Crystal growth and dendritic solidification
Journal of Computational Physics
Variational algorithms and pattern formation in dendritic solidification
Journal of Computational Physics
A front-tracking method for dendritic solidification
Journal of Computational Physics
A simple level set method for solving Stefan problems
Journal of Computational Physics
Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids
Journal of Computational Physics
Modeling melt convection in phase-field simulations of solidification
Journal of Computational Physics
Journal of Computational Physics
Front-tracking finite element method for dendritic solidification: 765
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
Numerical simulation of dendritic solidification with convection: two-dimensional geometry
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A volume of fluid method based on multidimensional advection and spline interface reconstruction
Journal of Computational Physics
Numerical simulation of dendritic solidification with convection: three-dimensional flow
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Short Note: Analytical and geometrical tools for 3D volume of fluid methods in general grids
Journal of Computational Physics
Estimating curvature from volume fractions
Computers and Structures
Hi-index | 31.45 |
A new approach to simulating the dendritic growth of pure metals, based on a recent volume of fluid (VOF) method with PLIC (piecewise linear interface calculation) reconstruction of the interface, is presented. The energy equation is solved using a diffuse-interface method, which avoids the need to apply the thermal boundary conditions directly at the solid front. The thermal gradients at both sides of the interface, which are needed to obtain the front velocity, are calculated with the aid of a distance function to the reconstructed interface. The advection equation of a discretized solid fraction function is solved using the unsplit VOF advection method proposed by Lopez et al. [J. Comput. Phys. 195 (2004) 718-742] (extended to three dimensions by Hernandez et al. [Int. J. Numer. Methods Fluids 58 (2008) 897-921]), and the interface curvature is computed using an improved height function technique, which provides second-order accuracy. The proposed methodology is assessed 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.