A more accurate three-dimensional grain growth algorithm

In a previous paper, the authors described a simulation method for the evolution of two-dimensional cellular structures by curvature flow that satisfied the von Neumann-Mullins relation with high accuracy. In the current paper, we extend this method to three-dimensional systems. This is a substantial improvement over prior simulations for two reasons. First, this method satisfies the MacPherson-Srolovitz relation with high accuracy, a constraint that has not previously been explicitly implemented. Second, our front-tracking method allows us to investigate topological properties of the systems more naturally than other methods, including Potts models, phase-field methods, cellular automata, and even other front-tracking methods. We demonstrate this method to be feasible in simulating large systems with as many as 100,000 grains, large enough to collect significant statistics well after the systems have reached steady state.