STUDYING THE ACCURACY OF DIFFERENT METHODS OF AVERAGING THE HEAT CONDUCTIVITY COEFFICIENT ON AN INTEGRATION CELL SIDE DURING THE NUMERICAL SIMULATION OF THE HEAT TRANSFER EQUATION
E. V. Avdoshina, Yu. A. Bondarenko, A. A. Gorbunov, Yu. S. Dmitrieva, A. O. Naumov, S. N. Pronevich, N. M. Rud'ko, B. P. Tikhomirov
VANT. Ser.: Mat. Mod. Fiz. Proc 2014. Вып.3. С. 32-46.
The way of averaging the heat conductivity coefficient on an integration cell side during the numerical simulation of the 2D and 3D heat transfer equations has a significant effect on the accuracy of simulations for nonlinear heat waves. To find an average value of the heat conductivity coefficient during the numerical simulation of the heat transfer equation, some codes use arithmetic, harmonic, half-harmonic, modified harmonic and some other averaging methods. The paper gives analytical assessment of the accuracy of different methods used for averaging the heat conductivity coefficient on an integration cell side. Simulation results are presented for two problems, for which exact solutions are available. It is demonstrated that the most accurate results have been obtained using some types of the modified harmonic method of averaging, where temperature on a cell side can be found by solving the nonlinear equation constructed with the requirement of continuity of the heat flux across the cell side. Keywords: radiation heat transfer, heat conductivity coefficient, heat-transfer resistance, the flow balance method, test simulations.
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