Discontinuous diffusion synthetic acceleration for S n transport on 2D arbitrary polygonal meshes

Bruno Turcksin, Jean C. Ragusa

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

In this paper, a Diffusion Synthetic Acceleration (DSA) technique applied to the S n radiation transport equation is developed using Piece-Wise Linear Discontinuous (PWLD) finite elements on arbitrary polygonal grids. The discretization of the DSA equations employs an Interior Penalty technique, as is classically done for the stabilization of the diffusion equation using discontinuous finite element approximations. The penalty method yields a system of linear equations that is Symmetric Positive Definite (SPD). Thus, solution techniques such as Preconditioned Conjugate Gradient (PCG) can be effectively employed. Algebraic MultiGrid (AMG) and Symmetric Gauss-Seidel (SGS) are employed as conjugate gradient preconditioners for the DSA system. AMG is shown to be significantly more efficient than SGS. Fourier analyses are carried out and we show that this discontinuous finite element DSA scheme is always stable and effective at reducing the spectral radius for iterative transport solves, even for grids with high-aspect ratio cells. Numerical results are presented for different grid types: quadrilateral, hexagonal, and polygonal grids as well as grids with local mesh adaptivity.

Original languageEnglish
Pages (from-to)356-369
Number of pages14
JournalJournal of Computational Physics
Volume274
DOIs
StatePublished - Oct 1 2014
Externally publishedYes

Keywords

  • Diffusion synthetic acceleration
  • Discontinuous finite element method
  • Interior penalty method
  • Piece-wise linear finite element

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