Analysis of the Moment-Of-Fluid Method for Polygonal Meshes in Axisymmetric Coordinate System

One of the important features of the arbitrary Lagrangian-Eulerian (ALE) hydrodynamics methods is the appearance of mesh cells containing fractional amounts of more than one material. To resolve sub-scale material dynamics, interfaces between materials inside a cell have to be calculated from material moments. The moment-of-fluid (MOF) method is one of the most accurate interface reconstruction methods. Unlike other methods, it is local and does not require data from neighboring cells which makes it amenable for emerging computer architectures. We analyze this method for axisymmetric problems. Our analysis closes a few gaps in its theoretical justification and provides useful insight on its properties and practical implementation. The theoretical conclusions are confirmed with numerical experiments.