In the present study, mean field models of grain growth (Hillert and Burke-Turnbull models) are compared with 3D full field simulations considering an isotropic grain boundary energy and mobility and under the absence of second-phase particles. The present 3D full field simulations are based on a level set description of the grain interfaces within a finite element framework. The digital initial microstructures are generated using a coupled "Vorono <-Laguerre/dense sphere packing" algorithm. Based on full field simulation results, new formulations of Burke-Turnbull and Hillert models are proposed. In contrast with classical formulations, the new ones account for the possible heterogeneity of the initial grain size distribution.