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

Discrete ordinate (SN) and filtered spherical harmonics (FPN) 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 SN and FPN schemes using four test problems and is found to perform well when one of the other methods fail.& COPY; 2023 Elsevier Inc. All rights reserved.

Automated summary

A new method that combines the strengths of SN and FPN schemes and mitigates their disadvantages is proposed based on a finite element approach in angle. The method specifies angular variables 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 found to perform well when one of the other methods fails.