A 3D unsplit-advection volume tracking algorithm with planarity-preserving interface reconstruction

A new volume tracking method is introduced for tracking interfaces in three-dimensional (3D) geometries partitioned with orthogonal hexahedra. The method approximates interface geometries as piecewise planar, and advects volumes in a single unsplit step using fully multidimensional fluxes that have their definition based in backward-trajectory remapping. By using multidimensional unsplit advection, the expense of high-order interface reconstruction is incurred only once per timestep. Simple departures from strict backward-trajectory remapping remove any need for consideration of volume computations involving shapes consisting of non-planar ruled surfaces. Second-order accuracy of the method is demonstrated even for vigorous 3D deformations.