DISCONTINUOUS GALERKIN FINITE-ELEMENT METHOD FOR EULER AND NAVIER-STOKES EQUATIONS

A finite element method for the Euler and Navier-Stokes equations has been developed. The spatial discretization involves the discontinuous Galerkin finite element method and Lax-Friedrichs flux method. The temporal discretizations used are the explicit Runge-Kutta time integrations. The scheme is formally second-order accurate in space and time. A dynamic mesh algorithm is included to simulate flows over moving bodies. The inviscid flows passing through a channel with circular arc bump, through the NACA 0012 airfoil, and the laminar flows passing over a flat plate with shock interaction are investigated to confirm the accuracy and convergence of the finite element method. Also the unsteady flow through a pitching NACA 0012 airfoil is performed to prove the capability of the present method.