Hokkaido Mathematical Journal

TABATA M.,

Finite element schemes based on energy-stable approximation for two-fluid flow problems with surface tension.

Hokkaido Mathematical Journal, 36 (2007) pp.875-890

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Abstract

For two-fluid flow problems with surface tension we present finite element schemes based on energy-stable approximation. In the case of no surface tension, those schemes are unconditionally stable in the energy-sense. When there exists surface tension, they are proved to be stable if a quantity remains bounded in the computation. Some numerical results of rising bubble problems show the robustness and applicability of these schemes.

MSC(Primary)76D45
MSC(Secondary)65M12, 76M10
Uncontrolled Keywordsfinite element method, two-fluid flow problems, energy-stability, Navier-Stokes equations, surface tension