Nonlinear Behaviour in Coupled Problems: Experiment, Computation and Theory

Abstract

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 (http://www.oomph-lib.org) 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.

Speaker

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