A Discontinuous Galerkin Method Based on a BGK Scheme for the Navier-Stokes Equations on Arbitrary Grids (Advances in Applied Mathematics and Mechanics, 2018)
A discontinuous Galerkin Method based on a Bhatnagar-Gross-Krook(BGK) formulation is presented for the solution of the compressibleNavier-Stokes equations on arbitrary grids. The idea behind thisapproach is to combine the robustness of the BGK scheme with theaccuracy of the DG methods in an effort to develop a more accurate,efficient, and robust method for numerical simulations of viscousflows in a wide range of flow regimes. Unlike the traditionaldiscontinuous Galerkin methods, where a Local Discontinuous Galerkin(LDG) formulation is usually used to discretize the viscous fluxesin the Navier-Stokes equations, this DG method uses a BGK scheme tocompute the fluxes which not only couples the convective anddissipative terms together, but also includes both discontinuous andcontinuous representation in the flux evaluation at a cell interfacethrough a simple hybrid gas distribution function. The developedmethod is used to compute a variety of viscous flow problems onarbitrary grids. The numerical results obtained by this BGKDG methodare extremely promising and encouraging in terms of both accuracyand robustness, indicating its ability and potential to become notjust a competitive but simply a superior approach than the currentavailable numerical methods.