ECCOMAS 2024

A Controlled Thickness Volume of Fluid Method for the simulation of Interfacial Flows at High Reynolds Numbers

  • Aknine, Mustapha (Institut Jean Le Rond D'Alembert)
  • Fuster, Daniel (Institut Jean Le Rond D'Alembert)
  • Sultan, Eric (Institut Jean Le Rond D'Alembert)

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The numerical simulation of multiphase flows has been a subject of extensive research up to the present day. Several methodological approaches, including Front Tracking Methods, Level Set methods, and Volume of Fluid (VoF) methods, have been identified as capable of tracking the interface between two fluids with varying precision depending on the specific case in which they are applied. Most of these methods, obtain the solution of the Navier--Stokes equations by defining averaged properties in cells containing an interface by resorting to the so-called one-fluid approach. During our research, we delved into the coupling between the one-fluid model and the VoF method, which is capable of tracing the interface at a sub-grid level, to investigate the impact of numerical errors on the development of instabilities. The standard implementation of the method is shown to have several numerical drawbacks, two of which became the focus of our investigation. The first is its inability to converge to a result for very high Reynolds numbers, regardless of the density ratio. The second limitation relates to challenges in obtaining coherent results for high-density ratios, due to the escalation of numerical errors. In this work, we present a new coupled one-fluid/VOF method, implemented in Basilisk, to address such issues. While preserving the accurate and sharp representation of the interface, the method artificially introduces a density transition layer with a controlled thickness that regularizes the appearance of poorly resolved discontinuities at lengthscales compared to the grid size. The new method shows a significant improvement of the stability and robustness of the code at high Reynolds numbers compared to the standard implementation of the VOF method. In addition, we show that the errors associated with this artificial layer, which compels the density field to be continuous everywhere, can be analytically obtained. The new method is shown to converge to the result of a sharp interface for relatively high Reynolds numbers as well as for high-density ratios preventing the appearance of undesirable numerical artifacts.