An accurate adaptive solver for surface-tension-driven interfacial flows. (English) Zbl 1280.76020
Summary: 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.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76D45 | Capillarity (surface tension) for incompressible viscous fluids |
Keywords:
adaptive mesh refinement; surface-tension; Navier-Stokes equations; height-function; parasitic currents; volume-of-fluid; octreeReferences:
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