A DNS criterion for the simulation of interfacial instabilities using the one-fluid approach

In this work, we investigate the impact of regularization errors introduced by the one-fluid model on the onset and growth of interfacial instabilities of parallel flows. A first-order error model is derived from the continuum equations and validated against the full solution of the linear problem for the regularized equations in the context of the Rayleigh-Taylor instability. The analyses allow us to clarify the conditions upon which the values of the growthrate obtained are governed by physical effects and not by the regularization method itself. For sufficiently small regularization thicknesses, the results from the one-fluid model converge to the physical solution with first-order accuracy in ∆, while for large values of ∆ regularization errors control the response of the instability. The theoretical predictions are validated through numerical simulations showing the importance of the one-fluid formulation on the accuracy of the results obtained with standard numerical methods used for the solution of the two-phase Navier-Stokes equations. The results emphasize the effect of regularization errors in CFD solvers resorting to one-fluid models, providing a theoretical quantification of the accuracy of the numerical results as a function of the gridsize.