A finite element method for angular discretization of the radiation transport equation on spherical geodesic grids

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.