Starting with the effect of forced flows on the morphologies of growing dendrites, previous work on simulating dendritic growth with convection is summarized. In our work a fixed mesh for the temperature and a conformable mesh for velocity and concentration in a binary alloy are used; this method captures the morphology and motion of the complex solid-liquid interface. Convection is driven by thermo-solutal buoyancy and solidification contraction. Examples include: the natural convection near a dendrite of a pure substance growing in its under-cooled liquid; the dendritic growths of a pure substance and an alloy in their undercooled liquids, in which the convection is driven by buoyancy and solidification contraction; and the effects of convection driven by thermosolutal buoyancy and solidification contraction during the directional solidification of an alloy. Solidification contraction dominates the convection pattern, when the concentration of the alloy-element is dilute.