A first collision source method for coupling Monte Carlo and discrete ordinates for localized source problems

A difficult class of problems for the discrete-ordinates neutral particle transport method is to accurately compute the flux due to a spatially localized source. Because the transport equation is solved for discrete directions, the so-called ray effect causes the flux at space points far from the source to be inaccurate. Thus, in general, discrete ordinates would not be the method of choice to solve such problems! It is better suited for calculating problems with significant scattering. The Monte Carlo method is suited to localized source problems, particularly if the amount of collisional interactions is minimal. However, if there are many scattering collisions and the flux at all space points is desired, then the Monte Carld method becomes expensive. To take advantage of the attributes of both approaches, we have devised a first collision source method to combine the Monte Carlo and discrete-ordinates solutions. That is, particles are tracked from the source to their first scattering collision and tallied to produce a source for the discrete-ordinates calculation. A scattered flux is then computed by discrete ordinates, and the total flux is the sum of the Monte Carlo and discrete ordinates calculated fluxes. In this paper, we present calculational results using the MCNP and TWODANT codes for selected two-dimensional problems that show the effectiveness of this method.