Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T19:27:39.438Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Email: [email protected]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Lee, C. and Seo, Y., A new compact spectral scheme for turbulence simulations, J. Comput. Phys., 183 (2002), pp. 438–469.Google Scholar
[2]Nagarajan, S., Lele, S. K. and Ferziger, J. H., A robust high order compact method for large eddy simulation, J. Comput. Phys., 191 (2003), pp. 392–419.Google Scholar
[3]Ekaterinaris, J. A., Implicit high-resolution compact schemes for gas dynamics and aeroacoustics, J. Comput. Phys., 156 (1999), pp. 272–299.Google Scholar
[4]Lerat, A. and Corre, C., A residual-based compact scheme for the compressible Navier-Stokes equations, J. Comput. Phys., 170 (2001), pp. 642–675.Google Scholar
[5]Tam, C. K. W. and Webb, J. C., Dispersion-relation-preserving finite difference schemes for computational acoustics, J. Comput. Phys., 107 (1993), pp. 262–281.CrossRefGoogle Scholar
[6]Zingg, D. W., Comparison of high-accuracy finite-difference methods for linear wave propagation, SIAM J. Sci. Comput., 22 (2000), pp. 476–502.CrossRefGoogle Scholar
[7]Lele, S. K., Compact difference schemes with spectral-like resolution, J. Comput. Phys., 103 (1992), pp. 16–42.Google Scholar
[8]Tolstykh, A. I. and Lipavskii, M. V., On performance of methods with third- and fifth-order compact upwind differencing, J. Comput. Phys., 140 (1998), pp. 205–232.Google Scholar
[9]Tam, C. K. W., Webb, J. C. and Dong, Z., A study of the short wave components in computational acoustics, J. Comput. Acoust., 1 (1993), pp. 1–30.Google Scholar
[10]Zhong, X., High-order finite-difference schemes for numerical simulation of hypersonic boundary- layer transition, J. Comput. Phys., 144 (1998), pp. 662–709.CrossRefGoogle Scholar
[11]Adams, N. A. and Shariff, K., A high-resolution hybrid compact-ENO scheme for shock- turbulence interaction problems, J. Comput. Phys., 127 (1996), pp. 27–51.Google Scholar
[12]Jiang, G. S. and Shu, C.-W., Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), pp. 202–228.Google Scholar
[13]Jameson, A., Schmidt, W. and Turkel, E., Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes, AIAA-81-1259, (1981).Google Scholar
[14]Pirozzoli, S., Conservative hybrid compact-WENO schemes for shock-turbulence interaction, J. Comput. Phys., 178 (2001), pp. 81–117.Google Scholar
[15]Ren, Y. X., Liu, M. and Zhang, H. X., A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws, J. Comput. Phys., 192 (2003), pp. 365–386.Google Scholar
[16]Kim, D. and Kwon, J. H., A high-order accurate hybrid scheme using a central flux scheme and a WENO scheme for compressible flowfield analysis, J. Comput. Phys., 210 (2005), pp. 554–583.Google Scholar
[17]Zhou, Q., Yao, Z., He, F. and Shen, M., A new family of high-order compact upwind difference schemes with good spectral resolution, J. Comput. Phys., 227 (2007), pp. 1306–1339.Google Scholar
[18]Gustafsson, B., The convergence rate for difference approximations to mixed initial boundary value problems, Math. Comput., 29 (1975), pp. 396–406.Google Scholar
[19]Borges, R., Carmona, M., Costa, B. and Don, W. S., An improved weighted essentially nonoscillatory scheme for hyperbolic conservation laws, J. Comput. Phys., 227 (2008), pp. 3191–3211.Google Scholar
[20]Wang, Z. and Huang, G. P., An essentially nonoscillatory high-order Pade-type (ENO-Pade) scheme, J. Comput. Phys., 177 (2002), pp. 37–58.Google Scholar