Boundary Treatment of the Diffusion Synthetic Acceleration Method for Fixed-Source Discrete-Ordinates Problems in x-y Geometry

A study on the development of acceleration equations for boundary cells and the associated boundary conditions for the diffusion synthetic acceleration method of neutron transport problems in x-y geometry is described. Alcouffe’s algebraic manipulation of the P, equations resulting in a single diffusion equation is modified to obtain explicit acceleration equations for the boundary cells. To accomplish this, the discretization in space is performed according to the ordinary box-centered method. The resulting synthetic computation scheme is linear in its differenced form. The boundary cell difference equations are derived in a manner that exactly parallels the discretization of the diffusion equation for interior mesh cells and that of the transport equation. The importance of these equations in improving overall efficiency without sacrificing stability is discussed, as is the optimum choice of the boundary conditions associated with these equations.