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The mathematical modelling of radiation processes, based on experimental data of modern physics and traditional approaches of dimension theory, thermodynamics and gas dynamics is considered. Dimensional analysis allows predicting important characteristics of radiation processes (mass of particles-bosons radiation, the magnitude of the radiation pressure, the characteristic linear dimensions), and also indicate the possibility of superluminal motion (without violating the principle of causality). Methods of thermodynamics lead to the refined modelling of equilibrium radiation, the equation of state of radiation protection, determine the heat capacity and the value of radiation pressure in the source. Gas dynamics approaches to formulate a closed system is thermodynamically consistent conservation laws for radiation heat-conducting gas. In this direction we present one-velocity two-temperature and one-temperature approximation. Demonstrate some practical applications of the methods of modelling

Dimensional Analysis, Thermodynamics and Conservation Laws in a Problem of Radiation Processes Simulation