Convergence to steady-state solutions for stabilized finite element simulations of compressible flows

The main objective of the paper is to compare the numerical performance of several pseudo-time integration algorithms, used for driving finite element solutions of compressible flow equations towards the steady state. The algorithms are implementations of four strategies: explicit, linear implicit, multistage linear implicit, and nonlinear. All, except the explicit scheme, employ a particular implementation of GMRES to solve systems of linear equations. The nonlinear algorithm uses at each time step two iterations of the Newton method with an approximate Jacobian. The finite element formulation is a version of the stabilized FEM with h-adaptivity. The comparison is done for three flow problems, in three flow regimes: subsonic, transonic, and supersonic. Final conclusions concerning relative performance of the methods are drawn.