Shape Related Colour Graphic Presentation of FDM-Results Modeling Solidification Processes in Near Net Shaped Castings

"Until now FDM-Techniques have been widely used for Modeling Solidification Processes in Castings. Often a rigid, regular type of enmeshment (cubes, , --) have been used. This has the advantage of low CPU-costs, but the disadvantage of a zig-zag presentation of the interface between the casting and the mold. The last point is the reason why FEM-Techniques, giving the possibility of a true presentation of the shape in the enmeshment, are increasingly used. The disadvantage is the high CPU-costs. In this paper, a technique is presented, which uses the FDM-Mesh with the zig-zag presentation of shape and ADI-Algorithms to calculate temperatures and gradients. The new idea is that the calculated parameters are not presented related to the mesh in which they are calculated, but displayed using the true shape of the casting. Such an advantage of both low CPU-costs and shape correct presentation of the calculated results are achieved. IntroductionThe main reason for using a regular type of enmeshment is that it gives the possibility, via ADI-Algorithms, of obtaining a very fast FDM-Technique. The technique presented by P.R. Sahm and P. N. Hansen (1984), and also used by E. Flender (1985), is numerically so stable that average time steps, at least 200 times larger than the limit given by the explicit FDM-Technique, can be applied. To obtain reasonably good results, average time steps in the range of 20 to 50 times the explicit limit seems to be applicable. It should be pointed out,however, that FDM-Techniques can be used on arbitrary nets, the disadvantages being the same as for the FEM-Techniques. This has, among others, been discussed by P.R. Sahm and P.N. Hansen (1984)."