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:
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
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.
- 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.
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:
- Mathematics for
industry (~17 Mb) and
Careers in industry for
mathematicians, PIMS Graduate Summit, Jasper, AB, 26-28
- Immersed boundary method:
Recent developments in analysis, algorithms and applications,
ICIAM Congress, Beijing, China, 10 August 2015.
- Immersed boundary
simulations of gravitational settling, MIT Conference on
Computational Fluid and Solid Mechanics, Boston, MA, 12 June
- Sap flow and heat
transport in trees, 4th International Conference on Porous
Media and its Applications in Science, Engineering and
Industry, Potsdam, Germany, 21 June 2012.
- Mathematical modelling of
concrete, CAIMS Annual Meeting, St. John's, NL, 18-20
- Mathematical modelling of
atmospheric contaminant dispersion, University of Alberta, 22
- Math and the Olympics, Taste
of Pi seminar (to high school students), Simon Fraser University,
10 April 2010.
- Porous immersed
boundaries, Duke University, 23 March 2009.
- On the mesh relaxation time
in the moving mesh method, Adaptivity and Beyond:
Computational Methods for Solving Differential Equations,
Vancouver, BC, 3-6 August 2005.
- Simulation of transport
processes in PEM fuel cells, International Conference on
Scientific Computing, Nanjing, China, 4-8 June 2005.
- Parametric resonance in
immersed elastic boundaries, University of Washington, 2
I gratefully acknowledge the financial support for these research
projects provided by the following sponsors:
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Last modified: Thu Dec 7 2017