CRX: A code for rectangular and hexagonal lattices based on the method of characteristics

Abstract

A transport theory code CRX based on the method of characteristics with a general geometric tracking routine for rectangular and hexagonal geometrical problems is developed and tested for heterogeneous cell and assembly calculations. Since the method of characteristics uses the characteristic form of the Bolzmann transport equation, CRX has no practical limitations placed on the geometry of the problem and gives accurates solutions in strongly absorbing media. To relax the constraints of the existing characteristic transport calculation codes, a new treatment of the reflective condition is introduced. In this treatment, the external reflective boundary is discretized into small segments and the angular fluxes for rays along a segment are assumed to be uniform. Also, a new calculational procedure for condensation is devised to obtain an accurate energy spectrum of absorber cells: after the characteristic cell calculation, an S N transport calculation is performed for the assembly comprised of homogenized cells. The result is used to calculate group and angular octant dependent albedos on absorber cell boundaries. Then, the two-dimensional characteristic transport calculation with the albedo boundary conditions is performed again for absorber cells. Using the condensed group macroscopic cross sections, a two-dimensional characteristic transport calculation is performed for the heterogeneous assembly. To test the code, it is applied to several benchmark problems which consist of complex meshes and compared with other codes. The results show that the CRX code is very accurate.