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：离散纵标（$S_N$）方法及滤波球谐（$FP_N$）方法已被证明在求解玻尔兹曼输运方程时具有鲁棒性和准确性，但两者在不同物理场景下各有优劣。本文提出一种基于角度有限元方法的新型算法，兼具二者优势并弥补其不足。角变量在球面测地网格上进行定义，球面上的函数通过有限元基函数表示。采用保正限制策略以防止解中出现非物理值。通过四个测试问题将该方法与$S_N$和$FP_N$方案进行对比，结果表明当其他方法失效时，本方法仍能取得良好表现。