标题： 球面测地网格上辐射输运方程角度离散的有限元方法 显示英文标题

标题： A Finite Element Method for Angular Discretization of the Radiation Transport Equation on Spherical Geodesic Grids

摘要： 基于离散纵坐标（$S_N$）和滤波球谐函数（$FP_N$）的求解方法已被证明在求解玻尔兹曼输运方程时稳健且精确，但在不同的物理场景中各有优缺点。 我们提出了一种基于角度有限元方法的新方法，结合了这两种方法的优点，并缓解了它们各自的缺点。 角度变量被定义在一个球面测地网格上，球面上的函数用有限元基表示。 采用保正性限制策略以防止非物理值出现在解中。 然后通过四个测试问题将该方法与$S_N$和$FP_N$方案进行比较，发现当其他方法失效时，该方法表现良好。 显示英文摘要

摘要： 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.