Finite difference methods front tracking

Sankaranarayanan, K., I.G. Kevrekidis, S. Sundaresan, J. Lu and G. Tryggvason. A Comparative Study of Lattice Boltzmann and Front-Tracking Finite-Difference Methods for Bubble Simulations. Int. J. Multiphase Flow 29 109-116 (2003). 

Swaminarayan and Charbon presented two methods of simulating the growth of an isolated spherulite the arborescent method and the front-tracking method [44]. In a second article [45], the same authors coupled the front-tracking techniques with (1) a stochastic model for spherulite nucleation, (2) a cellular model for spherulite impingement and solid fraction evolution, and (3) a finite difference method for solving the energy equation. This multiscale approach predicts the final microstructure in a macroscopic part. 

Both models can be solved by different numerical schemes. The boundary element method has the advantage that the velocity gradient can be obtained more accurately than the finite-element method, which is important for predicting the fiber orientation (Barone and Caulk, 1986 Osswald and Thcker, 1988). However, it is restricted to single charge, flat parts and cases of uniform thickness. Hence, many simulation efforts have converged to the use of the finite-element/control-volume method (Erwin and Thcker, 1995 Osswald and Tucker, 1990) coupled with the volume of fluid (VOF) method to track the position of flow front (Hirt and Nichols, 1981). 

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