The phase-field (PF) method for solidification phenomena is an open formulation based on a free-energy functional. Two common a rigorous thermodynamic formulation for nonisothermal choices for the PF potential, here referred to briefly as the Caginalp systems [11] and to encompass fluid-flow phenomena [12],
and Kobayashi models, are compared with respect to their numeric the PF technique is likely to offer a practical alternative results within the classical sharp-interface limit. Both qualitative to the more traditional (and cumbersome) interfaceand quantitative behavior are addressed, and an assessment of tracking methods. the computational effort required to approximate a sharp-interface problem is made. It is shown that the specific form of the free-
The basic PF equation arises from the classical Landau energy potential does have a strong influence on the convergence theories of phase transitions by considering a first-order of the PF results to their sharp-interface limit. Compliance of the expansion of the free energy density in the ''order parame-PF solutions with the linear kinetic model for the interface temperater'' p:
ture is also investigated. A simple one-dimensional solidification problem in the presence of kinetic undercooling is solved by the PF model and also by a deforming grid method. Our results support the view that, if care is exercised in formulating the phase-
temperature coupling, there is a high degree of confidence in using the PF method for the numerical modeling of general solidification phenomena. แฎ 1997 Academic Press F( p, u) is a double-well potential having local minima at the p-values corresponding to the two possible choices of the phase state at the bulk (solid or liquid), while is a