A Power Consistent Mathematical Forumulation For Joulean Heat Release

In the existing literature on mathematical simulation of electric boosting in glass melts, the approximation methods used to calculate the Joulean heat release in the melt are omitted. The total heat release as calculated from the potentials and currents at the electrodes should match the power that is released in the volume cells. In this article, it is shown that a straightforward finite volume discretisation lacks this consistency property and an alternative method is proposed. Also, for boosting with multiple transformers, an algorithm is described that guarantees current conservation for each group of electrodes that connect to the same transformer.