Incompressible interfacial flows here refer to those incompressible flows possessing multiple distinct, immiscible fluids separated by interfaces of arbitrarily complex topology. A prototypical example is free surface flows, where fluid properties across the interface vary by orders of magnitude. Interfaces present in these flows possess topologies that are not only irregular but also dynamic, undergoing gross changes such as merging, tearing, and filamenting as a result of the flow and interface physics such as surface tension and phase change. The interface topology requirements facing an algorithm tasked to model these flows inevitably leads to an underlying Eulerian methodology. The discussion herein is confined therefore to Eulerian schemes, with further emphasis on finite volume methods of discretization for the partial differential equations manifesting the physical model. Numerous algorithm choices confront users and developers of simulation tools designed to model the time-un...

Tracer-particles, massless particles that are advected throughout the flow domain, are an important factor in computational solutions. The utility of tracer-particles, which sample and report relevant solution data, is predicated upon an accurate advection algorithm. The objective of this research was to investigate the ability of existing techniques, physical-space and logical-space advection, to accurately predict tracer-particle pathlines within various grid topologies. The physical-space technique, using a higher-order integration method, accurately predicted pathlines for a curved flow-field within a nonorthogonal grid. In contrast, the logical-space technique failed to accurately predict pathlines for a uniform flow-field within a nonuniform rectilinear grid. Existing logical-space advection techniques are, therefore, limited to uniform rectilinear grids. Introduction A primary goal of computational simulation research is the development of accurate and efficient methods to sol...