Research Interests:

My research focuses on solving problems in fluid dynamics through the use of mathematical analysis and numerical methods. Most of the problems I study are inspired by fluid flows arising from applications in either engineering or biology. My current research activities can be broadly classified into four areas:

  1. Industrial mathematics: Mathematical modelling of real problems from industry using of partial differential equations (PDEs) and then employing analytical and computational approaches to gain insight into their solution. Current projects include studies of atmospheric pollutant transport, sap flow in maple trees, and traffic flow.

  2. Fluid-structure interaction: Applying the immersed boundary method to simulate the interaction of an elastic deformable interface or structure with an incompressible fluid flow. I am motivated by diverse applications from biology and engineering such as pulp fiber suspensions, biofilm dynamics, and swimming marine organisms.

  3. Porous media flow: Studying moisture transport in porous media that gives rise to nonlinear diffusion equations from the application of Darcy's Law. I am working on a diverse range of applications including water uptake in concrete, gravity-driven fingering instabilities in soil, sap flow in trees, and osmotic transport through vesicle or cell membranes.

  4. Scientific computation: A major component of all projects mentioned above is the development of accurate and efficient numerical methods for solving systems of nonlinear (and mostly parabolic) PDEs. My expertise is primarily in finite volume schemes, although I am known to dabble in other methods . . .

Some Recent (and Not-so-recent) Talks:

Support:

I gratefully acknowledge the financial support for these research projects provided by the following sponsors:
AFMnet NCE Alexander von Humboldt Stiftung Mprime NCE North American Maple Syrup Council NSERC Teck Metals
Ballard Power Systems Mitacs SFU

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