Computations of Multiphase Flows by a Finite Dierence/Front Tracking Method. I. Multi-Fluid Flows

A numerical method for direct simulations of multiphase ows is presented. The method is based on writing one set of governing equations for the whole computa-tional domain and treating the dierent phases as one uid with variable material properties. Interfacial terms are accounted for by adding the appropriate sources as -functions at the interface between the phases. The ow is taken to be in-compressible. The unsteady Navier-Stokes equations are solved by a conventional nite volume method on a xed, structured grid and the interface, or front, tracked explicitly by connected marker points. Interfacial source terms such as surface ten-sion are computed on the front and transfered to the xed grid. Advection of uid properties such as density is done by following the motion of the front. The method has been implemented for fully three-dimensional ow as well as two-dimensional and axisymmetric ones. This approach has been shown to be reasonably accurate, versatile, and robust. In part I of these lecture notes, the method is described for the ow of two or more isothermal phases. The representation of the moving interface, and its dynamic restructuring, as well as the transfer of information between the moving front and the xed grid is discussed. Various validation studies are shown and the relation of the method to other computational techniques discussed. A recent parallelization of the method is also presented. In part II, several applications are shown. Those include detailed studies of drop collisions, motion of single bubbles and drops in shear ows, and the collective interaction of many bubbles and drops. Part III describes extensions of the methodology to problems with more compli-cated physics such as variable surface tension, solidication, and boiling.