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Consistent Dirichlet boundary conditions for numerical solution of moving boundary problems

<13>Accurately predicting interface and boundary movement is crucial in fluid flow simulation. However, imposing the conditions that govern this movement, e.g. temperatures at solid-liquid interfaces, typically violates fundamental physical conservation laws (of mass, momentum, etc.). This work solves this issue for the widely-used finite element method, tracking multidimensional interfaces without artificial stabilisation or spurious smoothing. Subsequent international collaboration (doi:10.4208/cicp.2009.v6.595) demonstrated ~10x error reduction over the state-of-the-art when tracking solid-liquid interfaces during solidification. Follow-on work, linked with Hubbard's sabbatical, provided preliminary predictions of solid tumour growth rates, laying the foundations for further cancer modelling research ([Hubbard3] and Maths-for-Medicine initiative EP/K039342/1, £1.2M).