@Article{AAMM-1-3,
author = {Luo, Hong and Luqing, Luo and Xu, Kun},
title = {A Discontinuous Galerkin Method Based on a BGK Scheme for the Navier-Stokes Equations on Arbitrary Grids},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2009},
volume = {1},
number = {3},
pages = {301--318},
abstract = {<p style="text-align: justify;">A discontinuous Galerkin Method based on a Bhatnagar-Gross-Krook
(BGK) formulation is presented for the solution of the compressible
Navier-Stokes equations on arbitrary grids. The idea behind this
approach is to combine the robustness of the BGK scheme with the
accuracy of the DG methods in an effort to develop a more accurate,
efficient, and robust method for numerical simulations of viscous
flows in a wide range of flow regimes. Unlike the traditional
discontinuous Galerkin methods, where a Local Discontinuous Galerkin
(LDG) formulation is usually used to discretize the viscous fluxes
in the Navier-Stokes equations, this DG method uses a BGK scheme to
compute the fluxes which not only couples the convective and
dissipative terms together, but also includes both discontinuous and
continuous representation in the flux evaluation at a cell interface
through a simple hybrid gas distribution function. The developed
method is used to compute a variety of viscous flow problems on
arbitrary grids. The numerical results obtained by this BGKDG method
are extremely promising and encouraging in terms of both accuracy
and robustness, indicating its ability and potential to become not
just a competitive but simply a superior approach than the current
available numerical methods.</p>},
issn = {2075-1354},
doi = {https://doi.org/2009-AAMM-8371},
url = {https://global-sci.com/article/73688/a-discontinuous-galerkin-method-based-on-a-bgk-scheme-for-the-navier-stokes-equations-on-arbitrary-grids}
}