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Volume 25, Issue 2
Construction of the High Order Accurate Generalized Finite Difference Schemes for Inviscid Compressible Flows

Xue-Li Li, Yu-Xin Ren & Wanai Li

DOI: 10.4208/cicp.OA-2017-0040

Commun. Comput. Phys., 25 (2019), pp. 481-507.

Published online: 2018-10

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  • Abstract

The construction of high order accurate generalized finite difference method for inviscid compressible flows still remains an open problem in the literature. In this paper, the high order accurate generalized finite difference schemes have been developed based on the high order reconstruction and the high order numerical flux evaluation on a local cloud of points. The WBAP limiter based on the secondary reconstruction is used to suppress oscillations near discontinuities. The implementation of high order accurate boundary conditions is of critical importance in the construction of high order schemes. A new method is proposed for the high order accurate boundary treatment. Several standard test cases are solved to validate the accuracy, efficiency and shock capturing capability of the proposed high order schemes.

  • Keywords

Cloud of points, high order accurate boundary treatment, high order schemes, generalized finite difference, shock capturing.

  • AMS Subject Headings

35L25, 74J40, 76N15, 74S20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-25-481, author = {Xue-Li Li, Yu-Xin Ren and Wanai Li}, title = {Construction of the High Order Accurate Generalized Finite Difference Schemes for Inviscid Compressible Flows}, journal = {Communications in Computational Physics}, year = {2018}, volume = {25}, number = {2}, pages = {481--507}, abstract = {

The construction of high order accurate generalized finite difference method for inviscid compressible flows still remains an open problem in the literature. In this paper, the high order accurate generalized finite difference schemes have been developed based on the high order reconstruction and the high order numerical flux evaluation on a local cloud of points. The WBAP limiter based on the secondary reconstruction is used to suppress oscillations near discontinuities. The implementation of high order accurate boundary conditions is of critical importance in the construction of high order schemes. A new method is proposed for the high order accurate boundary treatment. Several standard test cases are solved to validate the accuracy, efficiency and shock capturing capability of the proposed high order schemes.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0040}, url = {http://global-sci.org/intro/article_detail/cicp/12760.html} }
TY - JOUR T1 - Construction of the High Order Accurate Generalized Finite Difference Schemes for Inviscid Compressible Flows AU - Xue-Li Li, Yu-Xin Ren & Wanai Li JO - Communications in Computational Physics VL - 2 SP - 481 EP - 507 PY - 2018 DA - 2018/10 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2017-0040 UR - https://global-sci.org/intro/article_detail/cicp/12760.html KW - Cloud of points, high order accurate boundary treatment, high order schemes, generalized finite difference, shock capturing. AB -

The construction of high order accurate generalized finite difference method for inviscid compressible flows still remains an open problem in the literature. In this paper, the high order accurate generalized finite difference schemes have been developed based on the high order reconstruction and the high order numerical flux evaluation on a local cloud of points. The WBAP limiter based on the secondary reconstruction is used to suppress oscillations near discontinuities. The implementation of high order accurate boundary conditions is of critical importance in the construction of high order schemes. A new method is proposed for the high order accurate boundary treatment. Several standard test cases are solved to validate the accuracy, efficiency and shock capturing capability of the proposed high order schemes.

Xue-Li Li, Yu-Xin Ren and Wanai Li. (2018). Construction of the High Order Accurate Generalized Finite Difference Schemes for Inviscid Compressible Flows. Communications in Computational Physics. 25 (2). 481-507. doi:10.4208/cicp.OA-2017-0040
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