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An accurate adaptive solver for surface-tension-driven interfacial flows

Abstract : A method combining an adaptive quad/octree spatial discretisation, geometrical Volume-Of-Fluid interface representation, balanced-force continuum-surface-force surface tension formulation and height-function curvature estimation is presented. The extension of these methods to the quad/octree discretisation allows adaptive variable resolution along the interface and is described in detail. The method is shown to recover exact equilibrium (to machine accuracy) between surface-tension and pressure gradient in the case of a stationary droplet, irrespective of viscosity and spatial resolution. Accurate solutions are obtained for the classical test case of capillary wave oscillations. An application to the capillary breakup of a jet of water in air further illustrates the accuracy and efficiency of the method. The source code of the implementation is freely available as part of the Gerris flow solver. 1
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Stéphane Popinet. An accurate adaptive solver for surface-tension-driven interfacial flows. Journal of Computational Physics, Elsevier, 2009, 228, pp.5838 - 5866. ⟨10.1016/j.jcp.2009.04.042⟩. ⟨hal-01445445⟩

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