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Thursday, Nov 14, 9:30 am in MTH 3206, University of Maryland, College Park

Computing interfacial flows with surface tension

Prof. Michael Shelley

Courant Institute, New York University, New York

Many fundamental problems in fluid mechanics and materials science concern the dynamics of interfaces mediated by surface tension or energy -- pattern and singularity formation are two important examples. For a computational scientist, surface tension leads to severe time-step constraints that are both nonlinear and dynamical in nature. I will discuss an approach, based on a "Small-Scale Decomposition", that for a class of such problems circumvents these difficulties. By reposing the dynamics in intrinsic coordinates, and analyzing the equations of motion at small length-scales, the contribution of the surface tension can be isolated as a linear term that can be treated implicitly, which leads to efficient and accurate time-stepping methods. These methods are illustrated through computational studies of the effect of surface tension on the Kelvin-Helmholtz instability, pattern formation problems in the Hele-Shaw cell, and others.