Applied Mathematics is a broad subdiscipline within mathematics, and the theme of my work over the past two decades has been the application and practice of mathematics to fields in engineering and science.  In particular, my
research program centers on the development or implementation of mathematical models in areas of fluid dynamics, interfacial dynamics, porous media flows, electromagnetic energy harnessing, and geothermal energy collection and storage.  In all of  these scientific fields, my research centers on formulating mathematical descriptions of these scenarios, and then using techniques such as nondimensionalization and asymptotic analysis, find effective, simpler mathematical models whose accuracy is known and whose relevance is specialized to a particular experimental or field situation.  These models typically consist of nonlinear partial differential equations, and they are still sufficiently complicated that analytical solutions may not be known in closed form, but simulating them computationally is feasible.  The computational resources needed to solve these simpler models allow for simulation over a wide range of experimental parameters, which can aid significantly in engineering design choices.