My research concerns the study of continuum mechanics, principally fluid and solid mechanics, with application to biological and physical phenomena. Many complex fluid, solid and fluid-solid interaction problems occur naturally in the human body; for example, the veins in the arm collapse when raised above the level of the heart. Fluid-structure interaction is also important in pathologies of the body. The collapse and occlusion of the airways in the lung is driven by an interplay between the elastic properties of the airway wall and the surface tension of the lung-lining fluid.
I am also interested in non-linear phenomena in large-scale systems and have been developing methods to determine and track bifurcations of large-scale systems. These will allow the systematic investigation of solutions of complex systems.
Current projects include:
- the development of oomph-lib , an object-oriented library of C++ functions for the numerical solution of multi-physics problems; with Matthias Heil
- a study of the modes of bubble propagation in rectangular tubes containing localised constrictions in their cross-section; with Anne Juel
- bifurcations and instabilities in cellular solids; with Tom Mullin
- an investigation into the applicability of exact solutions of the Navier--Stokes equations (e.g. stagnation-point flows) in finite domains; with Rich Hewitt
- development of computational methods for the fast evaluation of unit-cell problems in homogenisation theory; with Will Parnell
- the simulation of the non-linear evolution of interfacial instabilities; with Anne Juel and Matthias Heil
- a study of the motion of rigid and deformable bodies in bounded fluid domains.