My research interests were initially in fluid dynamics but working in industrial mathematics has led me to problems in a wide variety of fields.
The unifying theme of my work is the use of continuum models and the application of asymptotic methods to physical problems in order to provide useful simplifications and illuminate the model and its predictions.
Among problems on which I have worked in fluid mechanics are nonlinear wave propagation in gases including real gas effects and resonant sloshing in gases and liquids. Many industrially relevant problems involve thin layer models of viscous fluids, and similar mathematics can apply in very varied situations. Examples include injection moulding, concentration polarization in ultra filtration, contact lens modelling and the drying of paint. Following my early work in relaxing gases, I have had a continuing interest in two-phase flows and I have developed several fluid-fibre and fibre-fibre interaction models for problems in the textile industry. This last example has proved a fruitful area of research for over ten years and resulted in one MSc and four PhD theses in collaboration with industry.
Mathematical modelling of elastoplasticity at high stress, P.D.Howell, H.Ockendon, J.R.Ockendon, Proc. Roy. Soc. A, vol 468, p3842-3863, 2012.
Waves and Compressible Flow, H.Ockendon, J.R.Ockendon, Springer 2004.
Viscous Flow, H.Ockendon, J.R.Ockendon, Cambridge 1995.