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Abstract
A finite-element (FE) formulation suitable for a multigrid algorithm in solving three-dimensional phase-change problems is described. This formulation is based on the averaged specific heat model. The algorithm has been proved to be very useful for large problems where the computational complexity can be reduced from O(n3) to O(n In 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 the numerical solutions at the symmetric surface of the long axis are in very good agreement with the two-dimensional exact solutions for slender ratio = 5. The magnitudes of time steps and freezing-temperature intervals are insensitive to the maximal and average absolute errors when the time step is less than 0.01 s. Consequently, a larger time step can be used to save computing time and retain the same order of accuracy. This algorithm is also available far pure metals and alloys that exhibit a very large or small (or zero) freezing-temperature interval.
Notes
Address correspondence to Dr. Rong-Tsong Lee, Department of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan 80424, Republic of China. E-mail: tsong@ mail.nsysu.edu.tw