A study of spurious currents in finite element based simulations of the incompressible Navier-Stokes equations for two phase flows is presented, based on computations on a circular drop in equilibrium. The interface is accounted for by a level set method. It is shown that a sharp surface tension force, expressed as a line integral along the interface, can give rise to large spurious currents and oscillations in the pressure. If instead a regularized surface tension representation is used, exact force balance at the interface is possible, both for a fully coupled discretization approach as well as for a fractional step projection method. We illustrate that with exact force balance, the spurious currents are of the order of the tolerance of the linear solver. However, the numerical curvature calculation introduces errors, that cause spurious currents. Different ways to extend the curvature from the interface to the whole domain are discussed and investigated. It is shown that the choice of curvature extension has a significant impact on the error in pressure. The impact of using different finite element spaces is also investigated.
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