A MODIFIED EFFECTIVE CAPACITANCE METHOD FOR SOLIDIFICATION MODELING USING LINEAR TETRAHEDRAL FINITE-ELEMENTS

In this paper a new formulation for modelling solidification is discus sed. The formulation has similar features to both the apparent and eff ective heat capacitance methods used for solidification problems where conduction predominates over other heat transfer mechanisms. The main feature of the new method is that a modified form of effective heat c apacitance is calculated from the solution of non-linear equations tha t describe the energy loss for linear tetrahedral finite elements. Thi s approach ensures that the predicted temperature field corresponds ex actly with the energy loss and so providing an extremely stable formul ation The method is tested against a range of problems including some with non-linear liquid fractions. The predictions are compared against known analytical solutions and the method is shown to provide reasona ble accuracy even for relatively large time-steps. A comparison is mad e between the method and the well-known temporal and spatial approxima tions of apparent heat capacitance, and effective capacitance. Accurac y is maintained over a greater variation in time-step and mesh density with comparable computational requirements. In addition, the method l ends itself to the use of relatively simple bisection techniques for t he solution of the non-linear finite element equations. Also demonstra ted is the method's innate ability to predict energy loss to a high de gree of accuracy for large time steps.