Development of numerical method for two-phase flow on polyhedral meshes (Part 1, Development of advection scheme and curvature calculation method)

Although the advantage of using arbitrarily-shaped polyhedral meshes for the industrial flow applications is clear, their employment to two-phase flows is rather limited due to difficulty in deriving and implementing algorithms without overwhelming complexity on such meshes. We present a numerical method based on the VOF (Volume of Fluid) method which works on arbitrarily-shaped three-dimensional polyhedral meshes with comparable accuracy to the methods for structured meshes. We extend the THINC (Tangent of Hyperbola Interface Capturing) method and the RDF (Reconstructed Distance Function) method respectively, to solve the advection equation of the color function and to estimate the interface curvature on polyhedral meshes without laborious geometric arithmetics.