Performance analysis of an efficient finite element solver for solidification simulation of continuous casting of steel billets

Abstract

The Gauss-Seidel iterative technique of solving a set of linear algebraic equations was applied for solving the system matrices in the Finite Element Analysis of 2-D dynamic heat diffusion problems encountered in the solid-ification analysis of continuous casting of steel,billets. An efficient algorithm for storing. and manipulating only the non-zero terms of the system matrices was developed. The CPU time per iteration for solving the system matrix was independent of bandwidth. The oscillatory character-istics of the algorithm with respect to different one-step recurrence schemes, the number of iterations for solution convergency and error propagation with respect to over-relaxation factor and convergence limit were studied for a standard problem and compared with analytical solution. The accuracy of the iterative solution was compared with the standard method of direct reduction based on Gauss elimination (active column reduction method). The itera-tive technique performed better than the direct method with respect to memory requirement and CPU time, achieving acceptable actuary limits. The solver was applied for the solidification simulation of continuously cast billets at Tata Steel. The 1-D heat flux formulation of the type q = A - B Alt applicable for the C.C. mould region was modi-fied to account for the lower heat flux at the billet corners. The midface shell thickness obtained by simulat-ion at mould exit was compared with the measured thickn-esses obtained from a breakout strand. The heat transfer coefficient in the spray cooling zone was adjusted to get an acceptable match between the measured and simulated shell thicknesses in the secondary cooling zone. The pro-gram was run on IBM PC AT computer with Intel 80486 CPU (33 MHz). The present implementation of the iterative techni-que for solving the system equations reduces the matrix solution time to (1/18) and the overall time for each time step to 1/8 the times required under direct methods, for the parameters considered. There was no appreciable error in the estimated shell thickness within the CC mould. However, the error in the •secondary cooling and the radi-ation zone ranged from 2 to -5%. The second norm of tempe-rature distribution across the billet- cross section varied from 0.001 to 0.005 for the entire strand.