Crystal growth and solute precipitation is a Stefan problem. It is a free boundary problem for a parabolic partial differential equation with a time-dependent phase interface. The velocity of the moving interface betw...Crystal growth and solute precipitation is a Stefan problem. It is a free boundary problem for a parabolic partial differential equation with a time-dependent phase interface. The velocity of the moving interface between solute and crystal is a local function. The dendritic structure of the crystal interface, which develops dynamically, requires high resolution of the interface geometry. These facts make the Lagrangian front tracking method well suited for the problem. In this paper, we introduce an upgraded version of the front tracking code and its associated algorithms for the numerical study of crystal formation. We compare our results with the smoothed particle hydrodynamics method （SPH） in terms of the crystal fractal dimension with its dependence on the Damkohler number and density ratio.展开更多
基金supported in part by the ITAPS Award from US Department of Energy DEFC0206ER25770the ARO Award W911NF0910306+1 种基金supported in part by the DOE subaward through RPI with the Prime Award DEFG0707ID14889supported in part by NSF Award DMS0809285
文摘Crystal growth and solute precipitation is a Stefan problem. It is a free boundary problem for a parabolic partial differential equation with a time-dependent phase interface. The velocity of the moving interface between solute and crystal is a local function. The dendritic structure of the crystal interface, which develops dynamically, requires high resolution of the interface geometry. These facts make the Lagrangian front tracking method well suited for the problem. In this paper, we introduce an upgraded version of the front tracking code and its associated algorithms for the numerical study of crystal formation. We compare our results with the smoothed particle hydrodynamics method （SPH） in terms of the crystal fractal dimension with its dependence on the Damkohler number and density ratio.
