Simulating interfacial flows: a farewell to planes

TL;DR

This paper introduces a three-dimensional piecewise-parabolic interface reconstruction method for the volume-of-fluid technique, improving accuracy and stability in simulating surface-tension-driven flows compared to traditional linear methods.

Contribution

It presents the first 3D piecewise-parabolic interface reconstruction integrated with VOF, enabling single-step curvature estimation and enhanced simulation fidelity.

Findings

Improved accuracy in interface curvature estimation.

Enhanced stability in surface-tension-driven flow simulations.

Better performance on canonical and instability test cases.

Abstract

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.