LAUSR

Abstract We present novel test cases to study the effect of density ratio on free and forced capillary oscillations at an interface separating two immiscible, inviscid fluids. Using these tests, results obtained from two in-house developed, Volume of Fluid (VoF) based codes for solving the incompressible Euler equations with surface tension, are reported. The first solver (FSS: free surface solver) ignores the dynamics of the lighter phase solving only for the denser phase, explicitly accounting for free surface boundary conditions using the approach presented in Malan et al. (2015). The second is an interfacial solver which implements the one-fluid algorithm (OFS: one fluid solver) for simulating two-phase flows. We present four test cases involving inviscid, free and parametrically forced, capillary oscillations on Cartesian and circular base states. Explicit closed form analytical solutions in the linearised limit are presented for each case. It is found that for small value of the nonlinearity parameter (ϵ or ϵaz  50 − 10 3 , the FSS shows excellent agreement with linearised analytical predictions. For lower values of density ratio approaching  ∼ 10 and below, the FSS results display substantial disagreement with those obtained from the OFS as well as with analytical predictions. At large density ratios ( ∼ 103) (and larger values of ϵ or ϵaz), the FSS shows better accuracy over longer times, when compared to the OFS, partly due to less numerical dissipation. The analytical results presented here add to the repository of test cases in the two-phase CFD literature and are expected to be useful for validating numerical models for surface tension. The comparison of the OFS with the FSS also provides useful rule-of-thumb estimates for choosing between speed (FSS) and accuracy (OFS) in numerical computations of capillary, interfacial flows.