Discontinuous diffusion synthetic acceleration for S_n transport on 2D arbitrary polygonal meshes Academic Article

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. 2014 Elsevier Inc.

authors

• Ragusa, Jean

published proceedings

• JOURNAL OF COMPUTATIONAL PHYSICS

author list (cited authors)

• Turcksin, B., & Ragusa, J. C.

citation count

• 14

complete list of authors

• Turcksin, Bruno||Ragusa, Jean C

publication date

• October 2014

publisher

• Elsevier  Publisher

keywords

• Diffusion Synthetic Acceleration
• Discontinuous Finite Element Method
• Interior Penalty Method
• Piece-wise Linear Finite Element
• S-n Transport Equation

Digital Object Identifier (DOI)

• 10.1016/j.jcp.2014.05.044

start page

• 356

end page

• 369

volume

• 274

URL

• http://dx.doi.org/10.1016/j.jcp.2014.05.044