FINITE-ELEMENT ANALYSIS OF HEAT CONDUCTION PROBLEMS WITH IRREGULAR REGION BOUNDARY USING MULTILEVEL TECHNIQUES

The main goal of this article is to introduce a numerical procedure for the calculation of solidification and melting using the PISO algorithm. Since coupling among velocity, pressure, temperature, and liquid fraction is important in phase-change problems, an improved PISO algorithm is required to couple these variables properly. To achieve this goal, the present study proposes the use of the enthalpy method for the inner iterations of the matrix solver, in order to predict more accurate temperature and liquid fraction that satisfy the energy balance criterion simultaneously. Another difference of the present method from other conventional coupling methods is in updating the permeability term of the momentum equation with liquid fractions predicted in the first correction step. This may couple the velocities with the liquid fractions more closely. A comparison of the proposed method with a standard iterative method is made for three different cases, showing that improved predictions are obtained in terms of computing speed and solution robustness.