A boundary conforming grid generation system for interface tracking

The development of an algebraic grid generation system to track a solid-liquid interface during directional solidification of a binary alloy is discussed. A single mapping, constructed with tensor product B-splines, is proposed for calculations of both shallow and deep solidification cells. The initial spline coefficients for the coordinate mapping are modified to minimize a discrete functional that regulates the smoothness and orthogonality of the mesh. The use of transfinite blending function interpolation to obtain an initial grid is examined.