Volume 10, Issue 1
A Direct Discontinuous Galerkin Method with Interface Correction for the Compressible Navier-Stokes Equations on Unstructured Grids

Jian Cheng, Huiqiang Yue, Shengjiao Yu & Tiegang Liu

Adv. Appl. Math. Mech., 10 (2018), pp. 1-21.

Published online: 2018-10

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  • Abstract

Since the original DDG method has been introduced by Liu et al. [8] in 2009, a variety of DDG type methods have been proposed and further developed. In this paper, we further investigate and develop a new DDG method with interface correction (DDG (IC)) as the discretization of viscous and heat fluxes for the compressible Navier-Stokes equations on unstructured grids. Compared to the original DDG method, the newly developed DDG (IC) method demonstrates its superior in delivering the optimal order of accuracy under demanding situations. Strategies in extension and application of this newly developed DDG (IC) method for solving the compressible Navier-Stokes equations and special treatments designed for handling boundary viscous fluxes are presented and examined in this work. The performance of the new DDG method with interface correction is carefully evaluated and assessed through a number of typical test cases. Numerical experiments show that the new DDG method with interface correction can achieve the optimal order of accuracy on both uniform structured grids and nonuniform unstructured grids, which clearly indicates its potential for further applications of real engineering practices.

  • Keywords

Direct discontinuous Galerkin method, high-order method, compressible Navier-Stokes equations.

  • AMS Subject Headings

65M60, 76N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-1, author = {}, title = {A Direct Discontinuous Galerkin Method with Interface Correction for the Compressible Navier-Stokes Equations on Unstructured Grids}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {1}, pages = {1--21}, abstract = {

Since the original DDG method has been introduced by Liu et al. [8] in 2009, a variety of DDG type methods have been proposed and further developed. In this paper, we further investigate and develop a new DDG method with interface correction (DDG (IC)) as the discretization of viscous and heat fluxes for the compressible Navier-Stokes equations on unstructured grids. Compared to the original DDG method, the newly developed DDG (IC) method demonstrates its superior in delivering the optimal order of accuracy under demanding situations. Strategies in extension and application of this newly developed DDG (IC) method for solving the compressible Navier-Stokes equations and special treatments designed for handling boundary viscous fluxes are presented and examined in this work. The performance of the new DDG method with interface correction is carefully evaluated and assessed through a number of typical test cases. Numerical experiments show that the new DDG method with interface correction can achieve the optimal order of accuracy on both uniform structured grids and nonuniform unstructured grids, which clearly indicates its potential for further applications of real engineering practices.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0060}, url = {http://global-sci.org/intro/article_detail/aamm/10498.html} }
TY - JOUR T1 - A Direct Discontinuous Galerkin Method with Interface Correction for the Compressible Navier-Stokes Equations on Unstructured Grids JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 1 EP - 21 PY - 2018 DA - 2018/10 SN - 10 DO - http://dor.org/10.4208/aamm.OA-2017-0060 UR - https://global-sci.org/intro/aamm/10498.html KW - Direct discontinuous Galerkin method, high-order method, compressible Navier-Stokes equations. AB -

Since the original DDG method has been introduced by Liu et al. [8] in 2009, a variety of DDG type methods have been proposed and further developed. In this paper, we further investigate and develop a new DDG method with interface correction (DDG (IC)) as the discretization of viscous and heat fluxes for the compressible Navier-Stokes equations on unstructured grids. Compared to the original DDG method, the newly developed DDG (IC) method demonstrates its superior in delivering the optimal order of accuracy under demanding situations. Strategies in extension and application of this newly developed DDG (IC) method for solving the compressible Navier-Stokes equations and special treatments designed for handling boundary viscous fluxes are presented and examined in this work. The performance of the new DDG method with interface correction is carefully evaluated and assessed through a number of typical test cases. Numerical experiments show that the new DDG method with interface correction can achieve the optimal order of accuracy on both uniform structured grids and nonuniform unstructured grids, which clearly indicates its potential for further applications of real engineering practices.

Jian Cheng, Huiqiang Yue, Shengjiao Yu & Tiegang Liu. (2020). A Direct Discontinuous Galerkin Method with Interface Correction for the Compressible Navier-Stokes Equations on Unstructured Grids. Advances in Applied Mathematics and Mechanics. 10 (1). 1-21. doi:10.4208/aamm.OA-2017-0060
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