EFFICIENT MULTILEVEL FINITE-ELEMENT APPROACH TO 3-DIMENSIONAL PHASE-CHANGE PROBLEMS

A finite-element (FE) formulation suitable for a multigrid algorithm i n solving three-dimensional phase-change problems is described. This f ormulation is based on the averaged specific heat model. The algorithm has been proved to be very useful for large problems where the comput ational complexity can be reduced from O(n(3)) to O(n ln n) with high storage efficiency in a personal computer. To evaluate the accuracy of the present algorithm, the numerical results for larger slender ratio are compared with previous analytical solutions. Results show that th e numerical solutions at the symmetric surface of the long axis are in very good agreement with the two-dimensional exact solutions for slen der ratio = 5. The magnitudes of time steps and freezing-temperature i ntervals are insensitive to the maximal and average absolute errors wh en the time step is less than 0.01 s. Consequently, a larger lime step can be used to save computing time and retain the same order of accur acy. This algorithm is also available for pure metals and alloys that exhibit a very large or small (or zero) freezing-temperature interval.