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

Abstract

Introduction. The widespread use of cast products made of aluminum and its alloys requires ensuring a highquality structure of the castings, on which their operational properties depend. Controlling the process of forming a high-quality structure of castings is possible, in particular, by the method of electrocurrent treatment of melts.Problem Statement. The melt medium being inaccessible for direct measurement of the processing parameters, the only way to realize the control of treatment conditions is numerical simulation of these parameters. However, the complexity and interdependence of multiphysics processes of melt electrocurrent treatment have led to an unconventional approach to the formulation of their mathematical models and computational procedures. These circumstances have determined the features of the tasks for the construction of appropriate computer models and their application.Purpose. The development of a new pattern-modular system for computer modeling of multiphysics processes of electric current treatment of melts to control the conditions of the formation of a qualitative structure of castings.Materials and Methods. The material of the research is a set of model problems of multiphysical processes of electrocurrent treatment and their ontology, the integral equations and their properties, as well as databases on the parameters of simulated objects, which describe these processes. The method of ontological taxonomy has been used to create a taxonomic codifier, with the help of which model problems and mathematical tools for their solution have been systematized. Based on the signs of similarity, the method of formalization of integral equations of coupled multiphysics processes has been applied. Results. The unified patterns of basic algorithmic procedures and a library of program modules for computing operations of partial tasks, for which a unique code is assigned according to the codifier have been developed. Combining the patterns with different modules that are identified by the indicated codes has made it possible to form a wide range of computer models reflecting multiphysics processes. A flexible system for computer modeling of multiphysical processes has been built and its efficiency for simulating the modes of electrocurrent treatment of melts has been confirmed.Conclusions. The results obtained have enabled controlling the conditions of electrocurrent treatment of melts to form a highquality structure of cast metal.

The Novel Mathematical Model and Methodology for Computer Simulation of Magnetic Field in a Nonlinear Medium

“…Their solution is carried out with numerical methods by reducing to systems of linear algebraic equations (SLAE) specifi ed on grids with a large number of fi nite or discrete elements (DE) [10,11]. Algorithms that are required to implement computational procedures in such methods have a complex arrangement with a multi-level structure of cyclic operations for processing the big arrays and require careful preparation of initial data [12,13].…”

“…The nonlinearity of the characteristics of the magnetic materials from which the MS is made complicates such calculations even more, because the original fi eld equations become nonlinear, and for their solution it is necessary to use iterative methods, the convergence of which often turns out to be uncertain [13,14]. Therefore, in some articles various forms of analytical approximation of the magnetization curve [6,15] are proposed to improve computer models of MS, which are declared as means of achieving high accuracy of results.…”

“…When solving presented problem, the author proceeded from the methodological principles applied in [13] for the synthesis of computer models of complex physical processes, which take into account the connections between the phenomenological interpretation of physical phenomena, their mathematical models, and computational algorithms. From such positions, ensuring the logi cal unity of the physical and mathematical aspects of the novel mathematical model of magnetic fi eld in a nonlinear medium proposed in this work requires, in particular, the defi nition of its phenomenological framework related to fi eld sour ces that are explicitly or implicitly present in all equations of magnetic fi elds.…”

“…Then equation ( 10) takes the form divH = -H  gradμ/μ, (13) and equation ( 11) turns into the Poisson equation:…”

Experimental study of the effect of the simultaneous treatment of the melt with different currents on the quality indicators of castings

“…When studying the effect of M -C, the previously obtained conditions of CECT with one type of current should be used [10][11][12][13][14]. To lead current into the melt, we use thin titanium electrodes with an insulated side surface.…”