A numerical study of the long-time evolution of two immiscible fluids
shearing past one another will be presented. The fluids are
incompressible and the interface between the bulk phases is subjected to
surface tension. It is known that in 2D inviscid flows of this type
surface tension can lead to the finite-time reconnection of the sheet.
Can such a topological singularity still occur in the viscous
counterpart with high Reynolds number? To investigate this question we
will introduce a novel fully adaptive non-stiff method to solve the 2D
Navier-Stokes equations in the presence of a free boundary. The
numerical methodology, anchored in the immersed boundary method,
combines dynamically adaptive mesh refinements on the Eulerian grid with
moving meshes on the Lagrangian (immersed boundary) grid. This dynamic
adaption, crucial to accurately resolve the flow, is performed
in concert with a predictor-corrector strategy to successfully treat the
well-known numerical difficulties associated with surface tension.
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