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The Unified Transform: A New Tool for Scattering Problems

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The interaction of acoustic or hydrodynamic fluctuations with thin elastic structures arise in numerous situations including both aeroacoustics, where elasticity of a wing is known to reduce the aerodynamic noise scattered by the sharp trailing edge, and oceanography, where ice sheets deform elastically on the ocean surface affecting acoustic scattering in the ocean beneath. Accurate and fast modelling of the fluid-structure interaction is key to predicting the effect of external forces on an elastic plate, or the effect of elasticity on the radiated field, and thus key for providing insight into a wide range of fluid dynamic problems. However, these types of problems are very difficult to analyse via traditional methods such as the Wiener-Hopf technique due to the complexity of the elastic kernel function (this becomes more difficult for finite structures due to the need to factorise a matrix kernel rather than a scalar kernel).

I will present a new boundary spectral collocation method for tackling such external acoustic scattering problems which may involve both rigid and elastic flat-plate boundaries. The method is ideally suited to mixed boundary value problems in unbounded domains and can handle solutions with corner singularities. The new method is fast and accurate, even for high frequencies, avoiding complications such as the evaluation of singular integrals that arise in typical boundary based methods. The method will be illustrated by application to aerodynamic noise generated by flexible wings.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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