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Fourier spectral modelling for multi-scale aero-thermal analysis

Many problems with large length scale disparities are amenable to spectral modelling. In this paper, two models are described to deal with multi-scale problems with a distinctive scale disparity in time and space, respectively. The first one makes use of a hybrid time-frequency domain formulation to realign hugely mismatched timescales in the fluid and solid domains for solving coupled convection–conduction heat transfer problems. An emphasis here is on the interface condition for multi-harmonic turbulent disturbances in conjunction with large eddy simulations. The second model deals with the spatial length scale disparity by using a block-spectral formulation. A small subset of discrete mesh blocks is solved with high local mesh resolution. The pointwise block-to-block variation is established by a discrete Fourier spectrum. An instantaneous whole domain solution can then be obtained efficiently by a simple spectral mapping. The validity and effectiveness of the models are illustrated with relevant computational examples.