球面测地网格上辐射输运方程角向离散化的有限元方法
A Finite Element Method for Angular Discretization of the Radiation Transport Equation on Spherical Geodesic Grids
AI总结：
本文提出一种基于球面测地网格的角向有限元方法，结合离散纵标与滤波球谐格式的优势，并通过保正限制策略和四个测试问题验证了其在其他方法失效时仍能良好表现。
摘要：
离散纵标（$S_N$）和滤波球谐（$FP_N$）格式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，但它们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，该方法结合了两种方法的优点并减轻了它们的缺点。角变量在球面测地网格上指定，球面上的函数使用有限元基表示。采用保正限制策略来防止解中出现非物理值。然后使用四个测试问题将所得方法与$S_N$和$FP_N$格式进行比较，发现当其他方法之一失败时，该方法表现良好。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
