Current projects

I am always open to new problems and ideas. Graduate and undergraduate students
interested in one of the projects or having in mind a topic of their own are welcome
to contact me.

Projects in green are open to new students.
Projects in purple are currently worked upon.
Projects in black are complete.

Landfill gas collection

A landfill is an underground cavity, where anaerobic decay processes produce usable gas.
Practices of gas collection and quantification of the amount of available gas are important
to a successful operation, both from the engineering and environmental point of view.
These projects are in collaboration with local industry.

† Modelling turbulence in a landfill gas network

† Landfill gas flow: effects of heterogeneity in medium permeability

† Controlling surface flux in landfill-well coupled flow in perforated horizontal wells

† Landfill-well flow coupling in perforated horizontal wells { Seth }

† Modelling turbulence in landfill gas flow: ingress into a horizontal well { Abhishek }

† Simulation of planar flow for multiple perforated horizontal wells { Damian, Seth }

† Evaluation of a network flow model for weakly compressible flow at a DLC landfill { Alyssa }

† User interface for flow solution in horizontal wells { Oamar }

† Simulation of planar flow for a perforated horizontal well { Damian }

† User interface for flow solution in a network { Oamar }

† 1D and 2D flow solution for perforated horizontal wells

† Visualisation of flow solution in a network { Alexis }

† Concentric pipes wellhead to replace an orifice flowmeter

† Accurate flow rate estimation in a landfill well with an orifice plate

River life subject to dam operation

Fish living in rivers, where dams have been built, experience water recessions when the
dam discharge is limited or stopped. Better understanding of the dynamics of the river and
fish spawning grounds will help control the impact of the dam operation in this ecosystem.
These projects concern the Columbia and Kootenay Rivers in Southern British Columbia
and are in collaboration with the local industry.

† Visualisation of flow in Columbia-Kootenay Rivers confluence

† Modelling fish egg hatching

† River flow solution with realistic riverbed data { Vishnu }

† Mesh refining for river flow solution with realistic riverbed data { Michelle, Tess, Merieme }

Special types of diffusion in Gierer-Meinhardt model

The Gierer-Meinhardt model is a paradigmatic reaction — diffusion system
that possesses fully non-linear solutions in the form of spikes. The spikes drift,
change heights and interact with each other. These projects explore spike
pattern evolution and relate the observed phenomena to diffusion peculiarities
in cell biology, geology, chemistry and other areas of science.

† Numerical soluton for Gierer-Meinhardt reaction--diffusion model with sub-diffusion

† Non-local drifting eigenvalue problem

† Bifurcations in reduced Gierer-Meinhardt system with and without anomalies

† Continuous variation of kinetic exponents { Sam }

† Continuously varying anomaly index with sub-diffusion

† Anomalous diffusion on surfaces {Khazhakanush}

† Accurate spike shape computation with Lévy flights (fractional Laplacian) { Kyle }

† Asymmetric spike constellations with time dependent diffusivity and anomaly exponent

† Spike drift with time dependent diffusivity (integer derivative)

† Spike drift with time dependent anomaly index (fractional derivative)

† Bifurcation delay with sub-diffusion