Volume 6, Issue 6
A Fifth-Order Low-Dissipative Conservative Upwind Compact Scheme Using Centered Stencil

Conghai Wu, Sujuan Yang & Ning Zhao

Adv. Appl. Math. Mech., 6 (2014), pp. 830-848.

Published online: 2014-06

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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

High-order scheme, compact scheme, conservative scheme, low-dissipative scheme.

  • AMS Subject Headings

65M06, 76M2, 76Q05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-6-830, author = {}, title = {A Fifth-Order Low-Dissipative Conservative Upwind Compact Scheme Using Centered Stencil}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {6}, pages = {830--848}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m-s3}, url = {http://global-sci.org/intro/article_detail/aamm/51.html} }
TY - JOUR T1 - A Fifth-Order Low-Dissipative Conservative Upwind Compact Scheme Using Centered Stencil JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 830 EP - 848 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2013.m-s3 UR - https://global-sci.org/intro/article_detail/aamm/51.html KW - High-order scheme, compact scheme, conservative scheme, low-dissipative scheme. AB -

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.

Conghai Wu, Sujuan Yang & Ning Zhao. (1970). A Fifth-Order Low-Dissipative Conservative Upwind Compact Scheme Using Centered Stencil. Advances in Applied Mathematics and Mechanics. 6 (6). 830-848. doi:10.4208/aamm.2013.m-s3
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