Advection-diffusion model for normal grain growth

This paper presents an advection-diffusion model that describes normal grai n growth in 'size-sides' space. Ordinary differential equations governing t he self-similar distributions at the steady state of normal grain growth ar e derived. By solving numerically the continuity equations (time-dependent) and the corresponding ordinary differential equations (time-independent), we get the self-similar grain size distributions in time-dependent and time -independent form. The two sets of distributions have nearly the same shape , confirming the self-consistency of the model. Some comparisons with other models and simulations are given.