Computational Studies of Convective Transport in Evolving Domains

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This program will develop a computational algorithm to calculate the coupled energy and hydrodynamic equations for domains with changing boundary conditions such as those experienced in problems involving solidification, deposition, and dissolution. The new algorithm will attempt to combine the features of the boundary integral method with the spectral element method to achieve high accuracy and efficiency while remaining sufficiently flexible to handle the changing geometries. Two formulations will be treated: One involving very slow flow using the Stokes approximation and employing the boundary integral method alone, and the second involving natural convection using the Navier-Stokes equations and the combined boundary element-spectral element approach. With the successful conclusion of this project, the tools will be available to study the most general convective heat transfer processes for evolving systems. This ability will lead to a better understanding of such phenomena as solidification, dissolution, etching, and corrosion.