ВИКОРИСТАННЯ ВКЛАДЕНИХ АДАПТИВНИХ СІТОК ДЛЯ МОДЕЛЮВАННЯ ПРОЦЕСІВ ТЕПЛОПЕРЕДАЧІ В ІНФОРМАЦІЙНО-КЕРУЮЧИХ СИСТЕМАХ СКЛАДНИХ ЗРАЗКІВ ТЕХНІКИ

Abstract

Modeling of processes on the use of adaptive grids for information and control systems of complex samples of equipment is offered. Application in the simulation of various natural phenomena and processes have obtained differential equations with partial derivatives. The principle of replacing the continuous domain of the unknown function by a discrete set of points (grid) is the basis of numerical methods for solving such equations. The complex solution of such problems is a definite scientific problem, the solution of which determines the accuracy of the numerical solution in areas where the gradient of the desired function reaches large values, significantly affects the accuracy of the solution throughout the region. The study considers the method of constructing nested adaptive difference grids for modeling heat transfer processes in information-control systems of complex samples of equipment, which are condensed in zones of rapid change of the desired function to solve two-dimensional nonstationary equation of thermal conductivity. Existing methods of constructing non-uniform grids before calculations, based on finding possible zones of high gradients are not effective in non-stationary problems, where these zones can change their position over time. The proposed algorithm for finding zones with significant gradients of the desired function in the process of the task analyzes the behavior of the function, controls the error and builds a time variable and a non-uniform difference grid. This significantly reduces the machine time required to solve problems with significant gradients in some areas of the computational domain. The solution of the problem for the main and nested grids can be performed in parallel, which will further reduce the time to solve when using multi-core systems. Keywords: computer model, finite difference method, difference mesh, nested mesh, modeling of heat transfer processes, information and control systems.