We present a new approach for modeling the time-dependent evolution of partially faceted melt/crystal interfaces in large-scale melt-growth systems. The method, developed here for two-dimensional computations, involves decoupling,, at each time step, between interface motion and thermal field calculations. Interface motion is calculated by directly applying an interface motion operator at each interface node-point, where this operator is consistent with step-flow and step-source kinetics, and depends on the topography of the interface, its thermal field and the type and availability of step-sources. The method is described in detail, and is shown to capture both nano-scale and macro-scale features of the evolving melt/crystal interface. Sample results accurately reproduce calculations obtained by other numerical as well as semi-analytical techniques. Additional computations, involving partially faceted and fully faceted interfaces in representative oxide and semiconductor systems are also presented and discussed. (C) 2004 Elsevier B.V. All rights reserved.