Mittelman The main emphasis of the project is the development of computational techniques, their implementation on advanced computer architectures, and their verification and utilization on nontrivial application problems of current interest. The area of research is capillary flows and surfaces. The investigator analyzes in detail static capillary surfaces in singular cases and searches for new surfaces with certain properties such as symmetry. A sophisticated computer code for partial differential equations, to which he has contributed (PLTMG), is generalized to the Navier-Stokes equations. Flows in which capillary effects are prominent are analyzed, including mixed buoyant-thermocapillary convection as it occurs in crystal growth and welding. The force that shapes waterdrops, lets nutrients rise to treetops, and is governing the flow of contaminated groundwater is called capillarity. While it is important in our terrestrial environment, it becomes dominant in the microgravity regime of space. Many environmental but also manufacturing issues, such as crystal growth and welding, will greatly benefit from a better understanding of the effects of capillarity. With state- of-the-art computational techniques and resources the investigator studies both the shape of liquid surfaces and the flow inside liquids. Challenging problems of current interest serve as paradigms and applications for the work.
