Compressible viscous flow calculations using compatible finite element approximations

We discuss in this paper the numerical simulation of compressible viscous flows by a combination of finite element methods for the space approximation, an implicit second‐order multistep scheme for the time discretization and GMRES iterative methods for solving the non‐linear problems encountered at each time step. Numerical results corresponding to flows around aerofoils and aerospace vehicles illustrate the possibilities of these methods.