- Thomas P. Witelski, Computing finite-time singularities in interfacial flows,
Modern Methods in Scientific Computing and Applications (NATO ASI series II proceedings, volume 75), 2002, pp. 451-487.
(last updated on 2003/02/27)
Finite-time singularities occuring in mathematical models of free-surface flows indicate that important qualitative changes are taking place; for problems in solid and fluid mechanics this includes topological transitions -- blow-up, and pinch-off. For many problems, the dynamics leading to the formation of such singularities are described by self-similar solutions of the governing nonlinear partial differential equations. We present an analytical and numerical study of these similarity solutions and discuss their stability.