Nonlinear Behaviour in Coupled Problems: Experiment, Computation and Theory


Many problems of practical interest involve coupling(s) between different physical processes. Classical examples include reaction-diffusion systems, fluid-structure interaction and thermal or solutal convection problems. At the Manchester Centre for Nonlinear Dynamics (MCND) we investigate the behaviour of such coupled systems using a combination of precise lab experiments, detailed numerical simulations and supporting theory. We strive to maintain a close connection between theory, simulation and experiments.

The numerical simulations are conducted using our open-source software library oomph-lib ( which has been designed to facilitate the specification of complex multi-physics problems and their efficient solution. The library is fully parallelised, includes spatial and temporal adaptivity; continuation and bifurcation tracking capabilities; and a powerful block-preconditioning framework that enables the development of optimal solvers for coupled systems by reusing solvers developed for single-physics problems.

I will give an overview of the library design and illustrate its capabilities by describing some of our recent research projects on free-surface flows, elastic buckling problems and optimal solver development for thermal convection problems.


Andrew Hazel
School of Mathematics and the Manchester Centre for Nonlinear Dynamics at the University of Manchester