Facets appearing on the liquid/solid interface, during directional crystal growth from the melt, advance via a combination of step-flow (i.e. linear) and step-source (i.e. non-linear) kinetics. In this manuscript we rigorously calculate a number of examples in which the macroscopic shape of the interface is dramatically affected by the type, distribution and dynamics of step sources along these facets. The new numerical algorithm employed, based on decoupling interface motion from thermal field calculations, is briefly described (further details are given elsewhere), after which several sets of results are presented. Specifically, an experimental observation of facet evolution dynamics during the melt growth of silicon, qualitatively explained in Voronkov and Pankov [Sov. Phys. Crystallogr. 20(6) (1975) 697], is quantitatively analyzed and explained here. Additional calculations include analyses of dynamics associated with the hypothetical sudden appearance of a dislocation step-source on a previously dislocation-free advancing facet. Large rates of latent heat release associated with such abrupt changes between growth mechanisms are shown, in some cases, to promote melt-back of rough portions of the interface. Finally, select semi-analytical solutions to the interface motion equation, in non-trivial situations involving transitions between growth mechanisms, are shown to verify numerical calculations of the advancing interface. (C) 2004 Elsevier B.V. All rights reserved.