Implementation and Verification of High-Order Accurate Discontinuous Galerkin Method on 2-D Unstructured Grids

In this paper, the discontinuous Galerkin method (DG) is applied to solve the 2D Euler equation. DG can be easily used in the unstructured girds, which has advantages in dealing with problems with complex boundaries. High order accuracy is achieved by higher order polynomial approximations within elements. In order to capture the shock without oscillation, the limiter is also applied. The performance of DG is illustrated by three numerical experimental tests, which show the potential of DG in engineering applications. The vortex propagation problem is to verify high-order accuracy of DG, while Sob problem and forward step problem are used to illustrate the ability to capture shock.