BDF-DGFE Method for the Compressible Navier-Stokes Equations

Abstract

We deal with a numerical solution of the compressible Navier-Stokes equations. We employ a combination of the discontinuous Galerkin finite element (DGFE) method for the space semi-discretization and the backward difference formulae (BDF) for the time discretization. Moreover, using a linearization of inviscid as well as viscous fluxes and applying a suitable explicit extrapolation to nonlinear terms, we obtain a numerical scheme which is almost unconditionally stable, has a higher degree of approximation with respect to the space and time coordinates and at each time step requires a solution of a linear algebraic problem. We present this approach and compare several variants of the DGFE techniques applied to a steady flow around the NACA0012 profile.