Numerical approximation of convective boundary conditions for grids with mobile nodes

Abstract

Usually, to solve the equation of heat conduction in the areas with variable time boundaries are used in
the method of catching a boundary node spatial grid, which necessitates the use in the calculations of the step
of alternating in time, moreover, be variable, and the number of spatial nodes. However, in many cases, may be more preferable method meshes with mobile nodes, in this case there is no need to change the number of spatial nodes and a time step. In this paper, for meshes with mobile nodes consider the problem of approximating
the convective boundary condition. Direct replacement of derivatives in the boundary condition by finite differ-ences leads to large error calculating surface temperature and, therefore, the whole temperature field of
the body. When using a grid with a constant pitch in space in order to increase the accuracy of calculations
for finite-difference replace the boundary condition formula can be used Beck. In the literature for meshes with mobile nodes formulas similar to Beck, is not, so there is the problem of determining such a formula. To solve the problem of approximation of the method of heat balance of the unit cell in the body surface. Performed testing of the resulting finite-difference formulas, including using a computational experiment. The results obtained can be used in the construction scheme for computing with mobile nodes.