An object-oriented implementation of a front tracking finite element method for directional solidification processes.

*(English)*Zbl 0943.76052Summary: This paper focuses on the numerical simulation of phase-change processes using a moving finite element technique. In particular, we study directional solidification and melting processes for pure materials and binary alloys. 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 with the Stefan condition. We review various streamline-upwind/Petrov-Galerkin based FEM simulators developed for the heat, flow and mass transport subproblems. We also discuss the use of classes, virtual functions and smart pointers to represent and link the particular simulators in order to model a phase change process. 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 analyzed to demonstrate the efficiency of the proposed techniques.

##### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76-04 | Software, source code, etc. for problems pertaining to fluid mechanics |

76T99 | Multiphase and multicomponent flows |

80A22 | Stefan problems, phase changes, etc. |

68N19 | Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.) |

##### Keywords:

object-oriented programming; front tracking technique; directional solidification; melting; binary alloys; Boussinesq fluid; Navier-Stokes equations; heat and mass transport equations; Stefan condition; streamline-upwind/Petrov-Galerkin based FEM simulators; freezing front; spline interpolation; transfinite mapping technique##### Software:

Diffpack
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\textit{R. Sampath} and \textit{N. Zabaras}, Int. J. Numer. Methods Eng. 44, No. 9, 1227--1265 (1999; Zbl 0943.76052)

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