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On the Ronen Method in Simple 1-D Geometries for Neutron Transport Theory Solutions
Journal of Computational and Theoretical Transport ( IF 0.7 ) Pub Date : 2020-11-23 , DOI: 10.1080/23324309.2020.1843496
Daniele Tomatis 1 , Roy Gross 2 , Erez Gilad 2
Affiliation  

Abstract

In this work, we apply the Ronen method to obtain highly-accurate approximations to the solution of the neutron transport equation in simple homogeneous problems. Slab, cylindrical, and spherical geometries are studied. This method demands successive resolutions of the diffusion equation, where the local diffusion constants are modified in order to reproduce new estimates of the currents by a transport operator. The diffusion solver employs here finite differences and the transport-corrected currents are forced in the numerical scheme by means of drift terms, like in the CMFD scheme. Boundary conditions are discussed introducing proper approximations to save the particle balance in case of reflection in the slab. The solution from the Ronen iterations is compared against reference results provided by the collision probability method. More accurate estimates of the currents are provided by integral transport equations using first flight escape probabilities. Slow convergence on the scalar flux is analyzed, although the results match the reference solutions in the limit of fine meshes and far from the bare boundary.



中文翻译:

中子输运理论解的简单一维几何中的Ronen方法

摘要

在这项工作中,我们应用Ronen方法获得简单均质问题中中子输运方程解的高精度近似值。研究了平板,圆柱和球形几何形状。该方法需要连续求解扩散方程,其中修改局部扩散常数以便由运输运营商重现电流的新估计值。扩散求解器在这里采用有限的差,并且像CMFD方案一样,在数字方案中,通过漂移项迫使经过输运校正的电流。讨论了边界条件,引入了适当的近似值,以防止在平板中发生反射的情况下保持粒子平衡。将Ronen迭代的解决方案与碰撞概率方法提供的参考结果进行比较。通过使用第一逃逸概率的积分输运方程式,可以更准确地估算电流。尽管结果在细网格的范围内且远离裸边界,但与参考解相匹配,但分析了标量通量的慢收敛性。

更新日期:2020-11-23
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