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首页> 外文期刊>Annals of nuclear energy >Least-squares finite-element S_N method for solving three-dimensional transport equation
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Least-squares finite-element S_N method for solving three-dimensional transport equation

机译：最小二乘有限元S_N法求解三维输运方程

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摘要

A discrete ordinates finite-element method for solving three-dimensional first-order neutron transport equation is proposed using a least-squares variation. It avoids the singularity in void regions of the method derived from the second-order equation. Different from using the standard Galerkin variation applying to the first-order equation, the least-squares variation results in a symmetric matrix, which can be solved ea.sily and effectively. The approach allows a continuous finite-element. To eliminate the discontinuity of the angular flux on the fixed flux boundary in the spherical harmonics method, the equation is discretized using the discrete ordinates method for angular dependency. A three-dimensional transport simulation code is developed and applied to some benchmark problems with unstructured geometry. The numerical results demonstrate the accuracy and feasibility of the method.
机译：提出了一种使用最小二乘方差的离散坐标有限元方法求解三维一阶中子输运方程。它避免了从二阶方程得出的方法的空白区域中的奇异性。与使用适用于一阶方程的标准Galerkin变量不同，最小二乘变量产生对称矩阵，可以轻松有效地求解该矩阵。该方法允许连续的有限元。为了消除球谐函数方法中固定通量边界上角通量的不连续性，使用离散纵坐标方法将方程离散化以获得角度依赖性。开发了三维运输仿真代码，并将其应用于非结构化几何的一些基准问题。数值结果证明了该方法的准确性和可行性。

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