Multiscale Modeling for Material Phase Change Problems SciDoc Publishers | Open Access | Science Journals | Media Partners

The fixed grid methods [1-5], including both finite element methods (FEM) and finite difference methods (FDM), were employed to model and simulate material phase change problems by solving the governing equations numerically. The major advantage of fixed grid methods is that the methods can handle multi-dimensional problems efficiently. However, the fixed grid methods may sometimes be unstable when the phase interface moves at a distance larger than the spatial increment in one time step. The extended finite element method (XFEM) [6, 7] has been used to overcome the above issue raised in most fixed grid methods. The basic idea is to explicitly track the phase interface and to construct enriched elements depending on the interface position while keeping the fixed meshes. Therefore, the approximation can present the phase interface and the associated discontinuity in the temperature gradient within an element. Another alternative solution is to employ the variable grid methods [8, 9]. In the variable grid methods, either the space or time domain is divided into equal intervals, and the corresponding grid interval in the other domain is determined. To study material change problems at the microscale, a thermal wave model [10] shall be employed