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A diffuse-interface model for axisymmetric immiscible two-phase flow. (English) Zbl 1299.76043
Summary: A diffuse-interface model is considered for solving axisymmetric immiscible two-phase flow with surface tension. The Navier-Stokes (NS) equations are modified by the addition of a continuum forcing. The interface between the two fluids is considered as the half level set of a mass concentration c, which is governed by the Cahn-Hilliard (CH) equation – a fourth order, degenerate, nonlinear parabolic diffusion equation. In this work, we develop a nonlinear multigrid method to solve the CH equation with degenerate mobility and couple this to a projection method for the incompressible NS equations. The diffuse-interface method can deal with topological transitions such as breakup and coalescence smoothly without ad hoc ‘cut and connect’ or other artificial procedures. We present results for Rayleigh’s capillary instability up to forming satellite drops. The results agree well with the linear stability theory.

76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
76T99 Multiphase and multicomponent flows
Full Text: DOI
[1] Atkinson, K., The numerical solution of integral equations of the second kind, (1997), Cambridge University Press
[2] R.T. Lynch, J.J. Reis, Haar transform image conding, in: Proceedings of the National Telecommunications Conference, Dallas, TX, 1976, pp. 44.3-1-44.3
[3] Maleknejad, K.; Mirzaee, F., Numerical solution of linear Fredholm integral equations system by rationalized Haar functions method, Int. J. comput. math, 8, 11, 1397-1405, (2003) · Zbl 1045.65115
[4] Ohkita, M.; Kobayashi, Y., An application of rationalized Haar functions to solution of linear differential equations, IEEE trans. circuit syst, 9, 853-862, (1986) · Zbl 0613.65072
[5] M. Razzaghi, J. Nazarzadeh, Walsh functions, Wiley Encyclopedia of Electrical and Electronics Engineering, vol. 23, 1999, pp. 429-440
[6] J.J. Reis, R.T. Lynch, J. Butman, Adaptive Haar transform video bandwidth reduction system for RPV’s, in: Proceedings of Annual Meeting of Society of Photo-Optic Institute of Engineering (SPIE), San Dieago, CA, 1976, pp. 24-35
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