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Volume 31, Issue 4
A DDG Method with a Residual-Based Artificial Viscosity for the Transonic/Supersonic Compressible Flow

Xiaofeng He, Kun Wang, Yiwei Feng, Tiegang Liu & Xiaojun Wang

DOI: 10.4208/cicp.OA-2021-0098

Commun. Comput. Phys., 31 (2022), pp. 1134-1161.

Published online: 2022-03

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  • Abstract

In this work, a direct discontinuous Galerkin (DDG) method with artificial viscosity is developed to solve the compressible Navier-Stokes equations for simulating the transonic or supersonic flow, where the DDG approach is used to discretize viscous and heat fluxes. A strong residual-based artificial viscosity (AV) technique is proposed to be applied in the DDG framework to handle shock waves and layer structures appearing in transonic or supersonic flow, which promotes convergence and robustness. Moreover, the AV term is added to classical BR2 methods for comparison. A number of 2-D and 3-D benchmarks such as airfoils, wings, and a full aircraft are presented to assess the performance of the DDG framework with the strong residual-based AV term for solving the two dimensional and three dimensional Navier-Stokes equations. The proposed framework provides an alternative robust and efficient approach for numerically simulating the multi-dimensional compressible Navier-Stokes equations for transonic or supersonic flow.

  • Keywords

Direct discontinuous Galerkin, transonic/supersonic flow, residual-based artificial viscosity.

  • AMS Subject Headings

76H05, 76J20, 65M60, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-31-1134, author = {He , XiaofengWang , KunFeng , YiweiLiu , Tiegang and Wang , Xiaojun}, title = {A DDG Method with a Residual-Based Artificial Viscosity for the Transonic/Supersonic Compressible Flow}, journal = {Communications in Computational Physics}, year = {2022}, volume = {31}, number = {4}, pages = {1134--1161}, abstract = {

In this work, a direct discontinuous Galerkin (DDG) method with artificial viscosity is developed to solve the compressible Navier-Stokes equations for simulating the transonic or supersonic flow, where the DDG approach is used to discretize viscous and heat fluxes. A strong residual-based artificial viscosity (AV) technique is proposed to be applied in the DDG framework to handle shock waves and layer structures appearing in transonic or supersonic flow, which promotes convergence and robustness. Moreover, the AV term is added to classical BR2 methods for comparison. A number of 2-D and 3-D benchmarks such as airfoils, wings, and a full aircraft are presented to assess the performance of the DDG framework with the strong residual-based AV term for solving the two dimensional and three dimensional Navier-Stokes equations. The proposed framework provides an alternative robust and efficient approach for numerically simulating the multi-dimensional compressible Navier-Stokes equations for transonic or supersonic flow.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0098}, url = {http://global-sci.org/intro/article_detail/cicp/20379.html} }
TY - JOUR T1 - A DDG Method with a Residual-Based Artificial Viscosity for the Transonic/Supersonic Compressible Flow AU - He , Xiaofeng AU - Wang , Kun AU - Feng , Yiwei AU - Liu , Tiegang AU - Wang , Xiaojun JO - Communications in Computational Physics VL - 4 SP - 1134 EP - 1161 PY - 2022 DA - 2022/03 SN - 31 DO - http://doi.org/10.4208/cicp.OA-2021-0098 UR - https://global-sci.org/intro/article_detail/cicp/20379.html KW - Direct discontinuous Galerkin, transonic/supersonic flow, residual-based artificial viscosity. AB -

In this work, a direct discontinuous Galerkin (DDG) method with artificial viscosity is developed to solve the compressible Navier-Stokes equations for simulating the transonic or supersonic flow, where the DDG approach is used to discretize viscous and heat fluxes. A strong residual-based artificial viscosity (AV) technique is proposed to be applied in the DDG framework to handle shock waves and layer structures appearing in transonic or supersonic flow, which promotes convergence and robustness. Moreover, the AV term is added to classical BR2 methods for comparison. A number of 2-D and 3-D benchmarks such as airfoils, wings, and a full aircraft are presented to assess the performance of the DDG framework with the strong residual-based AV term for solving the two dimensional and three dimensional Navier-Stokes equations. The proposed framework provides an alternative robust and efficient approach for numerically simulating the multi-dimensional compressible Navier-Stokes equations for transonic or supersonic flow.

He , XiaofengWang , KunFeng , YiweiLiu , Tiegang and Wang , Xiaojun. (2022). A DDG Method with a Residual-Based Artificial Viscosity for the Transonic/Supersonic Compressible Flow. Communications in Computational Physics. 31 (4). 1134-1161. doi:10.4208/cicp.OA-2021-0098
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