A HIGH-ORDER ACCURATE DISCONTINUOUS FINITE-ELEMENT METHOD FOR THE NUMERICAL-SOLUTION OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS

This paper deals with a high-order accurate discontinuous finite eleme nt method for the numerical solution of the compressible Navier-Stokes equations. We extend a discontinuous finite element discretization or iginally considered for hyperbolic systems such as the Euler equations to the case of the Navier-Stokes equations by treating the viscous te rms with a mixed formulation. The method combines two key ideas which are at the basis of the finite volume and of the finite element method , the physics of wave propagation being accounted for by means of Riem ann problems and accuracy being obtained by means of high-order polyno mial approximations within elements. As a consequence the method is id eally suited to compute high-order accurate solution of the Navier-Sto kes equations on unstructured grids, The performance of the proposed m ethod is illustrated by computing the compressible viscous flow on a f lat plate and around a NACA0012 airfoil for several flow regimes using constant, linear, quadratic, and cubic elements. (C) 1997 Academic Pr ess.