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2 2007

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The use of Morris method in sensitivity analysis of a numerical model of solidification

Sczygiol N., Dyja R.

Computer Methods in Materials Science

2007

Vol. 7, No. 2

250-254

Numerical models which are created nowadays can be characterised by a high degree of complication. This complication concerns mainly big number of parameters of a model. As it turns out, not all parameters have equal influence on received results. Some of parameters have dominant influence, whereas influence of the other parameters is marginal and can be neglected with success. This means that part of parameters which are costly to determine and determination of which can require long-lasting research can be skipped in a given model without large influence on received results. And vice versa: some parameters which have dominant influence on results should be specified with the highest possible precision. Sensitivity analysis deals with the task of division of these parameters with regard on received results. In the sensitivity analysis we can distinguish between a local approach as well as a global approach. In case of the local approach the task is to investigate the influence of changes of individual parameter on received results with an assumption of unchangeability of other parameters. On the other hand, the global approach implies that the values of remaining parameters undergo changes, too. Many methods, varying among other things in computational time, belong to the global sensitivity analysis. The presented work concentrates on global sensitivity analysis, and particularly on one of method which belongs to global sensitivity analysis methods. Method used in this work is known in literature as Morris method. The most important feature of Morris method is its cheapness, which means the possibility to obtain the results with comparatively small effort of calculations. This feature enables its usage in case of models requiring qualification of many parameters, as well as in case when the models require many calculations. Such a situation takes place in case of numerical modelling of solidification process. And for this reason Morris method was decided to be used in sensitivity analysis of numerical model of solidification, because numerical modelling of solidification requires long time of calculations. In the presented work a solver that is part of Nuscas system is analysed. Nuscas is developed in the Institute of Computer and Information Sciences at Czestochowa University of Technology. The solver, which is used in numerical simulation of solidification process makes it possible to choose between explicit capacity and basic enthalpy formulation. It is also possible to choose the model of solid phase growth from models of equilibrium, nonequilibrium and intermediate growth of solid phase. The executed sensitivity analysis permits to rank given parameters with respect to their influence on received results. That knowledge allows distinction of particularly important parameters, as well as these parameters, which have little influence.

W przedstawionej pracy zamieszczone jest omówienie analizy wrażliwości numerycznego modelu krzepnięcia za pomocą metody Morrisa. Analiza wrażliwości pozwala na badanie wpływu poszczególnych parametrów na uzyskiwane wyniki. Pozwala to ustalić parametry, które mają znaczny wpływ na wyniki, jak również te, których wpływ jest niewielki. Metoda Morrisa jest szczególnie przydatna do badania modeli, wymagających dużego nakładu obliczeń lub są opisane dużą liczbą parametrów, z powodu niewielkiej wymaganej przez nią wyk nanych symulacji komputerowych. Analiza wrażliwości numerycznego modelu krzepnięcia opracowanego przez autoró pracy jest przedstawiona jako przykład zastosowania metody Morrisa.

Evaluating the influence of selected parameters on sensitivity of a numerical model of solidification

Sczygiol N., Dyja R.

Archives of Foundry Engineering

2007

Vol. 7, iss. 4

159-164

Presented paper contains evaluation of influence of selected parameters on sensitivity of a numerical model of solidification. The investigated model is based on the heat conduction equation with a heat source and solved using the finite element method (FEM). The model is built with the use of enthalpy formulation for solidification and using an intermediate solid fraction growth model. The model sensitivity is studied with the use of Morris method, which is one of global sensitivity methods. Characteristic feature of the global methods is necessity to conduct a series of simulations applying the investigated model with appropriately chosen model parameters. The advantage of Morris method is possibility to reduce the number of necessary simulations. Results of the presented work allow to answer the question how generic sensitivity analysis results are, particularly if sensitivity analysis results depend only on model characteristics and not on things such as density of the finite element mesh or shape of the region. Results of this research allow to conclude that sensitivity analysis with use of Morris method depends only on characteristic of the investigated model.