On stable algorithms and accurate solutions for convection-dominated mass transfer in crystal growth modeling

Time-dependent, three-dimensional flow and mass transport during solution growth of potassium titanyl phosphate

“…The three components of velocity, the pressure, and the supersaturation are approximated as linear combinations of equalorder, piecewise-linear, Lagrangian interpolation functions over tetrahedral elements. Solute transport in the KTP system is convection-dominated; hence, stabilized finite element formulations are employed for solution of the governing continuum transport equations [34]. We employ a modified version of the Galerkin/least-squares (GLS) [35] stabilization to obtain finite element weak forms of the governing equations; details of this procedure are described in Ref.…”

“…To ensure that the meshes used in the time-dependent computations are adequate, the elements close to the crystal surfaces were made approximately two times smaller than those in the corresponding steady-rotation cases (see Ref. [34]). Aggressive grading of the meshes was used to optimize the total degrees of freedom in these computations.…”

On the validity of boundary layer analysis for flow and mass transfer caused by rotation during the solution growth of large, single crystals

“…To obtain solutions for the convection-dominated mass transfer problem, we employ the streamline-upwind/Petrov-Galerkin (SUPG) stabilized formulation [32]; details are provided in Refs. [31,33]. The discretized set of nonlinear algebraic equations resulting from these weak forms is then solved using a modified Newton-Raphson method [34] with the aid of a direct frontal solver.…”

“…Hence, we employed the SUPG stabilized method in our solute transport computations; additional detail on SUPG effects in this system is available in Ref. [33].…”

Computer Modelling of Bulk Crystal Growth

“…Thin boundary layers in concentration through the fluid near the crystal surfaces are evident, as is a depletion plume of low-concentration solution trailing behind the crystal. More results are discussed in [51,117].…”