This paper describes the application of the least-squares spectral element method to compressible flow problems. Special attention is paid to the imposition of the weak boundary conditions along curved walls and the influence of the time step on the position and resolution of shocks. The method is described and results are presented for a supersonic flow over a wedge and subsonic, transonic and supersonic flow problems over a bump.

spectral element methods, least-squares formulation, Euler equations
Life Sciences (theme 5), Energy (theme 4)
International Journal for Numerical Methods in Fluids
Scientific Computing

Gerritsma, M.I, van der Bas, R, De Maerschalck, B, Koren, B, & Deconinck, H. (2008). Least-squares spectral element method applied to the Euler equations. International Journal for Numerical Methods in Fluids, 57, 1371–1395.