STABLE EXCHANGABLE BOUNDARY CONDITIONS IN THE DIFFUSION-VACUUM MODEL OF THE RADIANT HEAT TRANSFER

A. A. Bazin, G. I. Skidan, B. P. Tikhomirov
VANT. Ser. Mat. Mod. Fiz. Proc 1998. Вып.3. С. 17-23.

      The stability of the method of separate computation by regions is considered for two diffusion and equation integration algorithms. The stability condition is discussed for the algorithm in which a radiation flux is transferred from the diffusion region into the vacuum one and temperature — from the vacuum region into the diffusion one. The conditionlessly stable algorithm for setting up exchangable boundary conditions is given, consisting in one-side flux transmission. Computed data of two model problems having an exact analytical solution are presented.

      The paper deals with calculation method for heat transfer problems based on diffusion and vacuum approximations. Stable exchange boundary conditions are introduced for solution conjugation of the nonlinear heat conduction equation (or radiation diffusion equation) with integral equation for heat exchange of radiation on the opacity boundary. The boundary conditions of diffusion type are discussed, a simple method for diffusion flux restriction is proposed.
      An example of a radiant heat exchange problem with analytical solution is constructed; the accuracy of the model problem calculation is estimated with this problem. Computed data for a model problem of temperature distribution on box and container walls at fire are presented.

      One of the possible options is discussed for the medium motion within the diffusion-vacuum model for radiant energy transfer calculation in the optically nonhomogeneous 2D and 3D systems.
      2D computed data are given for X-ray field in the laser cylindrical targets of small diameter. The radiation field symmetry on the capsule surface of the heavy-ion cylindrical target is considered.