A DDG Method with a Residual-Based Artificial Viscosity for the Transonic/Supersonic Compressible Flow

In this work, a direct discontinuous Galerkin (DDG) method with artificial viscosity is developed to solve the compressible Navier-Stokes equations for simulating the transonic or supersonic flow, where the DDG approach is used to discretize viscous and heat fluxes. A strong residual-based artificial viscosity (AV) technique is proposed to be applied in the DDG framework to handle shock waves and layer structures appearing in transonic or supersonic flow, which promotes convergence and robustness. Moreover, the AV term is added to classical BR2 methods for comparison. A number of 2-D and 3-D benchmarks such as airfoils, wings, and a full aircraft are presented to assess the performance of the DDG framework with the strong residual based AV term for solving the two dimensional and three dimensional Navier-Stokes equations. The proposed framework provides an alternative robust and efficient approach for numerically simulating the multi-dimensional compressible Navier-Stokes equations for transonic or supersonic flow.