Isogeometric analysis of multi-phase flows with surface tension and with application to dynamics of rising bubbles

•An Isogeometric multi-phase flow formulation with surface tension using RBVMS and level-set method is proposed.•Superior accuracy IGA in mean curvature computation is demonstrated.•Comparison of IGA and FEM on level-set convection, mean curvature calculation and bubble rising dynamics is shown.•Merging processes of two bubbles under a free-surface is presented to show the capabilities of the proposed formulation. A novel multi-phase flow formulation using a level-set-based interface-capturing approach is proposed, focusing on addressing numerical challenges associated with the modeling of surface tension. The surface tension is handled through the continuum surface force model. The residual-based variational multiscale (RBVMS) formulation is employed to solve the coupled Navier–Stokes and level-set convection equations. The RBVMS formulation is discretized using either standard low-order finite elements, or Isogeometric Analysis (IGA) based on Non-Uniform Rational B-Splines (NURBS), which are higher-order accurate and smooth. The proposed method is applied to the simulation of 3D bubbles moving in viscous liquids with large density and viscosity ratios representative of common two-phase flow systems. The accuracy of the proposed method is assessed by comparing the results with analytical solutions, experimental data, and computational results, reported in the literature. In all cases IGA showed superior performance to standard finite elements; this superiority is attributed to the higher-order accuracy of IGA and its ability to directly and accurately compute, using smooth NURBS functions, the curvature term, which is a key ingredient the surface tension formulation. For single-bubble rising problems, the proposed approach produced accurate predictions of the terminal bubble shape, velocity and Reynolds number. The advanced nature of the new multi-phase flow formulation is demonstrated with a simulation of merging of two bubbles in the presence of a deforming free-surface.