Вычисление индикаторов подобия и численное интегрирование критериев подобия, интервально-определённых в системе центр – радиус - Дубницкий, Валерий Юрьевич; Кобылин, Анатолий Михайлович; Кобылин, Олег Анатолиевич (Национальный технический университет "Харьковский политехнический институт", 2019)
Цель работы состоит в разработке методов вычисления и численного интегрирования критериев и индикаторов подобия, аргументами которых служат интервальные числа, заданные в системе центр –радиус. Результаты. Описано применение интервальных вычислений в системе центр – радиус для определения значений критериев и индикаторов подобия. Предложена методика численного интегрирования таблично заданной подынтегральной функции с произвольным расположением узлов интегрирования при условии, что исходные данные представлены в виде интервальных чисел, определённых в системе центр – радиус. Приведен численный пример, иллюстрирующий полученные результаты. Показано, что вычисление критериев и индикаторов подобия и функций от них без учёта их возможных интервалов определения может приводить к ошибочным выводам о результатах моделирования.

In frame of this work only physically realizable systems will be considered, namely such systems, which may be presented as unity of physical elements, structurally adjusted each to another and interacted with external medium. The physical modeling for such systems, that it is based on theory of similarities on starting stage of projecting, works as useful source of knowledge about their properties. It is known that theory of similarities studies the conditions for similarities of physical processes. Two physical processes are called similar, when they obey the same physical laws. Each quantitative characteristic for one of them is obtained from another by means of multiplication onthe constantvalue. This value is called the constant of similarity, and it is the same for all uniform values, which are involved in process under investigation. It is a rule in theory of similarities, that two phenomena are similar if and only if, when they are qualitatively similar and have equal values for some dimensionless parameters, which are called criterions of similarities. It is also rule in theory of similarities, that dimension of any physical value may be only the multiplication of values, which are in powers, and taken as basis values. Dimensions for both parts of equality, that presents same physical law, must be the same. Dimensionless multiplications of different powers are called as criteria of similarity. In this work some features of calculation processes, connected with definitions of numerical values for criterions of similarities, will be presented. Due to the fact, that numerical values of the similarity criterionsare obtained from the experimental results, these results are defined with some error, which influences the decision about similarities of the systems under comparison. To define this influence the procedure of calculation for criterions and indicators of similarities with the interval numbers is used, defined in the system center In frame of this work only physically realizable systems will be considered, namely such systems, which may physical model is considered, comparison was done for Reynolds criterion.
Derivation of the similarity indicators and numerical integration of the similarity criterions, which are interval-based in system center - radius
Keywords: теория подобия и размерностей; численное интегрирование таблично заданных функций с произвольно расположенными узлами; theory of similarity and dimensions; numerical integration of tabulated functions with arbitrary arrangement of nodes