A CONSERVATIVE DIFFERENCE SCHEME FOR TIME-DEPENDENT RADIATIVE HEAT TRANSFER PROBLEMS

B. P. Tikhomirov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1988. Вып.3. С. 27-33.

      Assuming a local thermodynamic equilibrium, boundary value problems are examined for a system of energy and time-dependent radiation transport equations in an absorbing, radiating.and isotropically dispersing medium. To solve boundary value problems numerically a weighted running computation scheme is proposed which contains (as a special case) a pure implicit difference approximation considered by others. The maximum principle is proved for radiation transport accounted by a spectral formulation. In a linear case a sufficient convergence condition is obtained for the scheme. An itaration method is developed for solving difference equations and the itarations are shown to converge with a geometric progression rate for cous- tant coefficient in a linear case. Computational results are given for text problems which have exact solutions.