Application of sensitivity analysis in numerical modelling of castings solidification

摘要

The modern methods of foundry technologies designing bases on the equations and mathematical formulas resulting directly from the analytical solutions of the models describing the physical processes or on the results of computer simulations of the processes discussed (e.g. solidification and cooling). The main advantage of the analytical methods is the general character of the formulas - in the place of symbols we can introduce practically optional numerical values. The essential fault of such approach are the numerous simplifications in mathematical models of the phenomena analysed because, as a rule, it is the necessary condition assuring the obtainment of effective and practical solution of the problem. The numerical methods allow to consider the physical process on the essentially higher level of complexity but on the other hand, the solution obtained concerns only the individual case. The researches working in the scope of thermal theory of foundry processes present two different points of view and they very often expose the good and bad points of both approaches. Professor W Longa for whom we have a pleasure and honour to dedicate this paper prefers rather the analytical methods, whereas we develop the numerical approach to the modelling of solidification. In this paper we are going to show the possibilities of the generalization of the results obtained using the numerical methods and the very effective tool for such problem solution is the sensitivity analysis.