Implicit and semi-implicit methods for the compressible Navier-Stokes equations.

Several methods are discussed for the numerical simulation of compressible viscous flows, modelled by the unsteady Navier Stokes equations using finite elements. The full Navier Stokes system of modelling is considered as well as the model obtained from the assumption that the total enthalpy is constant. Solution methods are compared using a fully implicit scheme of gear type and splitting operator techniques which decouple the various physical effects. Both linear and nonlinear sub-problems are considered. A direct method based on a cascade of Poisson problems is used for the generalized Stokes problem: the nonlinear subproblems are solved either by highly stable rational Runge-Kutta techniques using dynamic relaxation, or quasi Newton/conjugate gradient algorithms superlinearly convergent.