A Haar wavelet method for angularly discretising the Boltzmann transport equation
A Haar wavelet method for angularly discretising the Boltzmann transport equation
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DOI：
10.1016/j.pnucene.2018.05.023
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发表时间：
2018-09-01
影响因子：
2.7
通讯作者：
Pain, Christopher C.
中科院分区：
文献类型：
--
作者：
Adigun, Babatunde J.;Buchan, Andrew G.;Pain, Christopher C.
引入了一种新的层次Haar小波基来离散玻尔兹曼输运方程的角维。这与有限元子网格尺度方法结合使用。然后使用两个稳态辐射输运问题，即2D狗腿导管屏蔽问题和2D C5MOX OECD/NEA基准，验证了这种组合。该方案与传统的等加权离散坐标（S-n）角离散化有许多相似之处，但我们的分层Haar小波方法的强大动机是通过消除冗余小波以简单的方式适应角度的潜力。针对一个屏蔽和临界特征值实例，对该自适应方法进行了初步研究。结果表明，在大多数空间节点上所需的角度数量减少60%，在高流区域的节点上增加90%，而不会对解决方案的准确性产生不利影响。
A novel, hierarchical Haar wavelet basis is introduced and used to discretise the angular dimension of the Boltzmann transport equation. This is used in conjunction with a finite element subgrid scale method. This combination is then validated using two steady-state radiation transport problems, namely a 2D dogleg-duct shielding problem and the 2D C5MOX OECD/NEA benchmark. It is shown that the scheme has many similarities to a traditional equal weighted discrete ordinates (S-n) angular discretisation, but the strong motivation for our hierarchical Haar wavelet method is the potential for adapting in angle in a simple fashion through elimination of redundant wavelets. Initial investigations of this adaptive approach are presented for a shielding and criticality eigenvalue example. It is shown that a 60% reduction in the number of angles needed on most spatial nodes - and rising up to 90% on nodes located in high streaming areas - can be attained without adversely affecting the accuracy of the solution.