A POD reduced order model for resolving angular direction in neutron/photon transport problems
A POD reduced order model for resolving angular direction in neutron/photon transport problems
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DOI：
10.1016/j.jcp.2015.04.043
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发表时间：
2015-09
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通讯作者：
A. Buchan;A. Calloo;Mark G. Goffin;S. Dargaville;F. Fang;C. Pain;Ionel M. Navon
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文献类型：
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作者：
A. Buchan;A. Calloo;Mark G. Goffin;S. Dargaville;F. Fang;C. Pain;Ionel M. Navon
本文介绍了第一个降阶模型（ROM），有效地解决了与时间无关的，单能玻尔兹曼输运方程（BTE）的角维。它是基于本征正交分解（POD），并使用快照的方法来形成最佳的基函数，解决中子/光子输运问题中的粒子的行进方向。这项工作的一个独特的元素是，快照是从与BTE的角度维度的高分辨率扩展相关的角度系数的向量形成的。此外，单个快照不像标准POD那样通过时间来记录，而是通过空间来记录。在本质上，这项工作交换标准POD方法中的维度空间和时间的角色，分别与角度和空间。这里展示了POD模型如何以高效的方式从POD基函数形成。然后，该模型被应用到两个辐射问题，一个涉及通过屏蔽和其他通过无限阵列的针辐射的运输。这两个问题都是选择其复杂的角通量的解决方案，以提供一个适当的示范模型的能力。结果表明，POD模型可以有效、准确地求解这些通量。与高分辨率模型相比，该POD模型可以将问题的大小减少两个数量级，而不会影响精度。解决时间也减少了类似的因素。
This article presents the first Reduced Order Model (ROM) that efficiently resolves the angular dimension of the time independent, mono-energetic Boltzmann Transport Equation (BTE). It is based on Proper Orthogonal Decomposition (POD) and uses the method of snapshots to form optimal basis functions for resolving the direction of particle travel in neutron/photon transport problems. A unique element of this work is that the snapshots are formed from the vector of angular coefficients relating to a high resolution expansion of the BTE's angular dimension. In addition, the individual snapshots are not recorded through time, as in standard POD, but instead they are recorded through space. In essence this work swaps the roles of the dimensions space and time in standard POD methods, with angle and space respectively.It is shown here how the POD model can be formed from the POD basis functions in a highly efficient manner. The model is then applied to two radiation problems; one involving the transport of radiation through a shield and the other through an infinite array of pins. Both problems are selected for their complex angular flux solutions in order to provide an appropriate demonstration of the model's capabilities. It is shown that the POD model can resolve these fluxes efficiently and accurately. In comparison to high resolution models this POD model can reduce the size of a problem by up to two orders of magnitude without compromising accuracy. Solving times are also reduced by similar factors.