The geometric integrals method in modeling the processes of heat conduction with phase transformations

Applied Mathematics, Mechanics and Physics


Аuthors

Svetushkov N. N.

Abstract

To solve the problem of heat conduction in the media with temperature depended characteristics were applied approach, which generalizes the previously developed method, named «geometric integrals», for solving problems of heat transfer in heterogeneous media. This approach allows to arise the chained system of integral equations for solving 2D tasks with complex geometry. A distinctive feature of these equations is that the integral operator kernel has no singularities, and therefore the numerical solution derived no additional complexities associated with the need in some way to consider the special points (the points of discontinuity). This problem formulation allows one to perform uniform calculations over the entire solution area, including the near the boundary regions for geometrically complex objects.

Keywords:

heat treatment, structural changes, nanotechnology, modeling, numerical methods, partial differential equations, integral equations, the accuracy of calculations

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