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A Fifth-Order Low-Dissipative Conservative Upwind Compact Scheme Using Centered Stencil

Published online by Cambridge University Press:  03 June 2015

Conghai Wu ,
Sujuan Yang  and
Ning Zhao
Conghai Wu*
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang 621000, China College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Sujuan Yang
Affiliation:
College of Science, PLA University of Science and Technology, Nanjing 211101, China
Ning Zhao*
Affiliation:
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
*
Corresponding author. Email: wraiment@163.com
Email: zhaoam@nuaa.edu.cn
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Abstract

In this paper, a conservative fifth-order upwind compact scheme using centered stencil is introduced. This scheme uses asymmetric coefficients to achieve the upwind property since the stencil is symmetric. Theoretical analysis shows that the proposed scheme is low-dissipative and has a relatively large stability range. To maintain the convergence rate of the whole spatial discretization, a proper non-periodic boundary scheme is also proposed. A detailed analysis shows that the spatial discretization implemented with the boundary scheme proposed by Pirozzoli [J. Comput. Phys., 178 (2001), pp. 81–117] is approximately fourth-order. Furthermore, a hybrid methodology, coupling the compact scheme with WENO scheme, is adopted for problems with discontinuities. Numerical results demonstrate the effectiveness of the proposed scheme.

Keywords

65M0676M2076Q05High-order schemecompact schemeconservative schemelow-dissipative scheme
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 6 , December 2014 , pp. 830 - 848
Copyright
Copyright © Global-Science Press 2014

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