An analysis of the performance of a high-order stabilised finite element method for simulating compressible flows

Stabilised finite element methods are now well established and are used in both industrial and commercial flow solvers. However, these methods have traditionally been restricted to linear approximations in space and they are rarely implemented within a high-order context. In the present work, the numerical performance of a higher-order approach is investigated for the simulation of some inviscid and laminar viscous two dimensional subsonic and transonic flows. The results produced clearly demonstrate the benefits that the higher-order approach has to offer, in terms of a reduction in both the degrees of freedom and, more importantly, the CPU time required, when compared with a low-order finite element or finite volume method.