Computational and Analytical Problems in Fluid Mechanics

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This project consists of three subprojects on analytical and computational methods in fluid mechanics. Professors Krasny, Borgers and Harabetian will work in collaboration with each other as a group. They will attack the following problems: 1. Computation of vortex sheet evolution. This project is concerned with extending the so-called vortex blob method for computing vortex sheet evolution. One planned application is to determine the structure of the spiral which forms in a periodically perturbed vortex sheet. 2. Fast elliptic solver on locally refined meshes. This research will combine domain decomposition methods with the FAC algorithm developed by McCormick. These methods will be tested on Neumann problems for Laplace's equation on regions arising in fluid dynamics applications. 3. Numerical and analytical problems for systems of conservation laws. Problems with small viscous perturbations, with vanishing viscosity method, and with the incompressible limit of a contact discontinuity are going to be considered. Research performed under this grant will have potential applications to studies of aerodynamics and combustion, and will rely extensively on computational tools related to nonlinear partial differential equations.