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An object-oriented implementation of a front tracking finite element method for directional solidification processes. (English) Zbl 0943.76052
Summary: 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.)
Software:
Diffpack
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