A diffuse-interface model for axisymmetric immiscible two-phase flow.

*(English)*Zbl 1299.76043Summary: 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.

##### MSC:

76D05 | Navier-Stokes equations for incompressible viscous fluids |

35Q30 | Navier-Stokes equations |

76T99 | Multiphase and multicomponent flows |

##### Keywords:

Rayleigh instability; pinch-off; satellite drops; coalescence; Cahn-Hilliard equation; nonlinear multigrid method
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\textit{J. Kim}, Appl. Math. Comput. 160, No. 2, 589--606 (2005; Zbl 1299.76043)

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