DEVELOPMENT OF THE METHOD FOR REDUCING A MODEL TO THE NONDIMENSIONALIZED FORM
Keywords:modeling of technical systems, model nondimensionalization, decrease in dimensionality of modeling space
We proposed the method that makes it possible to transform a mathematical model into the nondimensionalized form with a less number of nondimensionalized magnitudes, than it is prescribed by the Pi-theorem (in English literature – the Buckingham theorem, in French literature – the Vaschy theorem). The procedure of transformations is formalized and does not require highly qualified researchers for its implementation. The method is based on the synthesis of principles of the standard approach to nondimensionalization and natural measurement units. The solution of a nondimensionalization problem is based on the use of matrix methods.
The desire to transform a model towards a decrease in the number of magnitudes, included in it, without losing information, is stimulated by a number of emerging benefits. The possibility to obtain an assigned amount of information at fewer physical and numerical experiments, as well as new solutions, is implemented.
As a result of the research, there is a possibility to decrease the number of magnitudes, included in the transformed mathematical model. This is due to the introduction of proper measurement units (normalizing magnitudes) for each model separately, which corresponds to introduction of a natural coordinate system. The procedure is standardized and can be applied to any model, which is characteristic of the standard nondimensionalization methods.
Feasibility of the method was demonstrated using an example of reducing the model of hydraulic impact in pipes to the nondimensionalized form. The variants with and without taking into consideration of dissipative forces were explored. In each case, nondimensionalization was performed using the standard method and by using the developed procedures. In both cases, the application of the proposed method made it possible to decrease the number of nondimensionalized magnitudes compared with the results of using the standard approach.
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Copyright (c) 2018 Olexander Brunetkin, Oksana Maksymova, Fedir Trishyn
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