On the Influence of Finite Element Discretisations on Spurious Velocities in Two-Phase Flows

The influence of continuous and discontinuous pressure approximation on spurious velocities is studied. The spurious velocities may generate in two-phase flows due to approximation errors in the curvature, in the incompressibility constraint, and in the pressure, which exhibits a jump across the interface. It may influence the mass conservation and other geometrical and physical parameters of the flow. In this study we investigate the spurious velocities generated due to the error in the pressure approximation and their influence on the flow dynamics. It is found that the influence of the spurious velocity in different discretisations is less for flows with large capillary number, which relates the viscous force and the surface tension force. Further, the geometrical and physical properties of the flow depend mainly on the mass of the liquid, and thus the mass conservation in each phase is essential to obtain physically reasonable solutions