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Journal of Scientific Computing

, Volume 54, Issue 1, pp 227–244 | Cite as

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

  • Meilin Yu
  • Z. J. Wang
Article

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.

Keywords

Correction procedure via reconstruction (CPR) Energy stable flux reconstruction Weighting function Correction function 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Aerospace Engineering and CFD CenterIowa State UniversityAmesUSA

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