High-order discontinuous Galerkin method for solving Euler equations

A fast and robust high-order discontinuous Galerkin algorithm using normal orthogonal basis functions is presented for the solution of compressible Euler equations on structured grids.The methodology is developed using both Roe upwind flux and TVD Runge-Kutta multiple method in temporal step.Moreover,this paper investigates 2D two-order Moment limiter and uses local time step technique to accelerate the convergence to a steady-state solution.The calculation results are presented for a flow over the NACA0012 airfoil,and show that the algorithm has good convergence and excellent ability to capture shocks,and Moment limiter can effectively suppress the numerical oscillations.