Manchester Applied Mathematics and Numerical Analysis Seminars Autumn 2000/2001

November 22, 2000, 2.30 pm

Lecture Theatre OF/B9 Oddfellows Hall (Material Science)

Analysis and Simulation for Coupled Particle-Field Models

Prof. Andrew Stuart, Mathematics Institute, University of Warwick

There are a variety of problems arising in the physical sciences which involve coupling between particles and a continuum. These models pose interesting challenges in their analysis, as well as giving rise to important computational issues.

One particular such model, to which we will devote the majority of our talk, arises in the modelling of particles suspended in a fluid; such models arise, for example, in the modelling of spray combustors where particles are used to describe the fuel, and a fluid continuum to describe the gaseous medium in which the combustion occurs. In these models collisions between particles are important and must be incorporated into the model. The particles have a small length scale relative to the fluid and hence appear as (smoothed) delta functions in the (fluid) continuum equations.

The primary challenges in the analysis of the model arise from the coupling of the particles to the continuum, through delta-like singularities. The primary computational challenges arise from the necessity to detect a large number of collisions between multiple spheres, whose paths are coupled through the continuum field, and from the delicate nature of the particle-continuum coupling. Some theoretical results will be presented concerning the analysis of such models and numerical algorithms will be described and analyzed.

For further info contact either Matthias Heil (mheil@ma.man.ac.uk), Mark Muldoon (M.Muldoon@umist.ac.uk) or the seminar secretary (Tel. 0161 275 5800).