@Article{AAMM-10-1,
author = {Jian, Cheng and Yue, Huiqiang and Yu, Shengjiao and Tiegang, Liu},
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 = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2017-0060},
url = {https://global-sci.com/article/73163/a-direct-discontinuous-galerkin-method-with-interface-correction-for-the-compressible-navier-stokes-equations-on-unstructured-grids}
}