Moments-based interface reconstruction, remap and advection

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