TY - JOUR

T1 - On the freestream preservation of high-order conservative flux-reconstruction schemes

AU - Abe, Yoshiaki

AU - Haga, Takanori

AU - Nonomura, Taku

AU - Fujii, Kozo

N1 - Funding Information:
We are grateful to the anonymous reviewers for their valuable comments and suggestions. We also express our gratitude to Dr. Eiji Shima for his helpful support for the computation. This research has received contributions from the JSPS Science Research Grant 225879 , which we would like to make mention here in expressing our appreciation.
Publisher Copyright:
© 2014 Elsevier Inc.

PY - 2015/1/5

Y1 - 2015/1/5

N2 - The appropriate procedure for constructing the symmetric conservative metric is presented with which both the freestream preservation and global conservation properties are satisfied in the high-order conservative flux-reconstruction scheme on a three-dimensional stationary-curvilinear grid. A freestream preservation test is conducted, and the symmetric conservative metric constructed by the appropriate procedure preserves the freestream regardless of the order of shape functions, while other metrics cannot always preserve the freestream. Also a convecting vortex is computed on three-dimensional wavy grids, and the formal order of accuracy is achieved when the symmetric conservative metric is appropriately constructed, while it is not when they are inappropriately constructed. In addition, although the sufficient condition for the freestream preservation with the nonconservative (cross product form) metric was reported in the previous study to be that the order of solution polynomial has to be greater than or equal to the twice of the order of a shape function, a special case is newly found in the present study: when the Radau polynomial is used for the correction function, the freestream is preserved even if the solution order is lower than the known condition. Using the properties of Legendre polynomials, the mechanism for this special case is analytically explained, considering the cancellation of aliasing errors.

AB - The appropriate procedure for constructing the symmetric conservative metric is presented with which both the freestream preservation and global conservation properties are satisfied in the high-order conservative flux-reconstruction scheme on a three-dimensional stationary-curvilinear grid. A freestream preservation test is conducted, and the symmetric conservative metric constructed by the appropriate procedure preserves the freestream regardless of the order of shape functions, while other metrics cannot always preserve the freestream. Also a convecting vortex is computed on three-dimensional wavy grids, and the formal order of accuracy is achieved when the symmetric conservative metric is appropriately constructed, while it is not when they are inappropriately constructed. In addition, although the sufficient condition for the freestream preservation with the nonconservative (cross product form) metric was reported in the previous study to be that the order of solution polynomial has to be greater than or equal to the twice of the order of a shape function, a special case is newly found in the present study: when the Radau polynomial is used for the correction function, the freestream is preserved even if the solution order is lower than the known condition. Using the properties of Legendre polynomials, the mechanism for this special case is analytically explained, considering the cancellation of aliasing errors.

KW - Aliasing error

KW - Conservative metric

KW - Flux-reconstruction scheme

KW - Freestream preservation

KW - Geometric conservation law

KW - High-order unstructured scheme

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U2 - 10.1016/j.jcp.2014.10.011

DO - 10.1016/j.jcp.2014.10.011

M3 - Article

AN - SCOPUS:84920083623

VL - 281

SP - 28

EP - 54

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -