TVDRSCHEMES TO SOLVE A SYSTEM OF RADIATIVE HEAT TRANSFER EQUATIONS
A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc 2019. Вып.2. С. 1736.
A great number of works are devoted to the problem of designing numerical methods to solve the radiative transfer equation. A separate group among them consists of the methods for solving the system of radiative heat transfer equations with an additional equation of internal energy of matter to account for the exchange processes of radiation/matter interaction. Due to the considerable nonlinearity of these processes, high requirements are set for the quality of the selected numerical techniques when solving the radiative heat transfer problems. Firstly, these techniques should incorporate an efficient method to resolve the nonlinearity of this problem. Secondly, because of the 7D space of all variables, the approximation system should be solved by a costeffective method, in which the number of arithmetic operations is proportional to the number of nodes of the difference mesh. Thirdly, along with natural requirements (approximation, absolute stability and convergence), the difference discretization should satisfy additional requirements of conservatism, unconditional monotonicity and positivity for positive functions. The paper presents the research on new implicit unconditionally monotone difference schemes of a higher order of approximation (higher than the first one) for the problems of radiative heat transfer. Keywords: radiative transfer equation, difference schemes.
