A balanced-force control volume finite element method for interfacial flows with surface tension using adaptive anisotropic unstructured meshes

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

Conservative and adaptive level-set method for the simulation of two-fluid flows

“…The interfaces of the two bubbles are very well captured and the boundary layers as well as the detachments are automatically detected. Our results agree with the experimental photographs in [49] and the numerical results of [51]. We can see that the evolution of the lower bubble is completely different from the leading one.…”

Bulk advection and interfacial flows in the binary coalescence of surfactant-laden and surfactant-free drops

“…The implementation of capillary/surface tension force in the framework using an unstructured mesh minimises spurious velocities often found in interfacial flows. 23 Finally, use of anisotropic, adaptive unstructured mesh 24 allows the grid resolution to be concentrated in relatively important regions, such as the vicinity of interfaces, while lower resolution can be used in other regions; this leads to a significant gain in computational efficiency without sacrificing accuracy. The numerical framework has been employed to study various multiphase flow problems, 25,26 and the dynamics of three-dimensional bubbles, droplet and liquid films.…”

“…The numerical framework has been employed to study various multiphase flow problems, 25,26 and the dynamics of three-dimensional bubbles, droplet and liquid films. 23,27 In order to carry out the computations, we take the initial shapes of the drops to be spherical, as shown in Fig. 11: we do not account for the fact that the drops are attached to two capillaries as is the case in the experiments (see Fig.…”

Doubly excited pulse waves on thin liquid films flowing down an inclined plane: An experimental and numerical study

“…The framework also features an interface capturing scheme based on a compressive controlvolume advection method [41]. The implementation of capillary forces in this framework using a balanced-force surface tension method on an unstructured mesh minimizes spurious velocities often found in interfacial flows [42]. Finally, use of anisotropic unstructured mesh adaptivity [43] allows the grid resolution to be concentrated in relatively important regions, such as the vicinity of interfaces, while lower resolution can be used in other regions.…”