SOLUTION OF THE TRANSPORT EQUATION BY THE Sn METHOD

The S/sub n/ method is a powerful tool for tne analysis and numerical solution of a large variety of reactor problems. Basically, S/sub n/ is a finite difference technique which proceeds in the following general way: The coatinuous angular variable in the transport equation is replaced by a discrete variable, whereupon the transport equation becomes a system of coupled partial differential equations, and, if certain specified conditions are met, a system of equations called the S/sub n/ equations. These have a number of desirable properties, in particular, the S/sub n/ equations may be readily solved successively. The solution of the S/sub n/ system approaches the solution of the transport equation as the number of discrete angles is increased, and the solution of the S/sub n/ difference equations converges to the solution of the S/sub n/ equations as the space mesh is refined. The transport equation is basically a conservation law and this feature can be carried to the S/sub n/ difference equations. The S/sub n/ method is then generalized to the cases of multiple velocity groups, inhomogeneous source terms, and geometrics of higher order. To solve the X difference equations for the many problem types annd physical situations which arise,more » a number of numerical techniques are required. Many of these are explained, in particular, the basic iteration methods annd the procedures used to establish and speed connvergennce. The accuracy of the S/sub n/ method is stated as a function of n, the number of space points, and other parameters. The accuracy of the S/sub n/ methods for reactor cell calculations and disadvantage factor calculations is discussed in some detail. Finally, a number of practical topics are reviewed, such as the selection of velocity groups, the problem of choosing cross section, and the comparison of calculation with experiment. (auth)« less