Adaptive Algorithm and Mesh Refinement

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This is a Minority Career Advancement Award. The research is directed toward the problem of manufacturing techniques used to miniaturize electronic components. These techniques have recently been applied to the construction of microscopic mechanical components. Devices using such components often include a gas flow as part of their design. However, the conventional methods for simulating gas flows are not accurate when applied to miniaturized systems. Instead one must perform calculations that track the motion of individual gas molecules. A major difficulty with performing numerical calculations that track individual particles is that they are extremely time-consuming, even on a modern supercomputer. This is especially true if the entire device is large but contains a crucial component that is small. For example, in a computer disk drive is relatively large (about the size of an ant) but the air flow that supports the read/write head above the spinning platter passes through a gap that is roughly one millionth of an inch wide (about the wavelength of visible light). The goal is to efficiently simulate microscopic flows that exist as part of a macroscopic device by combining particle calculations and traditional hydrodynamic computations into a hybrid computer program. Only the regions that require a particle description are calculated using particles while in the larger volume the equations for pressure, temperature, etc. are solved. The end result of this program will be a composite scheme that will permit the solution to flow problems that cannot be effectively computed by any single technique.