Two approaches to effectively reduce the size of radiative heat transfer problems in multidimensional geometry

Mathematical modelling of kinetic nonstationary transfer of radiation energy is a laborintensive and consuming task. This is due to nonlinearity and high dimensionality of the system to solve. Generaly the kinetic transfer equation is solved in 7-dimensional phase space, which requires vast computational resources. Historically, some attempts were made to simplify the initial system to solve. But simplifying assumptions can a priori degrade the solution quality. Quasi-diffuse approximation for neutron transfer proposed in 1964 by V.Ya. Gol'din was a meaningful step forward in this direction and later it became one of the effective methods to solve uncharged particle transfer problems. The quasi-diffusion method makes allowance for kinetic effects via coefficients calculated in periodic solving of the kinetic equation. There exist other approaches to simplify the initial system. In 2010 M.Yu. Kozmanov and N.G. Karlyhanov proposed a model for 1D geometry which was ideologically close to the quasi-diffusion algorithm. The coefficients obtained in solving the kinetic equation are entered into the model. The approach is being actively developed at RFNC-VNIITF on practical as well as on theoretical level and the user experience suggests its wide application. The paper briefly describes two models and set out the calculation results for two test problems in 2D axially symmetric geometry.