ON TWO APPROACHES ÒÎ SPEEDING-UP ITERATION CONVERGENCY AT NUMERICAL SOLUTION OF RADIATION TRANSFER EQUATION WITH THE "ROMB" METHOD

A. A. Gadzhiev, A. A. Shestakov
VANT. Ser.: Mat. Mod. Fiz. Rroc 1989. Вып.3. С. 56-65.

      Iteration speeding-up methods are considered for combined solution of energy and radiation transfer equations in multigroup P₁-approximation witn the "ROMB" method. Speeding-up of iteration convergency is achieved by means of introduction of additional stage at which temperature is computed with a certain simplified model of transfer equation. The speeding-up methods are based on either Jacobi-type iterations or spectrum-averaging method. Extension of Jacobi-type iterations to two-point-type differnce schemes is suggested, and a new algorithm of iteration convergency speeding-up is derived for the averaging method. The methods considered may be extended to other transfer equation approximations and to more complex geometries.

      Solution of radiation transfer equation in multigroup P₁-approximation combined with the energy equation is considered. The difference technique is based on the two-point scheme "ROMB", possessing a number of advantages, such as single difference cell approximation, single computation of absorbtion coefficient in cell per iteration, simplicity of formulating boundary conditions, extentionabi1ity to many dimensions. The difference scheme includes parameters, the appropriate choice of which allows to combine second-order accuracy and monotonicity in optically dense media.Solution of radiation transfer equation in multigroup P;-approximation combined with the energy equation is considered. The difference technique is based on the two-point scheme "ROMB", possessing a number of advantages, such as single difference cell approximation, single computation of absorbtion coefficient in cell per iteration, simplicity of formulating boundary conditions, extentionabi1ity to many dimensions. The difference scheme includes parameters, the appropriate choice of which allows to combine second-order accuracy and monotonicity in optically dense media.