Simulation of Dendritic Growth Using a VOF Method Available to Purchase

The volume of fluid (VOF) method is one of the most widely used methods to simulate interfacial flows using fixed grids. However, its application to phase change processes in solidification problems is relatively infrequent. In this work, preliminary results of the application of a new methodology to the simulation of dendritic growth of pure metals is presented. The proposed approach is based on a recent VOF method with PLIC (piecewise linear interface calculation) reconstruction of the interface. A diffused-interface method is used to solve the energy equation, which avoids the need of applying the thermal boundary conditions directly at the solid front. The thermal gradients at both sides of the interface, which are needed to accurately obtain the front velocity, are calculated with the aid of a distance function. The advection equation of a discretized solid fraction function is solved using the unsplit VOF advection method proposed by Lo´pez et al. [J. Comput. Phys. 195 (2004) 718–742] (extended to three dimensions by Herna´ndez et al. [Int. J. Numer. Methods Fluids 58 (2008) 897-921]). The interface curvature is computed using an improved height function (HF) technique, which provides second-order accuracy. The assessment of the proposed methodology is carried out by comparing the numerical results with analytical solutions and with results obtained by different authors for the formation of complex dendritic structures in two and three dimensions.