A DDG Method with a Residual-Based Artificial Viscosity for the Transonic/Supersonic Compressible Flow
Year: 2022
Author: Xiaofeng He, Kun Wang, Yiwei Feng, Tiegang Liu, Xiaojun Wang
Communications in Computational Physics, Vol. 31 (2022), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2021-0098
Communications in Computational Physics, Vol. 31 (2022), Iss. 4 : pp. 1134–1161
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Direct discontinuous Galerkin transonic/supersonic flow residual-based artificial viscosity.