论文标题
在球形测量网格上辐射传输方程的角度离散的有限元方法
A Finite Element Method for Angular Discretization of the Radiation Transport Equation on Spherical Geodesic Grids
论文作者
论文摘要
事实证明，基于离散的纵坐标（$ s_n $）和基于过滤的球形谐波（$ fp_n $）方案在解决Boltzmann传输方程方面是强大而准确的，但是在不同的物理场景中它们具有自己的优势和劣势。我们提出了一种基于有限元方法的新方法，以结合方法的优势并减轻其缺点。角变量是在球形地球网格上指定的，其函数在球体上使用有限元表示。采用具有积极性的限制策略来防止非物理值出现在解决方案中。然后将所得的方法与$ s_n $和$ fp_n $方案都使用四个测试问题进行比较，并且在其他方法之一失败时被发现表现良好。
Discrete ordinate ($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.
