A novel THINC scheme-based CLSVOF method for axisymmetric two-phase flows

This paper is on proposition of a THINC (Tangent of the Hyperbola for INterface Capturing) scheme in axisymmetric coordinate system for an algebraic Coupled Level Set and Volume of Fluid (CLSVOF) method-based simulation of two-phase flows. Novelty of the present work lies in consideration of two separate characteristic Heaviside functions in radial and axial directions. Such an approach is shown to yield two distinct forms of direct analytical expression for the advection fluxes of volume fraction in both directions unlike the identical forms used in the existing THINC schemes for Cartesian coordinates. Effectiveness of the proposed CLSVOF method is presented on various axisymmetric advection tests, where it is observed that the present axisymmetric THINC scheme is capable of conserving the volume fraction field up to machine precision level while maintaining the desired interface thickness without any adverse distortions. To ascertain the behavior of this novel scheme for practical problems, a comprehensive validation study is performed for sufficiently different two-phase flows like static droplet, droplet oscillations, droplet fall, bubble rise, and droplet coalescence. It has been demonstrated that the proposed algebraic CLSVOF method emulates the robustness and accuracy of the standard geometric CLSVOF methods, thus facilitating a straightforward approach to numerical implementation in practical scenarios.