Speaker:
Dr Peter Baddoo, Department of Mathematics, Imperial College London
Abstract:
We present a constructive procedure for analytically calculating flows through periodic domains. The calculus can account for a broad range of potential flow phenomena including point vortices, uniform/straining flows, the motion of the boundaries, and edge behaviours such as the Kutta condition. The solutions are each valid for arbitrary connectivities i.e. any number of boundaries per period window. Although conventional wisdom says that these complex analysis techniques are restricted to solving Laplace’s equation, we show how the ensuing solutions can be deployed to solve a range of non-harmonic problems. In particular, we apply the new theory to vortex dynamics, wave scattering and advection-diffusion problems, all taking place within multiply connected periodic domains. To this end, we leverage recent advances in complex function theory and numerical analysis to implement our new calculus. This work is in collaboration with Prof Darren Crowdy.