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Radial integration BEM for one-phase solidification problems. (English) Zbl 1297.80014

Summary: A new boundary element analysis approach is presented for solving one-phase solidification and freezing problems based on the radial integration method. Green’s function for the Laplace equation is adopted in deriving basic integral equations for time-dependent problems with constant heat conductivities and, as a result, a domain integral is involved in the derived integral equations. Based on the finite difference technique, an implicit time marching solution scheme is developed for solving the time-dependent system of equations. Front-tracking method is used to simulate the motion of the phase boundary. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the radial integration BEM. To validate the proposed method, two typical examples are given. Satisfactory results are obtained in comparison with semi-analytical solutions.

MSC:

80M15 Boundary element methods applied to problems in thermodynamics and heat transfer
65M38 Boundary element methods for initial value and initial-boundary value problems involving PDEs
80A22 Stefan problems, phase changes, etc.

Software:

XFEM
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Full Text: DOI

References:

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