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

Maitraya K. Bhattacharyya, David Radice

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Article number112365
JournalJournal of Computational Physics
Volume491
DOIs
StatePublished - Oct 15 2023

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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