Telescopic Time-Scale Bridging for Modeling Dispersion in Rapidly Oscillating Flows

Analytical solution of dispersion in rapidly oscillating flows becomes infeasible in complex geometries. Simulation over long durations can be prohibitively expensive when there is a wide separation between the oscillation and dispersion time scales. Here, we present a methodology based on an implicit envelope-tracking scheme coupled with telescopic projections. A test problem, with a known analytical solution, was simulated, and the effect of Péclet number on the dispersivities was investigated. The solution was unaffected by the time steps for telescopic projections while increasing Péclet numbers introduced errors. The error was found to decrease with mesh refinement, but a small inherent error was observed. The method was also applied to a practical problem of interest to us: drug dispersion due to sloshing in the vitreous humor of the eye. Relative to single-scale solution, the method, when applied to the vitreous sloshing problem, produced speedup values of up to 100. VC 2011 American Institute of Chemical Engineers AIChE J, 58: 1987–1997, 2012