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Stability of a numerical algorithm for gas bubble modelling
Author(s) -
Barkhudarov M. R.,
Chin S. B.
Publication year - 1994
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650190505
Subject(s) - volume of fluid method , instability , bubble , mechanics , discretization , computational fluid dynamics , oscillation (cell signaling) , physics , numerical stability , free surface , flow (mathematics) , numerical analysis , classical mechanics , mathematics , mathematical analysis , chemistry , biochemistry
A free‐surface‐tracking algorithm based on the SOLA‐VOF method is analysed for numerical stability when modelling gas bubble evolution in a fluid. It is shown that an instability can arise from the fact that the bubble pressure varies with its volume. A time step stability criterion is introduced which is a function of the natural oscillation period but does not depend on the mesh size. This dependence suggests that the instability is likely to arise in the case of a general motion of a bubble, especially if break‐up occurs. The effect is shown using linear Fourier analysis of the discretized equation for radial bubble oscillation and demonstrated numerically using a CFD code FLOW‐3D. One‐ and three‐dimensional situations are considered: a bubble in a fluid bounded by two concentric surfaces and a bubble floating in a fluid chamber with and without gravity. In cases where no analytical solution is available, a numerical method for the stability time step limit calculation is suggested based on finding the natural oscillation frequency. The nature of the instability suggests that it can be a feature of any numerical algorithm which models transient fluid flow with a free surface.