Diffusion Synthetic Acceleration for High Order S{sub N} Transport on Meshes with Curved Surfaces

Journal Article · Sat Jul 01 04:00:00 EDT 2017 · Transactions of the American Nuclear Society

OSTI ID:23047501

Woods, Douglas N.; Palmer, Todd S. ^[1]

---

1. Nuclear Science and Engineering, Oregon State University, Corvallis, OR (United States)

Thermal radiation transport is integral to multiphysics applications such as inertial confinement fusion and astrophysics. Materials in these problems can be exceptionally optically thick and diffusive. A transport solver must be capable of accurate and efficient solutions to such problems. Previously, Woods et al. established a proof-of-concept for high order (HO) discontinuous Galerkin finite element (DGFEM) transport on meshes with curved surfaces. They numerically demonstrated the spatial convergence is order p + 1. Remarkably, these convergence rates are relatively invariant to the amount of curvature of the spatial mesh. We present here an extension of this work that demonstrates a rapidly-convergent iterative solver for the FEM transport equations on meshes with curved sides. We use the modified interior penalty (MIP) diffusion synthetic acceleration (DSA) established by Wang and Ragusa. The partially consistent MIP equations stem from the symmetric interior penalty (IP) derivation of the diffusion equation. The IP method is not stable for optically thick cells so it was combined with the diffusion conforming form (DCF), a discretized diffusion equation derived from the discretized S N equations that is not stable for intermediate optical thicknesses. The MIP equations adapt a 'switch' to the IP method in optically thinner regions and the DCF method in optically thicker regions. The literature does not reveal any Fourier analyses performed for iterative transport on meshes with curved surfaces. Wang and Ragusa performed a Fourier analysis for orthogonal meshes and our results appear to be as expected. Previous literature has reported on some of the sensitivities that affect the spectral radius of DSA schemes: polynomial order, and scattering ratios. Presently, we focus on the sensitivity of the spectral radius to polynomial order, scattering ratio, the constant C, and mesh curvature for varying cell thicknesses. We also numerically study the behavior of the spectral radius to verify our DSA implementation. A sequence of problems is designed to exercise the acceleration. As the problems become more optically thick and diffusive, the accelerated solution continues to converge toward the analytic solution. We employ the Modular Finite Element Methods (MFEM) package, developed at Lawrence Livermore National Laboratory, to generate the linear algebraic system of equations for each angle in the discrete ordinates quadrature set, and use UMFPack to solve this system of equations.

• OSTI ID: 23047501
• Journal Information: Transactions of the American Nuclear Society, Journal Name: Transactions of the American Nuclear Society Vol. 116; ISSN 0003-018X
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
97 MATHEMATICS AND COMPUTING
ANALYTICAL SOLUTION
ASTROPHYSICS
DIFFUSION EQUATIONS
DISCRETE ORDINATE METHOD
FINITE ELEMENT METHOD
FOURIER ANALYSIS
INERTIAL CONFINEMENT
ITERATIVE METHODS
MATERIALS
NUMERICAL ANALYSIS
POLYNOMIALS
RADIATION TRANSPORT
SCATTERING
SENSITIVITY
SYMMETRY
THERMAL RADIATION
TRANSPORT THEORY