Moments-based interface reconstruction, remap and advection

Abstract

We present a new moment-of-fluid (MOF2) interface reconstruction method. It uses the zeroth, first, and second moments of the fragment of material inside a cell of the mesh to reconstruct a convex material polygon or a union of convex polygons that approximate the respective material fragment. The new method requires information about the material moments only for the cell under consideration. The MOF2 method allows to exactly reproduce several convex shapes: corners, filaments, and some concave shapes: cell-complements to corners and filaments.Interface reconstruction is formulated as a local (for each cell), non-linear, equality constrained optimization problem, which does not require additional communication and allows for an efficient parallel implementation.We present an extensive set of test problems, both for interface reconstruction on a single cell, and for reconstruction of a variety of shapes on a variety of meshes.We describe how to perform two-material advection using the MOF2 method and present the results for the classical advection tests.We also show the examples of material interface remapping needed in the framework of multi-material arbitrary Lagrangian-Eulerian methods, and give a brief description of a procedure that can be used to update the material moments on the Lagrangian stage of those methods.