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On the Connection Between the Correction and Weighting Functions in the Correction Procedure via Reconstruction Method

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Abstract

In this note, the connection between the correction and weighting functions for the correction procedure via reconstruction (CPR) method in 1D is addressed. A one-parameter family of weighting functions is constructed from the discontinuous test space. It is found that if the solution polynomials lie in the space P k, then the first k weighting functions can always be chosen as the basis of the polynomial space P k−1 and the last weighting function can be selected as a piece-wise continuous polynomial. There exists at least one set of weighting functions which can recover the energy stable flux reconstruction (ESFR) schemes. This strategy has been successfully applied to recover several known high-order discontinuous schemes, including DG, SD, SV, and Huynh’s g 2 scheme.

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Authors and Affiliations

  1. Department of Aerospace Engineering and CFD Center, Iowa State University, Ames, IA, 50011, USA

    Meilin Yu & Z. J. Wang

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  1. Meilin Yu
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  2. Z. J. Wang
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Correspondence to Meilin Yu.

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Yu, M., Wang, Z.J. On the Connection Between the Correction and Weighting Functions in the Correction Procedure via Reconstruction Method. J Sci Comput 54, 227–244 (2013). https://doi.org/10.1007/s10915-012-9618-3

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