Research Interests:
My research focuses on solving problems in fluid dynamics
through the use of mathematical analysis and numerical methods. My
current research activities can be broadly classified into four areas:
- 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. Applications include hydrogen fuel cells, traffic flow, and
reactive transport in concrete.
- Fluid-structure
interaction:
Applying the immersed boundary method to simulate the interaction
of an elastic, deformable interface with an
incompressible fluid flow. I am motivated by a number of
applications from biology and engineering such as pulp fiber
suspensions, biofilm dynamics, and swimming of marine organisms.
- Porous media flow:
Studying moisture transport in porous media that obeys nonlinear
diffusion equations arising 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
and cell membranes.
- Scientific
computation: A major part 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 do
dabble in other methods . . .
Some Recent (and not-so-recent) Talks:
- Mathematical modelling of
concrete, CAIMS Annual Meeting, St. John's, NL, 18-20
July 2010.
- Mathematical modelling of
atmospheric contaminant dispersion, University of Alberta, 22
June 2010.
- 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
November 2004.
My Team:
I have been extremely fortunate to have worked with a number of talented
students and postdoctoral fellows in recent years. Here are my
current students . . .
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| Sudeshna |
Jeff |
Bebart |
Will |
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| Haowen |
Maurizio |
Bamdad |
. . . and some information about what they are doing . . .
- Sudeshna Ghosh (PhD,
2007-): Simulating biofilm dynamics and deformation using the
immersed boundary method.
Received the President's PhD Research Stipend
in 2010.
- Jeffrey Wiens:
- MSc (2009-2011): Kinematic wave and cellular automaton models for traffic flow.
- PhD (2011-): Immersed boundary method
Holds an NSERC Postgraduate Scholarship (2011-2013).
- Haowen Fang (MSc, 2010-):
Immersed boundary simulations of swimming jellyfish.
- Bebart Janbek (MSc, 2010-):
Mathematical modelling of sap flow and heat transport in
trees.
- Maurizio Ceseri (postdoc, 2011-):
Porous media flow.
Holder of an
Mprime Postdoctoral
Fellowship.
- Will Ko (PhD, 2011-):
Parametric resonance in 3D immersed elastic boundaries.
- Bamdad Hosseini (MSc, 2011-):
Finite volume simulations of atmospheric contaminant transport.
Past students & post-doctoral fellows:
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| Reanne (MSc) |
Samir (BEng) |
Michael (Postdoc) |
Huijing (BSc) |
Amit (BSc/MSc) |
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| Badri (MSc) |
Evgeniy (BSc) |
Wentao (BSc) |
Enkeleida (MSc) |
- Reanne Bowlby (MSc, 2009-2011):
A Roe solver for a multi-class traffic flow model.
- Samir Jain (undergrad
from IIT Bombay, summer 2011):
Nonequilibrium models for gravity driven fingering instabilities.
Funded by a
MITACS Globalink scholarship.
- Eric Cai (undergrad, summer 2011):
A multiscale model for the PEM fuel cell catalyst layer.
-
Michael Chapwanya (Postdoc, 2006-2009): fingering instabilities in
porous media; coupled flow and reaction chemistry in
concrete.
Currently an
Assistant Professor at University of Pretoria.
- Nathan Nastili (BSc math major project, 2010):
Investigation of motion camouflage using numerical
simulation.
- Huijing Wang
(undergraduate, 2009-2010): Mathematics of sport.
- Kevin Lorimer (NSERC undergraduate research assistant, summer 2009):
Porous
medium model of sap flow in trees.
- Amit Chandra
(undergraduate research assistant from IIT Kanpur, summer 2009):
Modelling of heat transport in tree trunks.
-
Badri Ratnam (MSc, 2006-2008): Porous immersed
boundaries.
Currently a PhD student in Mechanical Engineering, University
of Waterloo.
-
Evgeniy Lebed (undergraduate research assistant, summer 2006):
Numerical simulations of pollutant dispersion.
Currently a PhD student in Engineering Science, SFU.
-
Wentao Liu (undergraduate research assistant, summer 2006):
A model for clogging in reactive porous media.
Currently a PhD student in Applied Mathematics, University of
Waterloo.
- Xin (Simon) Wang (MSc, 2004-2006):
An analytical
and numerical study of parametric resonance in immersed elastic
boundaries.
Currently a Quantitative Analyst, FINCAD Analytics.
- Enkeleida Lushi (MSc intern with Teck Cominco
Ltd., 2005):
Dispersion and deposition of particulate matter from stacks.
Currently a PhD student at the Courant Institute.
- Akeel Shah (Postdoc, 2004-2006).
Currently a Lecturer in Engineering Sciences at University of
Southampton.
- Pengtao
Sun (Postdoc, 2004-2005).
Currently an Assistant
Professor at University of Nevada Las Vegas.
- Mohammad Kermani
(Postdoc, Mechanical Engineering, UNB,
2000-2003).
Currently an Assistant Professor of Mechanical Engineering,
Amir Kabir University, Tehran, Iran.
Support:
I want to gratefully acknowledge financial support for these research
projects from:
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Last modified: Thu May 3 2012
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