Best practice for measuring grid convergence in numerical models of alloy solidification

Purpose - When a multi component alloy solidifies the redistribution of solute components leads to the formation of macrosegregation patterns. Blending ideas from a number of recent publications the purpose of this paper is to provide a "best practice" on how grid convergence of a given macrosegregation simulation can be measured and determined. Design/methodology/approach - The best practice is arrived at by considering a benchmark problem consisting of a 2D-casting simulation of an idealized Al-4.5%Cu alloy in a side cooled square (76×76 mm) cavity. The model for this simulation is based on a mixture treatment of the relevant heat and mass transfer equations. Simulations are made using three increasingly refined grid sizes. Findings - The best practice to determine grid resolution involves two steps: first, a visual evaluation of predicted segregation images leading to the evaluation of solute profiles along selected transects; and second, the construction of a cumulative distribution function (CDF) of the predicted segregation field. On application to the benchmark problem, it is concluded that current computer resources are insufficient to grid resolve macrosegregation patterns but that the CDF provides a useful signal of the nature of macrosegregation in a given system. Research limitations/implications - The benchmark is chosen to be representative. Exact convergence behavior, however, may depend on the system chosen. Originality/value - In addition to establishing a best practice for measuring grid resolution of macrosegregation simulations the work also highlights, even in the absence of complete grid convergence, how the recently proposed CDF treatment can inform solidification modeling and process understanding.