Arbitrary Lagrangian-Eulerian method for coupled Navier-Stokes and convection-diffusion equations with moving boundaries

摘要

Using the arbitrary Lagrangian-Eulerian method, an accurate description of the melt flow and impurity distribution in a time-dependent domain Ω(t), t∈[0, T], is performed. The procedure is developed for a crystal fiber grown from the melt by the edge-defined film-fed growth (EFG) technique, on the basis of the finite-element method using COMSOL Multiphysics software. For this, an EFG system without melt replenishment (the melt level in the crucible decreases in time) is considered. By coupling three application modes - incompressible Navier-Stokes, moving mesh arbitrary Lagrangian-Eulerian, and convection-diffusion - it is illustrated, in the time-dependent case, how the pull of the crystal, with a constant rate v_(in), generates the fluid flow, and it is shown how the resulting fluid flow and deformed geometry determine the impurity distribution in the melt and in the crystal.