Anthony Wachs (Departments of Mathematics and Chemical & Biological Engineering, University of British Columbia, Vancouver). Numerical modelling of particle-laden flows: multi-scale, arbitrary particle shape, heat transfer, non-Newtonian.

Particle-laden flows are ubiquitous in environmental, geophysical and engineering processes. The intricate dynamics of these two-phase flows is governed by momentum transfer between the continuous fluid phase and the dispersed particulate phase. When significant temperature differences exist between the fluid and particles and/or chemical reactions take place at the fluid/particle interfaces, the phases also exchange heat and/or mass, respectively. While some multi-phase processes may be successfully modelled at the continuum scale through closure approximations, an increasing number of applications require resolution across scales, e.g. dense suspensions, fluidized beds. Within a multi-scale micro/meso/macro-framework, we develop robust numerical models at the micro and meso scales, based on a Distributed Lagrange Multiplier/Fictitious Domain method and a two-way Euler/Lagrange method, respectively. Collisions between finite size particles are modeled with a Discrete Element Method. We discuss mathematical and computational issues associated to an accurate and reliable modelling of particle-laden flows at the micro and meso scales. We also broaden the scope of applications beyond momentum transfer of spherical particles in a Newtonian fluid towards arbitrary particle shape, heat transfer and particles suspended in a viscoplastic fluid. We also shortly address high performance computing issues related to our massively parallel numerical tools and discuss challenges to efficiently transfer knowledge from small scales to large scales.