High accuracy computational methods for materials science and multiphase flow applications

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My research expertise is in mathematical modelling and scientific computation. This combination of skills allows me to contribute to diverse applications. Modelling is the process in which a phenomena of interest is described approximately by mathematical equations. Usually such equations are too complex to solve with pen and paper and must be approximated numerically (scientific computation). This process allows some engineering development work (such as airplane design) to be done with computer simulation, which is faster and less expensive that experimental trial and error and can lead to more optimal designs. This process can also be used to extrapolate outcomes from limited data, such as weather forecasting or predicting pollutant dispersal. Collaboration with experimentalists and application experts is needed to formulate and validate the models. My research is strongly driven by applications. I would like to pursue two main research areas in the next five years. One involves pore formation at the nanoscale in functionalized polymer materials that are used for example in hydrogen fuel cell membranes. I have recently developed a fast and accurate numerical framework for models of this type of phenomena that I would like to further investigate and improve. The second area is in models of multi-phase flow in porous media. These models arise in two applications I am interested in: site remediation (removing unwanted contaminants from soil by flushing the area with water) and water management in fuel cells (liquid water movement in porous electrodes). The models of these phenomena have a mathematical and computational difficulty at boundaries to one phase flow that I would like to investigate. Resolving these difficulties would lead to more accurate computations of existing models and perhaps point the direction to improving the models so that they better describe the phenomena of interest. This work will be done in an abstract framework and the results can also be used for other applications with models with similar structure. Graduate students working with me on these projects can easily proceed to academic or industrial employment.