Diffusion Synthetic Acceleration for High-Order Discontinuous Finite Element SN Transport Schemes and Application to Locally Refined Unstructured Meshes

Journal Article · Sat Oct 01 04:00:00 EDT 2011 · Nuclear Science and Engineering

OSTI ID:1028830

Wang, Yaqi; Ragusa, Jean C

Diffusion synthetic acceleration (DSA) schemes compatible with adaptive mesh refinement (AMR) grids are derived for the SN transport equations discretized using high-order discontinuous finite elements. These schemes are directly obtained from the discretized transport equations by assuming a linear dependence in angle of the angular flux along with an exact Fick's law and, therefore, are categorized as partially consistent. These schemes are akin to the symmetric interior penalty technique applied to elliptic problems and are all based on a second-order discontinuous finite element discretization of a diffusion equation (as opposed to a mixed or P1 formulation). Therefore, they only have the scalar flux as unknowns. A Fourier analysis has been carried out to determine the convergence properties of the three proposed DSA schemes for various cell optical thicknesses and aspect ratios. Out of the three DSA schemes derived, the modified interior penalty (MIP) scheme is stable and effective for realistic problems, even with distorted elements, but loses effectiveness for some highly heterogeneous configurations. The MIP scheme is also symmetric positive definite and can be solved efficiently with a preconditioned conjugate gradient method. Its implementation in an AMR SN transport code has been performed for both source iteration and GMRes-based transport solves, with polynomial orders up to 4. Numerical results are provided and show good agreement with the Fourier analysis results. Results on AMR grids demonstrate that the cost of DSA can be kept low on locally refined meshes.

• Research Organization: Idaho National Laboratory (INL)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC07-05ID14517
• OSTI ID: 1028830
• Report Number(s): INL/JOU-11-23827
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 2 Vol. 166; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
ACCELERATION
ASPECT RATIO
CONVERGENCE
DIFFUSION
DIFFUSION EQUATIONS
FOURIER ANALYSIS
IMPLEMENTATION
POLYNOMIALS
SCALARS
TRANSPORT
diffusion synthetic acceleration