http://arxiv.org/abs/2212.01409
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.
M. Bhattacharyya and D. Radice
Tue, 6 Dec 22
82/87
Comments: 24 pages, 13 figures