High Order Discontinuous Galerkin Method for Solving Euler Equations on Unstructured Grids

The main purpose of this paper is to develop a discontinuous Galerkin method suitable for the numerical solution of the Euler equations on unstructured grids.Based on the theory of discontinuous Galerkin method,the approximate solution within each element is expanded in a series of local polynomials bases functions;the numerical flux of Euler equations are calculated by using the Gaussian quadrature rules and Roe scheme;and time is advanced by explicit fourth-order accurate Runge-Kutta method.The versatility of the discontinuous Galerkin method to obtain high-order accurate solutions in realistic geometries is demonstrated with the results obtained for subsonic and transonic inviscid flow over a NACA-0012 airfoil and low speed inviscid flow around a 2D cylinder.The Numerical results indicate that the presented discontinuous Galerkin method has properties of good convergence speed,smaller numerical dissipation and excellent ability to capture shocks.