@Article{CiCP-22-2,
author = {},
title = {A Symmetric Direct Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations},
journal = {Communications in Computational Physics},
year = {2017},
volume = {22},
number = {2},
pages = {375--392},
abstract = {<p style="text-align: justify;">In this work, we investigate the numerical approximation of the compressible
Navier-Stokes equations under the framework of discontinuous Galerkin methods.
For discretization of the viscous and heat fluxes, we extend and apply the symmetric
direct discontinuous Galerkin (SDDG) method which is originally introduced
for scalar diffusion problems. The original compressible Navier-Stokes equations are
rewritten into an equivalent form via homogeneity tensors. Then, the numerical diffusive
fluxes are constructed from the weak formulation of primal equations directly
without converting the second-order equations to a first-order system. Additional numerical
flux functions involving the jump of second order derivative of test functions
are added to the original direct discontinuous Galerkin (DDG) discretization. A number
of numerical tests are carried out to assess the practical performance of the SDDG
method for the two dimensional compressible Navier-Stokes equations. These numerical
results obtained demonstrate that the SDDG method can achieve the optimal
order of accuracy. Especially, compared with the well-established symmetric interior
penalty (SIP) method [18], the SDDG method can maintain the expected optimal order
of convergence with a smaller penalty coefficient.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0080},
url = {https://global-sci.com/article/80143/a-symmetric-direct-discontinuous-galerkin-method-for-the-compressible-navier-stokes-equations}
}