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Algorithm Design for Computational Fluid Dynamics, Scientific Visualization, and Image Processing

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Final rept.

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We developed a novel approach to extend the particle level set method to the simulation of as many regions as desired. The various regions can be liquids or gases of any type with differing viscosities, densities, viscoelastic properties, etc. We also proposed techniques for simulating interactions between materials, whether it be simple surface tension forces or more complex chemical reactions with one material converting to another or two materials combining to form a third. When discretizing the underlying Navier-Stokes equations for multiphase flow, an additional difficulty occurs since discretization stencils cross region boundaries naively combining non-smooth or even discontinuous data. Recently, we developed a new coding paradigm that allows one to incorporate physical jump conditions in data on the fly, which is significantly more efficient for multiple regions, especially at triple points or near boundaries with solids. This removes the need for any algorithm changes that might reduce the accuracy of the scheme, and moreover even removes the need for changes to the code itself. Besides this work we have also addressed scalability including methods on octree and Run Length Encoded RLE data structure, as well parallel implementation such as MPI. Other work includes work on fracture.

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  • Numerical Mathematics
  • Fluid Mechanics

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