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.

† The mysterious pi/4 singularity: anisotropic non-linear diffusion in generalised curvilinear coordinates

† Regularity corridors in anisotropic porous medium flow: power law dependence on permeability

† Turbulence near ingress to landfill wells: optimisation of collection efficiency

† Turbulence near ingress to landfill wells: unified analytical approach

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

† Landfill gas flow: effects of heterogeneity in medium permeability { }

† Visualisation of anisotropic flow in a porous medium: spherical coordinates { Piyush }

† Exact solutions to non-linear diffusion equation with variable permeability: elliptic coordinates { Kate }

† Exact solutions to non-linear diffusion equation with variable permeability: spherical coordinates { Mahendhar }

† Singularities in weakly compressible flow through a porous medium { Kate, Mahendhar }

† User interface for flow solution in landfill wells { Piyush }

† Modelling turbulence in landfill gas flow: ingress into a vertical well { Prashanna, Abhishek }

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

† Visualisation of ideal gas flow in a porous medium: broken axial symmetry { Michelle }

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

† Unsteady landfill gas flow { Seth }

† Exact solutions to steady flow in a porous medium with variable permeability

† 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

† River flow solution with realistic riverbed data { Vishnu }

† Modelling heat transfer for fish egg hatching { Mohammed }

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


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

† Continuously varying anomaly index with sub-diffusion

† Continuous variation of kinetic exponents { Sam }

† Numerical simulation of anomalous reaction-diffusion systems { Ying Hung, Kate }

† 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