Geometrical Platform of Big Database Computing for Modeling of Complex Physical Phenomena in Electric Current Treatment of Liquid Metals

Abstract

According to the principles of multiphysical, multiscale simulation of phenomena and processes which take place during the electric current treatment of liquid metals, the need to create an adjustable and concise geometrical platform for the big database computing of mathematical models and simulations is justified. In this article, a geometrical platform was developed based on approximation of boundary contours using arcs for application of the integral equations method and matrix transformations. This method achieves regular procedures using multidimensional scale matrices for big data transfer and computing. The efficiency of this method was verified by computer simulation and used for different model contours, which are parts of real contours. The obtained results showed that the numerical algorithm was highly accurate based on the presented geometrical platform of big database computing and that it possesses a potential ability for use in the organization of computational processes regarding the modeling and simulation of electromagnetic, thermal, hydrodynamic, wave, and mechanical fields (as a practical case in metal melts treated by electric current). The efficiency of this developed approach for big data matrices computing and equation system formation was displayed, as the number of numerical procedures, as well as the time taken to perform them, were much smaller when compared to the finite element method used for the same model contours.

Innovative System of Computer Modelling of Multiphysics Processes for Controlled Electrocurrent Treatment of Melts

“…All groups of data are transmitted to the first stage codifier (AMT-block) through separate information channels (buses): M and P types -through analogue (text) buses denoted by "A"; and S and T types -through digital buses denoted by "D".If "M-P" data are transferred to AMT-block directly in the form of introduced ontological lexemes, "S-T" data preliminarily come to autonomous processor block "GP-TP" for preparation of the numerical basis of MT. In this processor, with the use of the "geometric platform" (GP) algorithm [16], The results obtained are transmitted to the local processor "NL-GQ" in which the NLM-GQEI data protocols are formed, which are then used in ITIS. Note that actually the implementation of the above process on the basis of existing microprocessor elements is purely conditional, since it requires more powerful computing tools, but in fact they should be embodied in the algorithmic equivalent of the presented microprocessor chart.…”

“…In so doing, the correct calculation of the distribution of normals along the contour is extremely important for a clear numerical reproduction of the fundamental mathematical properties of kernels of type (3). Therefore for selected example the distribution of normals calculated with the use of the special algorithm named "geometrical platform" (GP) [16] developed by the authors is shown directly on the contour in Fig. 2, a.…”

“…Operators of SSSM software modules and their application. Integral operators and some other algorithmic manipulations that are used in procedural patterns (10)(11)(12)(13)(14)(15)(16) are specified in attributes B2-B3 and presented in the form of abstract prescriptions. Here is a more detailed description of the main operators.…”

Features of mathematical modeling of electromagnetic processing of bulk materials

“…One of the variants of such a procedure, quite compact and convenient under the name "Geometric IE platform" [38], was used for calculations in the example considered below.…”

Computer Models for Mode Control of Electric Current Treatment of Melts at Specified Quality Criteria for Cast Products. Part 1

“…В изложенных обстоятельствах стратегию построения системы УР-ЭТО и возможности ее автоматизации определяет тот факт, что практически единственным доступным средством получения информации об объекте в процессе ЭТО являются численные эксперименты [17,18]. Их суть заключается в поиске оптимальных сочетаний параметров режима обработки и получение оценок показателей качества отливки посредством решения задач о распределении локальных параметров внутренних процессов в расплаве с помощью математической модели.…”