A non linear frequency domain-spectral difference scheme for unsteady periodic flows /

Abstract

This research presents a new, more efficient computational scheme for complex periodic flows, and brings forward two novel ideas. The first consists in the use of a Fourier space time representation in conjunction with a high-order spatial discretization. The second is based on the efficient treatment of the resulting set of equations using a fast, implicit solver. This thesis describes the formulation and implementation of the proposed framework. Firstly, a high-order spectral difference scheme for the Euler equations is introduced. Secondly, the non-linear frequency domain method resolving the unsteady behavior of the flow is discussed. Thirdly, a mathematical and experimental validation of the proposed algorithm is carried out. Numerical experiments performed in this thesis suggest that the methodology could be an attractive new avenue for large scale time-dependent problems, alleviating the computational cost traditionally associated with such simulations