A face-oriented stabilized Nitsche-type extended variational multiscale method for incompressible two-phase flow

Summary A novel extended variational multiscale method for incompressible two‐phase flow is proposed. In this approach, the level‐set method, which allows for accurately representing complex interface evolutions, is combined with an extended finite element method for the fluid field. Sharp representation of the discontinuities at the interface related to surface‐tension effects and large material–parameter ratios are enabled by this approach. To capture the discontinuities, jump enrichments are applied for both velocity and pressure field. Nitsche's method is then used to weakly impose the continuity of the velocity field. For a stable formulation on the entire domain, residual‐based variational multiscale terms are supported by appropriate face‐oriented ghost‐penalty and fluid stabilization terms in the region of enriched elements. Both face‐oriented terms and interfacial terms related to Nitsche's method are introduced such that it is accounted for viscous‐dominated and convection‐dominated transient flows. As a result, stability and well‐conditioned systems are guaranteed independent of the interface location. The proposed method is applied to four numerical examples of increasing complexity: two‐dimensional Rayleigh–Taylor instabilities, a two‐dimensional collapsing water column, three‐dimensional rising bubbles, and a three‐dimensional bubble coalescence. Excellent agreement with either analytical solutions or numerical and experimental reference data as well as robustness for all flow regimes is demonstrated for all examples. Copyright © 2014 John Wiley & Sons, Ltd.