Finite-volume/multigrid methods are presented for solving incompressible he
at flow problems with an unknown melt/solid interface, mainly in solidifica
tion applications, using primitive variables on collocated grids. The metho
ds are implemented based on a multiblock and multilevel approach, allowing
the treatment of a complicated geometry. The inner iterations are based on
the SIMPLE scheme, in which the momentum interpolation is used to prevent v
elocity/pressure decoupling. The outer iterations are set up for interface
update through the isotherm migration method. V-cycle and full multigrid (F
MG) methods are tested for both two- and three-dimensional problems and are
compared with a global Newton's method and a single-grid method. The effec
ts of Prandtl and Rayleigh numbers on the performance of the schemes are al
so illustrated. Among these approaches, FMG has proven to be superior on pe
rformance and efficient for large problems. Sample calculations are also co
nducted for horizontal Bridgman crystal growth, and the performance is comp
ared with that of traditional single-grid methods. (C) 1999 Academic Press.