Finite-Element Analysis of Phase-Change Problems Using Multilevel Techniques

Abstract A simple and effective finite-element procedure is presented for the analysis of transient heat transfer with phase changes. An averaged specific heat is employed to simulate the elements including the phase-change zone in this finite-element analysis with fixed mesh. Due to the use of a Gauss-Seidel method and a multigrid algorithm, the computational complexity can be reduced from O(n3) to 0(n In n) with high storage efficiency. The computational results are also in very good agreement with the exact solutions. Results show that the magnitudes of the lime step and freezing-temperature interval have little effects on the maximal and average errors. As a result, a larger time step can be used to save computing time and achieve the same order of accuracy. This algorithm is available for pure metals and alloys that exhibit discontinuous specific heat.