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

Volume of fluid (VOF) method is a sharp interface employed for simulations two phase flows. Interface in VOF usually represented using piecewise linear line segments each computational grid based on the volume fraction field. While cartesian coordinates conserve mass exactly, existing algorithms do not show machine-precision conservation axisymmetric coordinate systems. In this work, we propose analytic formulae reconstruction coordinates, similar to those proposed by Scardovelli and Zaleski (2000) [12] coordinates. We also modifications advection schemes obtain higher accuracy conservation.