Inhomogeneous flow calculations by spectral methods - Mono-domain and multi-domain techniques

A spectral expansion in time technique is proposed in order to overcome the problems posed by geometry complexity and time scheme accuracy requirements in spectral methods. For time accuracy, a squared time pseudo-spectral approach is implemented in the cases of both two- and three-dimensional flows, and complex geometry flexibility is obtained by means of a multidomain spectral method which has the flexibility of finite elements. Due to the subdomain technique used there is no memory size problem, and the extension of the technique to three-dimensional unsteady flow is expected to be easy. The four examples presently considered are the square domain with stream function formulation and spectral time derivatives, the cubic or square domain with velocity pressure fluctuation and spectral time derivatives, the square duct with velocity pressure formulation and finite difference time derivatives, and the airfoil with velocity-pressure formulation, finite difference time derivatives and multidomain techniques.