Discontinuous Galerkin Using Multigrid for Solving Euler Equations

The goal of this paper is to investigate and develop a fast and robust algorithm for the solution to discontinuous Galerkin discretizations of non-linear systems of conservation laws on unstructured using hierarchical basis functions.The methodology is developed for the two-dimension Euler equations using both Roe upwind flux and explicit Runge-Kutta multiple method in temporal step.The calculation result is presented for flow over a uniform flow over the NACA0012 airfoil,and compared with single-grid discontinuous Galerkin method.It demonstrates that the algorithm’s convergence rate is higher than single-grid discontinuous Galerkin method.