A numerical model capable of simulating the solidification of binary d
endritic alloys and, in particular, the formation of a defect known as
freckles, is presented. An algorithm based on a penalty and Petrov-Ga
lerkin finite element formulation is used to solve the differential eq
uations for the velocity field, temperature field, and concentration o
f the solute. The demands for memory and CPU time require the use of s
upercomputers to execute the simulations, even though only small 2-D d
omains are considered, and the present code takes advantage of vectori
zation. In order to simulate practical solidification scenarios, the a
dvantages of parallel processing will have to be utilized to speed up
the calculations.