Development of Computational Fluid Dynamics (CFD) depends on both computer processing power and numerical/physical modelling and methodologies. The basic sense of proportion in engineering always motivates computational modellers to strive to develop the most suitable methods and models for the type of problems to be solved. For product designs in particular, the key to the successful applications of CFD is not to give an absolutely accurate answer, but rather it is to tell differences among different designs, and do so consistently. The speed of a CFD solution matters in a modern design system where different disciplines are increasingly closely coupled. Development of a fast method often tends to be regarded merely to provide a faster way to do the same job as its expensive counterpart. We should be reminded that a faster method may also enable to simulate, analyse and solve the problems which would be otherwise prohibitively expensive at the time. This was probably as true about two decades ago when the Fourier spectrum-based nonlinear methods began to be developed for spatial and temporal domain truncations for flow solutions, as it is today when computing power has increased by hundreds or thousands folds thanks to highly parallel systems and cheap hardware.
This special issue on the Fourier spectrum-based methods was intended to give an overview of past and current developments in this area. The main emphasis is placed on the development and demonstration of such methods for unsteady flow and aeroelasticity applications in turbomachinery and wings. We are fortunate to have the contributions by several leading experts. The original development and demonstration of the harmonic balance methodology for unsteady flow are thoroughly reviewed by Hall et al. Some illustrative applications of the harmonic balance method to multi-stage turbomachinery environment are presented by Sicot et al. A discussion on development and application of the frequency-domain solution method to external flow around wing sections is given by McCracken et al. The overview of development and application of the Non-Linear Harmonic (NLH) method is presented by Vilmin et al, extending the initial work by He. The Fourier method for a spatial domain truncation in conjunction with a time domain solution method is extensively reviewed by Gerolymos. In the turbomachinery applications, an issue of great interest is the capability to simulate unsteady flows in a multi-stage environment with multiple disturbances with distinctive frequencies, to which attention is paid by several contributors. Some modelling efforts in using a Fourier spectrum for spatial and temporal multi-scale problems are presented by He.
We are very grateful to the IJCFD for giving such a valuable platform and the editorial support for this special issue. Thanks also go to the contributing authors with established expertise for their willingness to share the experience and insightful thoughts and for their efforts to make the special issue possible. We hope that the reader will find it informative and thought-provoking reading.