Numerical analysis of melting/solidification phenomena using a moving boundary problem analysis method X-FEM

A numerical analysis method for melting/solidification phenomena has been developed to evaluate feasibility of the several candidate techniques in the nuclear fuel cycle. Our method is based on an extended finite element method, which has been developed for moving boundary problems. The basic idea of the method is to incorporate a signed distance function into a finite element interpolation to represent a discontinuous gradient of the temperature at a moving solid-liquid interface. This technique makes it possible to simulate movement of the solid-liquid interface without the use of a moving mesh. Construction of the finite element equation has been discussed in this study. The technique of quadrature and the method to solve the governing equations have also been constructed. The numerical solutions of the basic problems were compared to the approximate solutions or to the existing experimental data. Through these verifications, validity of the newly developed numerical analysis method has been demonstrated. (author)