A control volume capacitance method for solidification modelling with mass transport

Capacitance methods are popular methods used for solidi cation modelling. Unfortunately, they su er from a major drawback in that energy is not correctly transported through elements and so providing a source of inaccuracy. This paper is concerned with the development and application of a control volume capacitance method (CVCM) to problems where mass transport and solidi cation are combined. The approach adopted is founded on theory that describes energy transfer through a control volume (CV) moving relative to the transporting mass. An equivalent governing partial di erential equation is established, which is designed to be transformable into a nite element system that is commonly used to model transient heat-conduction problems. This approach circumvents the need to use the methods of Bubnov–Galerkin and Petrov–Galerkin and thus eliminates many of the stability problems associated with these approaches. An integration scheme is described that accurately caters for enthalpy uxes generated by mass transport. Shrinkage e ects are neglected in this paper as all the problems considered involve magnitudes of velocity that make this assumption reasonable. The CV approach is tested against known analytical solutions and is shown to be accurate, stable and computationally competitive