APPLICATION OF DISCONTINUOUS GALERKIN METHOD FOR THE SIMULATION OF 3D INVISCID COMPRESSIBLE FLOWS

We deal with the numerical solution of the Euler equations in three dimensions. We define the problem and propose a numerical method for its solution. Finaly, we employ a combination of the discontinuous Galerkin finite element method and backward difference formulae. Due to a linearization and a suitable explicit extrapolation we solve only a system of linear algebraic equations at each time step. This leads us to an efficient numerical scheme which has a higher degree of approximation with respect to the space and time coordinates. The determination of these semi-implicit schemes is briefly described. The three dimensional stabilization technique and the new method to choice the time step are developed and some numerical examples are presented.