Abstract

The quasi-transfer approximation reduces the numerical solution of the kinetic equation to solving the diffusion equation through introducing correction factors. The transition to the diffusion equation simplifies the numerical solution of the kinetic equation and makes it possible to use monotonic schemes of the second order of accuracy in solving problems of radiative heat transfer. In this case, it is very important to know the behavior of the correction coefficients, because, for the correctness of the diffusion equation, it is necessary that the diffusion coefficient be positive. This can be verified most easily in problems having analytical solutions. The aim of this work is to study the quasi-transfer approximation in problems with an analytical solution and the behavior of correction coefficients in optically dense and transparent media.

中文翻译：

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解析解中的准传递近似分析

摘要

准传递近似通过引入校正因子将动力学方程的数值解简化为求解扩散方程。向扩散方程式的转换简化了动力学方程式的数值解，并使得可以使用二阶精度的单调方案来解决辐射传热问题。在这种情况下，了解校正系数的行为非常重要，因为对于扩散方程的正确性，扩散系数必须为正。在具有解析解的问题中，可以最容易地验证这一点。这项工作的目的是研究具有解析解的问题中的准传递近似，以及在光密和透明介质中校正系数的行为。