A front-tracking method for dendritic solidification
Journal of Computational Physics
A variational level set approach to multiphase motion
Journal of Computational Physics
A simple level set method for solving Stefan problems
Journal of Computational Physics
Adaptive mesh refinement computation of solidification microstructures using dynamic data structures
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
Second-order phase field asymptotics for unequal conductivities
SIAM Journal on Applied Mathematics
Modeling melt convection in phase-field simulations of solidification
Journal of Computational Physics
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
Journal of Computational Physics
Front-tracking finite element method for dendritic solidification: 765
Journal of Computational Physics
Level set methods: an overview and some recent results
Journal of Computational Physics
Numerical simulation of dendritic solidification with convection: two-dimensional geometry
Journal of Computational Physics
Modelling dendritic solidification with melt convection using the extended finite element method
Journal of Computational Physics
Sharp interface tracking using the phase-field equation
Journal of Computational Physics
A level set simulation of dendritic solidification of multi-component alloys
Journal of Computational Physics
Multiscale modeling of alloy solidification using a database approach
Journal of Computational Physics
Modeling of solutal dendritic growth with melt convection
Computers & Mathematics with Applications
Short note: A volume of fluid approach for crystal growth simulation
Journal of Computational Physics
Lattice Boltzmann modeling of dendritic growth in forced and natural convection
Computers & Mathematics with Applications
Journal of Computational Physics
Extended stochastic FEM for diffusion problems with uncertain material interfaces
Computational Mechanics
Hi-index | 31.48 |
A method combining features of front-tracking methods and fixed-domain methods is presented to model dendritic solidification of pure materials. To explicitly track the interface growth and shape of the solidifying crystals, a front-tracking approach based on the level set method is implemented. To easily model the heat and momentum transport, a fixed-domain method is implemented assuming a diffused freezing front where the liquid fraction is defined in terms of the level set function. The fixed-domain approach, by avoiding the explicit application of essential boundary conditions on the freezing front, leads to an energy conserving methodology that is not sensitive to the mesh size. To compute the freezing front morphology, an extended Stefan condition is considered. Applications to several classical Stefan problems and two- and three-dimensional crystal growth of pure materials in an undercooled melt including the effects of melt flow are considered. The computed results agree very well with available analytical solutions as well as with results obtained using front-tracking techniques and the phase-field method.