NUMERICAL MODEL FOR DENDRITE GROWTH - AN APPLICATION OF THE RANK CONTROLLED DIFFERENTIAL QUADRATURE METHOD
DOI:
https://doi.org/10.7494/mafe.2012.38.1.55Keywords:
numerical modelling, rank controlled differential quadrature, dendrite growth, moving grid problem, crystallizationAbstract
Rank Controlled Differential Quadrature (RCDQ) is an innovative method for numerical approximation of problems described by Partial Differential Equations (PDEs). In this paper the authors apply the RCDQ for the numerical simulation of a simplified model for dendrite growth during Al-Ti alloy crystallization. The authors put most concern on building an accurate numerical model for this phenomenon. In the simplified model the symmetry and flux on boundary condition appears. Additionally, dendrite tip growth into adjacent liquid change the computation domain size, what indicates a need for node coordinate recalculation during each new time step. The authors analyze the results of numerical modelling of alloying element concentration and dendrite growth rate. The modelling results shows that the RCDQ method can be used for modelling problems with moving grid and that the method approximation proposed by the authors is proper.
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