## Applied and Computational Mathematics

The major research interests of the group are in theoretical and computational fluid mechanics. However, members of the group also undertake research in numerical analysis, structural and solid mechanics, inverse problems and applied analysis. Our research in the area of applied and computational mathematics is informed by problems at the interface with physical sciences, biological sciences and engineering and benefits from interdisciplinary collaborations within Cardiff University and further afield. Our national and international collaborators include research groups at Imperial, Oxford, Cambridge, Warwick, Swansea, Canberra, Curtin (Perth), Perth, Delft, Northwestern, Ljubljana and Montréal.

### Key Research Areas

- Fluid Mechanics: viscous buckling phenomena; wetting phenomena; free-surface flows; dynamics of liquid films and jets; hydrodynamic stability theory; laminar-turbulent transition mechanisms; boundary-layer and wake flow instabilities; boundary layer flow control; viscoelastic flows and computational rheology; bubble dynamics; kinetic theory models.
- Biological fluid mechanics: adhesion and dessication of biological cells; fluid-structure interaction problems.
- Structural and solid mechanics: numerical analysis of damage; multi-scale modelling, limit states analysis.
- Numerical analysis and scientific computing: finite element methods for elasticity; spectral element methods; immersed boundary method; lattice Boltzmann methods; proper generalized decomposition; dynamic density functional theory; numerical continuation; differential algebraic equation; automatic differentiation.
- Applied Analysis: inverse problems in materials modelling; homogenisation and the mechanics of composites.
- Applied mathematical modelling: singular perturbation methods; matched asymptotics; dynamical systems and bifurcation analysis; stochastic processes; physical resolution of singularities in mathematical models.

The group hosts meetings of the Cardiff University Student Chapter of SIAM which encompasses postgraduate students and faculty members from across Cardiff University who are interested in mathematics or scientific computing and their real-world applications.