Computer simulation models of casting processes which couple the veloc
ity potential approach with a transient Bernoulli equation are develop
ed. Instead of employing three primitive variables, displacement, velo
city and pressure, only one variable-velocity potential is needed. Whe
n the thickness integrated equation is also employed, the method can p
rovide practical results with very reasonable computing time and stora
ge for the 3-D casting of an arbitrary shape thin-walled cavity. In th
is study, the flexibility of the finite element method in dealing with
complex geometries and the efficient algorithm of volume of fluid (VO
F) approach for tracking moving free surfaces are combined for solving
casting filling problems. Multiple free surface contacts are develope
d when the stream finally turns back and impacts the original free sur
face. A double-node scheme is developed to treat these multiple free s
urface contacts. The movement of the interface is small and an inflexi
ble wall across the separating surface is assumed. Because the casting
process involves phase change, and the interface between the solid an
d liquid is generally an unknown curve, the enthalpy model with fixed
mesh is used to determine the temperature distribution and the thickne
ss of the filling. Numerical examples for prediction of filling patter
ns, effects of solidification on patterns and parametric studies are p
resented. Fairly good agreement between this method and experimental r
esults and other numerical simulations have also been obtained. The co
mputational techniques developed in this study can provide a powerful
and flexible tool for analyzing the fluid flow and heat transfer in me
tal casting of thin-walled cavities and can help design engineers redu
ce the costly and time-consuming process of designing complex molds fo
r the manufacture of casted parts.