An improved interpolation scheme for finite volume simulations on unstructured meshes

Chenoweth, Samuel; Soria, Julio; Ooi, Andrew

doi:10.1090/S0025-5718-2012-02639-1

An improved interpolation scheme for finite volume simulations on unstructured meshes
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by Samuel K. M. Chenoweth, Julio Soria and Andrew Ooi PDF

Math. Comp. 82 (2013), 803-830 Request permission

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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