Direct numerical simulations of multiphase flows, using a front-tracking method, are presented. The method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties. Interfacial terms are accounted for by adding the appropriate sources as delta functions at the boundary separating the phases. The unsteady Navier-Stokes equations are solved by a conventional finite volume method on a fixed, structured grid and the interface, or front, is tracked explicitly by connected marker points. interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid. Advection of fluid properties such as density is done by following the motion of the front. The method has been implemented for fully three-dimensional hows, as well as for two-dimensional and axisymmetric ones. First, the method is described for the flow 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 fixed grid, are discussed. Applications and extensions of the method to homogeneous bubbly flows, atomization, Rows with variable surface tension, solidification, and boiling are then presented. (C) 2001 Academic Press.