Simulating interfacial flows: a farewell to planes
arxiv(2024)
摘要
Over the past decades, the volume-of-fluid (VOF) method has been the method
of choice for simulating atomization processes, owing to its unique ability to
discretely conserve mass. Current state-of-the-art VOF methods, however, rely
on the piecewise-linear interface calculation (PLIC) to represent the interface
used when calculating advection fluxes. This renders the estimated curvature of
the transported interface zeroth-order accurate at best, adversely impacting
the simulation of surface-tension-driven flows.
In the past few years, there have been several attempts at using
piecewise-parabolic interface approximations instead of piecewise-linear ones
for computing advection fluxes, albeit all limited to two-dimensional cases or
not inherently mass conservative. In this contribution, we present our most
recent work on three-dimensional piecewise-parabolic interface reconstruction
and apply it in the context of the VOF method. As a result of increasing the
order of the interface representation, the reconstruction of the interface and
the estimation of its curvature now become a single step instead of two
separate ones. The performance of this new approach is assessed both in terms
of accuracy and stability and compared to the classical PLIC-VOF approach on a
range of canonical test-cases and cases of surface-tension-driven
instabilities.
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