Graduate Thesis Or Dissertation

Interpolation Schemes for Two Dimensional Flow with Applications

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  • In this thesis we study a numerical analysis problem motivated by the need to simulate an event such as an oil spill in a deep water environment. Numerical simulation can help to mitigate the disastrous effects of such events by aiding the management of risk assessment and recovery efforts. However, an accurate simulation of the physical processes involved in the oil spill requires highly sophisticated and accurate numerical models. Equally important is that such a simulation needs to have accurate hydrodynamics data which may either come from observations or from some other computation simulator which predicts the flow of water near the area involved in the spill. In this thesis we discuss a particular technical problem involved with proper interpretation and use of hydrodynamic data. In numerical analysis, it is often necessary to approximate a given function or interpolate from discrete data. One may have discrete data from sampling or due to solving a partial differential equation at discrete points but require information between the nodes. The motivation for this investigation of interpolation on scattered data is to recreate a smooth function from hydrodynamic data. In other words, we will discuss algorithms that provide a smooth field from given discrete data. The Blowout and Spill Occurrence Model (BLOSOM) developed by the Department of Energy's National Energy Technology Laboratory models hydrocarbon release events from the sea floor to the final fate of the oil. The generated smooth field could be used in such a model, potentially improving the predicted outcomes. The errors in prediction of the fate of oil arise, of course, from multiple sources. We study the errors due to the interpolation scheme applied. One particular aspect is also associated with whether the interpolated velocities have non-physical characteristics, specifically whether the interpolated velocities are conservative, given that the true velocities are. Ultimately, we achieve good results using radial basis function interpolation, but the scale of the problem needs to be considered further, as the large data sets in use may make the problem intractable.
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