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 alg orithms 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 equ ations. The nonlinear algorithm uses at each time step two iterations of th e Newton method with an approximate Jacobian. The finite element formulatio n is a version of the stabilized FEM with h-adaptivity. The comparison is d one for three flow problems, in three how regimes: subsonic, transonic, and supersonic. Final conclusions concerning relative performance of the metho ds are drawn. (C) 2000 Elsevier Science Ltd. All rights reserved.