, and these are identified in this paper. Since the mesh used by Kim and Choi to demonstrate the accuracy of their scheme was one of these special cases, this explains their results. Finally, an improved version of Kim and Choi's scheme is presented, which is shown to be truly second order accurate for function interpolation and first order accurate for spatial derivative approximation.


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Additional Information

Samuel K. M. Chenoweth
Affiliation: P.O. Box 1026, Salisbury, South Australia, S108, Australia
Email: samuelchenoweth@gmail.com

Julio Soria
Affiliation: Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical Engineering, Monash University, Victoria, 3800, Australia
Email: julio.soria@eng.monash.edu.au

Andrew Ooi
Affiliation: Department of Mechanical Engineering, University of Melbourne, Victoria, 3010, Australia
Email: a.ooi@unimelb.edu.au

DOI: http://dx.doi.org/10.1090/S0025-5718-2012-02639-1
PII: S 0025-5718(2012)02639-1
Keywords: Interpolation, unstructured meshes
Received by editor(s): June 24, 2010
Received by editor(s) in revised form: May 29, 2011
Published electronically: November 14, 2012
Additional Notes: The authors would like to acknowledge the support of the Australian Research Council for this research through grant DP0556098.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.