Accurate and Conservative Volume of Fluid Advection Method for General Grids

A conservative advection scheme based on the use of edge-matched flux polyhedra to integrate the volume fraction evolution equation on general grids is presented. The algorithm prevents the formation of over/undershoots of the volume fraction by enforcing that the flux polyhedra do not over/underlap, removing the need for unphysical and inaccurate redistribution algorithms. Accuracy of the scheme derives from the edge-matched flux polyhedra’s approximation of the local stream tube. Integrity of the interface representation is maintained by the use of height functions over a local, cartesian stencil. Kinematic test cases performed on various grid topologies demonstrate the superior accuracy of the new volume of fluid method.