High accuracy computational methods for materials science and multiphase flow applications

我的研究专长是数学建模和科学计算。这些技能的结合使我能够为不同的应用程序做出贡献。建模是用数学方程近似地描述感兴趣的现象的过程。通常这样的方程太复杂了，用笔和纸来解不出来，必须用数值近似（科学计算）。这个过程允许一些工程开发工作（如飞机设计）通过计算机模拟完成，这比实验试验和错误更快，更便宜，可以产生更优化的设计。这一过程也可用于从有限的数据推断结果，例如天气预报或预测污染物扩散。需要与实验人员和应用专家合作来制定和验证模型。我的研究受到应用程序的强烈推动。在接下来的五年里，我想从事两个主要的研究领域。其中一个涉及纳米级功能化聚合物材料的孔隙形成，例如用于氢燃料电池膜。我最近为这类现象的模型开发了一个快速而准确的数值框架，我想进一步研究和改进。第二个领域是多孔介质中多相流的模型。这些模型出现在我感兴趣的两个应用中：场地修复（通过用水冲洗去除土壤中不需要的污染物）和燃料电池中的水管理（液态水在多孔电极中的运动）。这些现象的模型在我想研究的一相流边界处具有数学和计算上的困难。解决这些困难将导致对现有模型进行更精确的计算，并可能指出改进模型的方向，以便更好地描述感兴趣的现象。这项工作将在一个抽象的框架中完成，结果也可以用于具有类似结构的模型的其他应用程序。与我一起从事这些项目的研究生可以很容易地进入学术或工业就业。

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.