Most efforts in the development of the discontinuous Galerkin methods (DGM) in computational fluid dynamics are primarily focused on the time accurate compressible Euler and Navier-Stokes equations. Its accuracy, efficiency, capability, robustness for steady state flow problems are relatively unexplored. In order for DGM to become a viable, attractive, probably even better alternative to the more traditional, more elaborate, well established finite volume methods (FVM), and finite element methods (FEM) for steady state computations, the following three issues have to be addressed: 1) Lack of efficient flow solver for steady state computations: Most efforts in the development of the discontinuous Galerkin methods are primarily focused on the spatial discretization.