Modelling and Simulation of Fluid Flows with Industrial Applications

John Stockie

Abstract

This project centres around the application of advanced mathematical and computational techniques to the study of complex fluid flows, motivated largely by industrial applications. The complexity in the flow arises from the presence of nonlinear coupling between the flow and some other physical process, such as when a fluid interacts with a deformable elastic interface, or capillary forces drive the flow through a porous medium, or social and behavioural forces affect an individual's motion in a group of pedestrians. These "multi-physics" phenomena give rise to challenging mathematical problems and also typically require specialized algorithms for their numerical solution. Some concrete examples of the problems under study are: (1) Parallel simulations of suspension flows, such as flexible wood pulp fibersin the paper-making industry (with J. Wiens). Here, we make use of a parallelized "immersed boundary" code that permits simulations of interaction between up to thousands of individual deforming particles. (2) Fluid dynamics and self-organized behaviour in flows containing large numbers of swimming marine organisms such as jellyfish, worms or flagellated cells (with S. Mirazimi and T. Chen). Current work involves studying the influence of organism dynamics on the resulting flow properties of these "active suspensions", as well as capturing more realistic swimming dynamics by including the detailed muscle structure into an immersed boundary model. (3) Modelling of sap flow in maple trees, in order to develop a better fundamental understanding of the essential bio-physical mechanisms underlying the generation of elevated stem pressure during the maple harvest season (with M. Zarrinderakht and B. Janbek). This project is part of a collaboration with the maple syrup industry that aims to assist producers in not only optimizing syrup production but also developing informed strategies for responding to regional climate changes affecting eastern North American forests. Although these problems seem extremely diverse in nature, they are unified by the underlying theme of multi-physics (fluid dynamics coupled with other physical and biological processes) occurring on multiple scales (widely-varying spatial scales ranging from microscopic to macroscopic). There is also a unifying computational theme in our work through the use of finite volume methods for solving the governing time-dependent PDEs and use of high performance computing algorithms. The interdisciplinary aspects of these projects are extensive, involving connections with mechanical engineers (project #1), zoologists (project #2), plant biologists (project #3), and computer scientists (projects #1 and 2). This research is supported by NSERC, Mitacs and the North American Maple Syrup Council.