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A novel finite element framework is proposed for the numerical simulation oftwo phase flows with surface tension. The Level-Set (LS) method with piece-wisequadratic (P2) interpolation for the liquid-gas interface is used in order toreach higher-order convergence rates in regions with smooth interface. Abalanced-force implementation of the continuum surface force model is used totake into account the surface tension and to solve static problems asaccurately as possible. Given that this requires a balance between thediscretization used for the LS function, and that used for the pressure field,an equal-order P2/P2/P2 scheme is proposed for the Navier-Stokes and LSadvection equations, which are strongly coupled with each other. This fullyimplicit formulation is stabilized using the residual-based variationalmultiscale framework. In order to improve the accuracy and obtain optimalconvergence rates with a minimum number of elements, an anisotropic meshadaption method is proposed where the unstructured mesh is kept as fine aspossible close to the zero iso-value of the P2 LS function. Elements areautomatically stretched in regions with flat interface in order to keep thecomplexity fixed during the simulation. The accuracy and efficiency of thisapproach are demonstrated for two and three dimensional simulations of a risingbubble.

A higher-order finite element method with unstructured anisotropic mesh adaption for two phase flows with surface tension