ON THE PROBLEM OF MODELING TEMPERATURE FIELDS IN BODIES WITH VARIABLE BOUNDARIES

Abstract

Introduction. When melting, solidifying and oxidizing a metal, the problem arises of calculating the temperature field in areas with time-varying boundaries. Usually, to solve the heat equation in such cases, the method of catching the boundary into a node of a spatial grid is used, which necessitates the use of a variable time step in calculations, in addition, the number of spatial nodes will also be variable. All this leads to a change in the amount of computational work. However, in many cases the method of grids with moving nodes may be more preferable, in this case there is no need to change the number of spa-tial nodes and the time step. Purpose of the study. Develop an algorithm for approximating the convective boundary condition for grids with moving nodes. Materials and methods. The analysis and generalization of literature data on the problem is carried out. It has been established that the direct replacement of derivatives in the boundary condition by finite differences leads to a large error in calculating the surface temperature and, as a result, the entire temperature field of the body. When using a grid with a constant spatial step for a finite-difference approximation of the boundary condition, one can use the Beck formula. There is no formula similar to the Beck formula in the literature for meshes with moving nodes, so the problem arises of determining such a formula. To solve the stated problem of approximation, the method of heat balance for an elementary cell near the surface of the body is applied. Results. An analogue of the Beck for-mula for grids with moving nodes is found. The obtained finite-difference formula was tested, including with the help of a computational experiment. Conclusion. The obtained formula for approximating the convective boundary condition for grids with moving nodes can be a kind of addition to the theoretical foundations of the method of grids with moving nodes used in practice for calculating temperature fields in areas with variable boundaries; its application makes it possible to increase the accuracy of calculating the temperature field of a body.