  The thin interface limit aims at minimizing the effects arising from a
numerical interface thickness, inherent in diffuse interface models of
solidification and microstructure evolution such as the phase field model.
While the original formulation of this problem is restricted to transport by
diffusion, we consider here the case of melt convection. Using an analysis of
the coupled phase field-fluid dynamic equations, we show here that such a thin
interface limit does also exist if transport contains both diffusion and
convection. This prediction is tested by comparing simulation studies, which
make use of the thin-interface condition, with an analytic sharp-interface
theory for dendritic tip growth under convection.
