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Shapes of liquid drops obtained using symbolic computation. (English) Zbl 1120.76070

Summary: The first aim is to show how two free boundary problems arising from fluid mechanics can be solved with a domain perturbation method. The second aim is to analyse the range of validity of series solutions. The analysis will aim at identifying the location and the nature of singularities characterizing these series. After expansion, the equations obtained are linear, but at each stage the length of the expressions grows exponentially. Herein we implement techniques for automatic generation of hierarchical expression sequences, and we present several tools for reducing the combinatorial blow-up of expressions arising in these two problems.

MSC:

76U05 General theory of rotating fluids
76T10 Liquid-gas two-phase flows, bubbly flows
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
68W30 Symbolic computation and algebraic computation
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