On the accuracy and efficiency of discontinuous Galerkin, spectral difference and correction procedure via reconstruction methods

Authors:
Meilin Yu;Z. J. Wang;Yen Liu
Affiliations:
The University of Kansas, Lawrence, KS 66045, USA;The University of Kansas, Lawrence, KS 66045, USA;NASA Ames Research Center, Moffett Field, CA 94035, USA
Venue:
Journal of Computational Physics
Year:
2014

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Abstract

Numerical accuracy and efficiency of several discontinuous high-order methods, including the quadrature-based discontinuous Galerkin (QDG), nodal discontinuous Galerkin (NDG), spectral difference (SD) and flux reconstruction/correction procedure via reconstruction (FR/CPR), for the conservation laws are analyzed and compared on both linear and curved quadrilateral elements. On linear elements, all the above schemes are one-dimensional in each natural coordinate direction. However, on curved elements, not all schemes can be reduced to a one-dimensional form, although the SD and CPR formulations remain one-dimensional by design. The efficiency and accuracy of various formulations are compared on highly skewed curved elements. Several benchmark problems are simulated to further evaluate the performance of these schemes.