International Conference on Mathematics, Computational Methods & Reactor Physics (M&C 2009) Saratoga Springs, New York, May 3-7, 2009, on CD-ROM, American Nuclear Society, LaGrange Park, IL (2009) ON THE ADEQUACY OF CARTESIAN GEOMETRY DISCRETE ORDINATES SOLUTIONS FOR ASSEMBLY CALCULATIONS Sebastian Schunert and Yousry Y. Azmy Department of Nuclear Engineering North Carolina State University 1110 Burlington Laboratories, Raleigh, NC 27695-7909 snschune@ncsu.edu; yyazmy@ncsu.edu ABSTRACT The current generation of lattice codes employs the method of Collision Probabilities (CP), the Method of Characteristics (MOC) or methods derived thereof to solve the two-dimensional multigroup transport equation on the assembly level. We compare the attainable solution accuracy of the lattice code DRAGON to the accuracy of the Discrete Ordinates (DO) code DORT on the basis of the two-dimensional GE-13 assembly in order to determine if the DO on Cartesian meshes is suitable as flux solver in future lattice codes. If DO exhibits high accuracy for assembly configurations, the next question is at what computational expense compared to traditional assembly codes. For this purpose DORT and DRAGON are required to converge to a reference solution, obtained by a multigroup MCNP calculation, with increasing angular quadrature order and decreasing spatial cell size; additionally for DRAGON the reference solution must be approached with increasing tracking density. The convergence of the two codes is judged via the multiplication factor, the pinwise relative error in the fission production rate, it’s RMS and the maximum of it’s absolute value over all pins. Additionally the computational cost of the obtained solutions is judged via the user CPU time. Although the multiplication factor computed by both codes converges with refinement of the employed meshes, the maximum deviation error of the fission production rate in the central region of the assembly remains unsatisfactorily high for CP and MOC. Key Words: Benchmark, Discrete Ordinates, Collision Probabilities, Method of Characteristics, Fuel Assembly 1. INTRODUCTION Contemporary lattice codes employ the method of Collision Probabilities (CP) and the Method of Characteristics (MOC) as flux solver because these methodologies permit exact representation of the circular shape (in 2D) of the fuel pin, whereas the method of Discrete Ordinates (DO) requires staircasing or tessellating the fuel pin’s circumference. However, both the method of CP and the MOC suffer from other drawbacks some of which are essential to the respective computational scheme and thus indispensable. For example, CP only allows employing isotropic and isotropic transport-corrected scattering cross section sets[3]. While tranport-corrected scattering cross sections might be a sufficient representation of the scattering in PWR assemblies, they are demonstrated in [8] to be in general insufficient for BWR assemblies. In contrast, the MOC is not limited with respect to it’s ability to accurately represent scattering anisotropy, but it suffers from slow convergence and massive memory demand, which often requires storing the tracking information to a binary file. We conjecture that DO on Cartesian meshes, given appropriate stair-casing is employed, can supply numerical results of an accuracy comparable to CP and