A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
A level set formulation of Eulerian interface capturing methods for incompressible fluid flows
Journal of Computational Physics
Computation of three dimensional dendrites with finite elements
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
Second-order phase field asymptotics for unequal conductivities
SIAM Journal on Applied Mathematics
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
Multiscale finite-difference-diffusion-Monte-Carlo method for simulating dendritic solidification
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
Numerical simulation of dendritic solidification with convection: three-dimensional flow
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Optimal Control of the Classical Two-Phase Stefan Problem in Level Set Formulation
SIAM Journal on Scientific Computing
Journal of Scientific Computing
Hi-index | 31.45 |
Dendritic solidification of pure materials from an undercooled melt is studied using the extended finite element method/ level set method for modelling the thermal problem and a volume-averaged stabilized finite element formulation for modelling fluid flow. The extended finite element method using evolving enrichment functions allows accurate modelling of the discontinuous thermal conditions at the moving sharp freezing front thus capturing its motion precisely. The solution of the velocity field in the melt is obtained assuming that the sharp-interface is diffused over the length of two finite elements. The methodology presented is shown to be an effective tool for capturing the interface phenomena and freezing interface growth using a single uniform finite element grid. The whole formulation is packaged into a flexible, modular and parallel library with the ability to incorporate new physics. Comparisons with other numerical methods as well as analytical results emphasize the fidelity of the method in modelling the underlying physical phenomena and growth mechanisms. Various examples of dendritic growth in two- and three-dimensions are presented.