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SUMMARYThis paper focuses on the numerical simulation of phase-change processes using a moving ÿnite element technique. In particular, directional solidiÿcation and melting processes for pure materials and binary alloys are studied. The melt is modelled as a Boussinesq uid and the transient Navier-Stokes equations are solved simultaneously with the transient heat and mass transport equations as well as the Stefan condition. The various streamline-upwind=Petrov-Galerkin-based FEM simulators developed for the heat, ow and mass transport subproblems are reviewed. The use of classes, virtual functions and smart pointers to represent and link the particular simulators in order to model a phase change process is discussed. The freezing front is modelled using a spline interpolation, while the mesh motion is deÿned from the freezing front motion using a transÿnite mapping technique. Various two-and three-dimensional numerical tests are analysed and discussed to demonstrate the e ciency of the proposed techniques.

SUMMARYA computational method for the design of directional alloy solidiÿcation processes is addressed such that a desired growth velocity v f under stable growth conditions is achieved. An externally imposed magnetic ÿeld is introduced to facilitate the design process and to reduce macrosegregation by the damping of melt ow. The design problem is posed as a functional optimization problem. The unknowns of the design problem are the thermal boundary conditions. The cost functional is taken as the square of the L 2 norm of an expression representing the deviation of the freezing interface thermal conditions from the conditions corresponding to local thermodynamic equilibrium. The adjoint method for the inverse design of continuum processes is adopted in this work. A continuum adjoint system is derived to calculate the adjoint temperature, concentration, velocity and electric potential ÿelds such that the gradient of the L 2 cost functional can be expressed analytically. The cost functional minimization process is realized by the conjugate gradient method via the FE solutions of the continuum direct, sensitivity and adjoint problems. The developed formulation is demonstrated with an example of designing the boundary thermal uxes for the directional growth of a germanium melt with dopant impurities in the presence of an externally applied magnetic ÿeld. The design is shown to achieve a stable interface growth at a prescribed desired growth rate.

This paper focuses on the numerical simulation of phase‐change processes using a moving finite element technique. In particular, directional solidification and melting processes for pure materials and binary alloys are studied. The melt is modelled as a Boussinesq fluid and the transient Navier–Stokes equations are solved simultaneously with the transient heat and mass transport equations as well as the Stefan condition. The various streamline‐upwind/Petrov–Galerkin‐based FEM simulators developed for the heat, flow and mass transport subproblems are reviewed. The use of classes, virtual functions and smart pointers to represent and link the particular simulators in order to model a phase change process is discussed. The freezing front is modelled using a spline interpolation, while the mesh motion is defined from the freezing front motion using a transfinite mapping technique. Various two‐ and three‐dimensional numerical tests are analysed and discussed to demonstrate the efficiency of the proposed techniques. Copyright © 1999 John Wiley & Sons, Ltd.