Mathematical fuel cell modelling and computational methods for interface problems

我的研究领域是数学建模和科学计算，并将其应用于氢燃料电池。利用数学模型，我建立了近似描述燃料电池运行的方程。这些方程是近似的，因为并不是细胞内发生的事情的所有方面都可以包括在内。由此产生的方程不能精确求解，但可以使用计算机(科学计算)找到近似解。我们现在有了一个可以在计算机上模拟的燃料电池运行模型。这个模型并不准确。然而，它可以用来研究燃料电池是如何以比实验测试更低的成本工作的。使用计算模型可以更快地完成燃料电池的优化设计。燃料电池可能的故障模式是什么，以及操作对部件公差的容忍度--所有这些都可以通过计算进行建模。对该模型的信心只能通过将其与一些实验测量进行比较来建立。当模型与实验不匹配时，必须修改模型(必须添加更多最初未包括的内容)。对该模型的一些补充涉及到新的数学。我努力从分析的角度更好地理解新术语。如果他们恰当地描述了我想要他们描述的过程，我会努力弄清楚如何有效地计算他们。我特别建议建立聚合物电解质膜氢燃料电池启动的计算模型。当氢被引入电池时，可能会出现在出气口附近出现反向电流的情况。这种电流会降低燃料电池的催化层，是当前设计中燃料电池寿命的主要限制之一。在计算模型中捕捉这种影响将允许对缓解策略进行虚拟(快速和廉价)测试。我的主要数学兴趣是理解多孔介质中空气和水的组合流动模型，并有效地计算近似解。有水的区域和只有空气的区域的分界线称为自由边界。我对一般自由边值问题的计算方法感兴趣。

My research areas are mathematical modelling and scientific computation with application to hydrogen fuel cells. Using mathematical modelling, I develop equations that approximately describe the operating fuel cell. The equations are approximate because not all aspects of what is happening in the cell can be included. The resulting equations cannot be solved precisely, but approximate solutions can be found using computers (scientific computing) . We now have a model of an operating fuel cell that can be simulated on a computer. The model is not exact. However, it can be used to investigate how the fuel cell works less expensively than experimental testing. Optimizing fuel cell designs can be done more quickly using the computational model. What the likely failure modes of the fuel cell are and how tolerant the operation is to component tolerances - all these can be modelled computationally. Confidence in the model is only built by comparing it to some experimental measurements. When the model does not match the experiments, the model must be modified (more things not originally included must be added). Some additions to the model involve new mathematics. I work to understand the new terms better analytically. If they appropriately describe the process I want them to describe, I work to figure out how to compute them efficiently. I propose specifically to develop computational models of the start-up of Polymer Electrolyte Membrane hydrogen fuel cells. As hydrogen is introduced into the cell, a situation can exist where there is a reverse current near the air outlet. This current degrades the fuel cell catalyst layer, and is one of the major limitations of fuel cell lifetime in current designs. Capturing this effect in a computational model would allow virtual (fast and inexpensive) testing of mitigation strategies. My main mathematical interest is in understanding models of combined air and water flow in porous media and efficiently computing approximate solutions. The line dividing areas where there is water and where there is only air is known as a free boundary. I am interested in computational methods for general free boundary value problems.