Abstract
A balanced-force control volume finite element method is presented for three-dimensional interfacial flows with surface tension on adaptive anisotropic unstructured meshes. A new balanced-force algorithm for the continuum surface tension model on unstructured meshes is proposed within an interface capturing framework based on the volume of fluid method, which ensures that the surface tension force and the resulting pressure gradient are exactly balanced. Two approaches are developed for accurate curvature approximation based on the volume fraction on unstructured meshes. The numerical framework also features an anisotropic adaptive mesh algorithm, which can modify unstructured meshes to better represent the underlying physics of interfacial problems and reduce computational effort without sacrificing accuracy. The numerical framework is validated with several benchmark problems for interface advection, surface tension test for equilibrium droplet, and dynamic fluid flow problems (fluid films, bubbles and droplets) in two and three dimensions.
Highlights
Interfacial flows with surface tension appear in many engineering applications, e.g. micro-fluidics, oil-and-gas transportation systems, geophysical flows and nuclear reactors
In this paper a new balanced-force control volume finite element method with adaptive anisotropic unstructured meshes has been presented for interfacial flows with surface tension
A forcebalanced algorithm for the surface tension implementation has been presented, with two different approaches to accurately estimate the curvature for a fully unstructured mesh, minimising the spurious velocities often found in such flow simulations
Summary
Interfacial flows with surface tension appear in many engineering applications, e.g. micro-fluidics, oil-and-gas transportation systems, geophysical flows and nuclear reactors. The balanced-force algorithm for surface tension model has become popular in structured Cartesian grids due to the use of a height function for curvature calculation in the volume of fluid method [22] and the level set function in the CLSVOF method [23]. It has been extended for adaptive mesh refinement for structured Cartesian grids [13].
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