A deferred approach to include solid↔liquid phase change effects in the solution of advection–conduction heat transfer problems via the improved element-free Galerkin method

In this communication, a novel strategy is presented for addressing advection–conduction problems with solid$\leftrightarrow$liquid phase change by using a modified implementation of the improved element-free Galerkin (IEFG) method. The approach involves a deferred inclusion of non-linear effects related to temperature-dependent material properties and the latent heat exchanged during phase change, incorporated within thermal load vectors. The temperature and solid phase fraction gradients needed to construct these thermal load vectors are computed iteratively within the non-linear solution process, delaying their assembly until required. This deferred approach eliminates the need for temperature derivatives of the solid or liquid fraction in the core problem formulation, a component that often complicates convergence when using conventional effective specific heat methods. A comprehensive description of the iterative process is given, along with the method for obtaining solid phase fraction gradients using a global reconstruction based on improved moving least squares (IMLS). The technique is rigorously validated through a 1-D advection–conduction phase change problem with an analytical solution and a 3-D application in direct chill casting of AA-1050 aluminium alloy. Outcomes demonstrate that this method not only enhances convergence over traditional effective specific heat techniques, but also achieves a substantial reduction in computational time.