Research On Angular Discretization Errors Elimination In Discrete Ordinates Method

In the analysis of radiation shielding calculation,discrete ordinates method(SN method)is one of the main international calculation methods for nuclear device shielding currently.Because of solving transport equation along only a few specific directions,setting the continuous angular variables into finite number of discrete directions,SN method would produce angular discretization errors.Especially for isolated point sources,strongly absorbing media and large volume of void regions,angular discretization errors would be very obvious.There would be large difference between real value and calculated value.Therefore,to improve the accuracy of nuclear device shielding design,it makes great significance to research on eliminating angular discretization errors.Based on the theory of solving particle transport equation by SN method,the nature and cause of angular discretization errors are described and analyzed.Through deep researching and analyzing on angular discretization errors elimination methods,the advantages/disadvantages of fictitious source method and first collision source method are compared.Finally first collision source method is selected as major research direction.The detailed deducing of multi-group high order anisotropic scatter source is introduced during the study.Meanwhile,some advanced improvement such as source region treatment,modifying factor calculation and reflective boundary treatment are proposed.Based on the above theory,the 2D/3D angular discretization errors elimination programs RAY2D/3D are developed.To verify the feasibility of research method and the correctness of program,a series of test problems are calculated.The self-imposed problems,which include multi-sources model,multi-regions model and reflection boundary model,are calculated to show that RAY can treat point sources more than one placed at arbitrary positions,all point sources could not be placed on reflected boundaries in cases with reflection boundaries and ray tracing could improve computational efficiency.Kobayashi benchmarks and Azmy benchmarks which are proposed by radiation transport expert group in OECD/NEA.The calculated results are in good agreement with the benchmark report.In addition,the function of modifying factor calculation and source region treatment improve computational accuracy.China spallation neutron source problem is calculated to show the ability of multi-group anisotropic scatter source treatment,angular discretization errors can be effectively eliminated.