Discontinuous Galerkin method based on artificial viscosity

The discontinuous Galerkin finite-element method based on artificial viscosity is developed. The method is modified for better adaptability and extended to curvilinear meshes. Typical test cases are simulated to evaluate the method. The calculation results of a one-dimensional shock tube problem show that the modified method is able to suppress spurious oscillations well while preserving high resolution. Furthermore, with second order scheme, the artificial viscosity method is rather diffusive, and with the order of the scheme further increased, the resolution of the results is greatly improved. Also in a hypersonic cylinder flow, the artificial viscosity method shows advantage over the third-order MUSCL scheme and the fifth-order WENO scheme.