REDUCTION OF THE CALCULATION TIME IN THE MODELING OF THE MICROSTRUCTURE FOTMATION BY CARD METHOD

Abstract

In the CAFD solidification modeling (Cellular Automaton + Finite Difference) as the growing grains shape, as the final microstructure of the alloy were not superimposed beforehand but were obtained in the simulation. CAFD models take into account heat transfer, components diffusion in the solid and liquid phases, nucleation kineties, solid border migration and liquid phase vanishing etc. Computer methods that include the solutions for all above mentioned phenomena are very time-consuming. The "bottleneck" of the models is the temperature field calculation. Acceleration of the well-known Gauss-Seidel (GS) iterative method of the numerical solution of the difference equations set was proposed by mean the selective reduction of the iteration number for the different equations used in the temperature field modeling. Computer modeling results obtained by the known GS method and results of the proposed reduced scheme using were compared with the known analytical solution of the Schwarz task. It was shown that the reducing of the solution tolerance results in the substantial increase of the solution time but has a smali influence on the mean quadrate deviation between the numerical results and the analytical one. Proposed solution scheme results in the significant reduction of the calculation quantity and the simulation time.