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A fast convergent and accurate temperature model for phase-change heat conduction. (English) Zbl 0942.76038
Summary: This work proposes a temperature-based finite element model for transient heat conduction involving phase change. Like preceding temperature-based models, it is characterized by the discontinuous spatial integration over the elements affected by the phase change. Using linear triangles or tetrahedrals, integration can be performed in a closed analytical way, assuring an exact evaluation of the discrete balance equation. Because of its unconditional stability, an Euler-backward time-stepping scheme is implemented. A crucial fact is the computation of the exact tangent matrices for the Newton-Raphson solution of the nonlinear system of discretized equations. Efficiency of the model is tested by means of the results obtained for the Neumann problem and for the solidification of a steel ingot.

MSC:
76M10Finite element methods (fluid mechanics)
76T10Liquid-gas two-phase flows, bubbly flows
80A22Stefan problems, phase changes, etc.
80A20Heat and mass transfer, heat flow