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The use of smoothed particle hydrodynamics for simulating crystal growth from solution. (English) Zbl 1213.80024

Summary: Most numerical simulations for crystal growth processes have been performed using the finite volume and finite element techniques. Both of these methods require adaptive meshes to track the growth and dissolution interfaces. In addition, in the growth of ternary systems the solid and liquid phases must be solved simultaneously, which requires iterations at the interfacial boundaries between solid and liquid regions. Such iterations slow down simulations tremendously, and also lead to numerical instabilities. In order to address these issues, an alternative mesh-free, Lagrangian method, known as smoothed particle hydrodynamics (SPH) has been investigated. For the simulation, the liquid phase diffusion (LPD) growth of Si\(x\)Ge\(1 - x\) has been selected, since both experimental and finite volume simulation results were available for comparison. This comparison between finite volume and SPH simulations shows that although SPH has the potential to accurately model the crystal growth process, the number of SPH particles required for accurate predictions is upwards of 60,000 particles for the Reynolds number of the LPD system. This high number of particles translates to a computational time of approximately six times longer than the equivalent finite volume simulations. However, future improvements made to the relatively young SPH method may overcome such computational difficulties.

MSC:

80A22 Stefan problems, phase changes, etc.
82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
76M28 Particle methods and lattice-gas methods
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