Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Computation of dendrites using a phase field model
Proceedings of the twelfth annual international conference of the Center for Nonlinear Studies on Nonlinearity in Materials Science
A front-tracking method for dendritic solidification
Journal of Computational Physics
A simple level set method for solving Stefan problems
Journal of Computational Physics
Modeling melt convection in phase-field simulations of solidification
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
A Level Set Approach for the Numerical Simulation of Dendritic Growth
Journal of Scientific Computing
Journal of Computational Physics
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In this paper we simulate the evolution and free particle motion of an individual nucleus that grows into a dendritic crystal. The melt flow and the convective heat transfer around the crystal are simulated as they settle due to gravity. There is an intricate coupling between the settling and the evolution of the crystal. The relative flow induced by the settling enhances the growth at the downward facing parts, which in its turn affects the subsequent settling motion. Simulations have been done in two dimensions using a semi-sharp phase-field model. The flow was constrained to a rigid body motion by using Lagrange multipliers inside the solidified part. The model was formulated using two different meshes. One is a fixed background mesh, which covers the whole domain. The other is an adaptive mesh, where the node points are also translated and rotated with the movement of the solid particle. In the latter, the dendritic growth is simulated by the semi-sharp phase-field method.