三维球床几何稀疏条数长特征线加速方法

Sparse Macro-track Transport Acceleration Method for 3-D Pebble-bed Geometry

特征线法具有非常强的几何适应性,可用于三维球床高温气冷堆全堆芯求解,但存在迭代次数多、计算速度慢的缺点。本文将长特征线加速方法应用于三维球床高温气冷堆以解决非规则几何数值加速的问题,基于三维模型特征线布置较二维模型稠密的分析,提出了稀疏条数长特征线加速方法,极大地减少了加速方程的计算量,在不降低角度离散精度的前提下,获得了非常好的加速效果。通过基准题对加速参数的选取方式进行了研究,条数稀疏度取3~5、长特征线长度取2.0 cm左右、加速迭代步取20~60步可获得良好的加速效果。小型轻水堆三维基准题和球床堆芯简化模型的计算结果表明,采用稀疏条数长特征线加速可获得7倍左右的时间加速比,此时对应的迭代步加速比为20倍左右。

The method of characteristics has very strong geometric adaptability and can be used to solve the 3-D whole core problem of high temperature gas-cooled pebble-bed reactor.However,it suffers from the disadvantages of thousands of iterations and slow calculation speed.At present,there have been some attempts to reduce calculation time for method of characteristics,including coarse mesh finite difference(CMFD),general coarse mesh rebalance(GCMR)and general coarse mesh finite difference(GCMFD).The CMFD method is applied to realize the acceleration of regular region like squares.Furthermore,to break through the limitation of macroscopic regular geometry for the numerical acceleration method,researchers successively propose the GCMR method and the GCMFD method,but these methods are very complex to implement in irregular geometries and some approximation factors must be introduced.Based on the analysis of more dense tracks are arranged for the 3-D model,the sparse macro-track transport acceleration method was proposed,which greatly reduces the calculation amount of the acceleration equation and obtains a very good acceleration efficiency without reducing the accuracy.The 2-D method of characteristics divides the angular space into M azimuthal angles and P pole angles.The 3-D method of characteristics generally uses a level symmetric quadrature set.In 2-D geometry,the angle is relatively more dense at the poles.As a result,the 2-D macro-track transport acceleration can select a small number of azimuth angles with reflection symmetry and one pole angle as the solution directions of the acceleration equation.The sparse macro-track transport acceleration method implemented in this paper used the same angles as the method of characteristics.The number of tracks for 3-D problems is an order of magnitude higher than for 2-D problems.That is why reducing the number of 3-D tracks is a promising method for reducing the amount of accelerated equation calculation.This paper applied the macro-track transport acceleration method to 3-D whole core problem of high temperature gas-cooled pebble-bed reactor to solve the problem of irregular geometric numerical acceleration.The sparsity,macro-track length limit,and the maximum iteration step limit of the macro-track method are the main factors that affect the acceleration performance.The selection method of acceleration parameters was studied through two benchmark problems.Excellent speedup ratio can be obtained by setting the sparsity to 3-5,the macro-track length to around 2.0 cm,the acceleration iteration steps limit to 20-60.The results of 3-D small light water reactor benchmark and simplified pebble-bed reactor core model show that about 7 times the time speedup ratio and about corresponding 20 times the iterative step speedup ratio can be achieved.