Interface reconstruction and advection schemes for volume of fluid method in axisymmetric coordinates

TL;DR

This paper introduces new analytic interface reconstruction formulas and improved advection schemes for the volume of fluid method in axisymmetric coordinates, enhancing mass conservation accuracy in two-phase flow simulations.

Contribution

It develops analytic formulas for interface reconstruction and modifies advection schemes to improve mass conservation in axisymmetric VOF simulations.

Findings

Achieved higher mass conservation accuracy in axisymmetric VOF simulations.

Demonstrated improved interface reconstruction in axisymmetric coordinates.

Validated methods through numerical experiments.

Abstract

Volume of fluid(VOF) method is a sharp interface method employed for simulations of two phase flows. Interface in VOF is usually represented using piecewise linear line segments in each computational grid based on the volume fraction field. While VOF for cartesian coordinates conserve mass exactly, existing algorithms do not show machine-precision mass conservation for axisymmetric coordinate systems. In this work, we propose analytic formulae for interface reconstruction in axisymmetric coordinates, similar to those proposed by Scardovelli and Zaleski (J. Comput. Phys. 2000) for cartesian coordinates. We also propose modifications to the existing advection schemes in VOF for axisymmetric coordinates to obtain higher accuracy in mass conservation