Simple metrics for verification and validation of macrosegregation model predictions

Abstract

While the numerical simulation of macrosegregation is now a common place activity efforts can still be enhanced by developing quantitative measures of the results. Here, on treating the nodal field of concentration predictions from a macrosegregation simulation as a sample from a statistical distribution, we demonstrate how statistical measures can be used in verification and validation. The first set of such measures is simply the central moments of the distribution, i.e., the mean, the standard deviation, and the skewness; measurements that provide quantitative checks of mass balance and grid convergence. In addition, building on recently reported work [1], we also demonstrate how to construct and use a cumulative distribution function (CDF) of the nodal concentration field; a measure that can be used to determine the fraction of the casting volume concentrations less than a specified value. We show how the CDF can be used to compare the influence of various process conditions and phenomena related to domain size, cooling rate, permeability, and micro-segregation.