Discrete ordinate ($S_N$) and filtered spherical harmonics ($FP_N$) based schemes have been proven to be robust and accurate in solving the Boltzmann transport equation but they have their own strengths and weaknesses in different physical scenarios. We present a new method based on a finite element approach in angle that combines the strengths of both methods and mitigates their disadvantages. The angular variables are specified on a spherical geodesic grid with functions on the sphere being represented using a finite element basis. A positivity-preserving limiting strategy is employed to prevent non-physical values from appearing in the solutions. The resulting method is then compared with both $S_N$ and $FP_N$ schemes using four test problems and is found to perform well when one of the other methods fail.

翻译：在解决Boltzmann运输方程式时,基于分光坐标(S_N$)和过滤的球形口音(FP_N$)的办法已证明是稳健和准确的,但是在不同的物理情景中,它们也有各自的优点和弱点。我们在角度上提出了一个基于有限元素方法的新方法,将两种方法的优点结合起来,并减轻其不利之处。三角变量在一个球形大地测量网格上指定,球体上的函数使用有限元素基数来表示。采用了假设性保留限制战略,以防止非物理值出现在解决方案中。然后,将由此产生的方法与使用四个测试问题的$S_N$和$FP_N$方案进行比较,并在其他方法之一失败时发现效果良好。