EXACT SOLUTIONS OF AN EQUATION SYSTEM FOR ISOTROPIC RADIATION AND ENERGY TRANSPORT IN THE CYLINDER SYMMETRIC GEOMETRY

A.S. Vershinskaya, V.Yu. Gusev, V.V. Zavyalov
VANT. Ser.: Mat. Mod. Fiz. Proc 2001. Вып.2. С. 63-71.

Exact solutions of the traveling wave type are constructed for nonlinear integro-differential equation system of isotropic time-dependent transport of radiation and energy in the cylinder symmetric geometry with suitably selected absorption and scattering factors both for a "grey matter" approximation and for a spectral case. In so doing the scattering factor is assumed to be proportional to the absorption factor which is in its turn completely estimated by logarithmic derivative of equilibrium density with respect to the self-similar variable x and similarly by Planck function for a spectral case. The analytical solutions obtained can be used for testing numerical methods for radiant heat exchange problems computation.

The paper presents a modification of the characteristic method that provides an interpolation within high accuracy for solving an equation set containing radiation transport and energy equations. The value at the characteristic endpoint at the n-th step is obtained using a high-order interpolation spline and corrected by balancing. The method allows for parallel computations of the above set of equations.