Computing interfacial flows of viscous fluids

We present a novel technique for solving for the flow of a viscous multi-fluid system in which interfaces are present. The Navier-Stokes equations are used in their exact form, without the need for phase-field approximations. A Boussinesq-type approach is invoked, in which the component fluids of differing densities are represented by a single fluid in which the density changes smoothly but rapidly across each narrow interfacial zone. This formulation is illustrated in detail for classical planar Rayleigh-Taylor flow containing two horizontal layers of fluid, in which the upper fluid has greater density. The interface be-tween the fluids is therefore unstable and overturns as time progresses. The results of this new approach are compared against the predictions of classical Boussinesq theory and a recent Extended Boussinesq model proposed by the authors. Finally, a comparison with the predictions of a smoothed-particle-hydrodynamics model gives strong support for this new technique.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

A novel technique is presented for solving flow problems of viscous multi-fluid systems with interfaces, utilizing exact Navier-Stokes equations and a Boussinesq-type approach. The technique is illustrated through a case study of classical Rayleigh-Taylor flow and compared with other models, showing strong support for its effectiveness.