A flexible nonlinear diffusion acceleration method for the S_N transport equations discretized with discontinuous finite elements

Journal Article · Tue Feb 21 00:00:00 EST 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2017.01.070· OSTI ID:1363728

Schunert, Sebastian ^[1]; Wang, Yaqi ^[1]; Gleicher, Frederick ^[1]; Ortensi, Javier ^[1]; Baker, Benjamin ^[1]; Laboure, Vincent ^[1]; Wang, Congjian ^[1]; DeHart, Mark ^[1]; Martineau, Richard ^[1]

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1. Idaho National Lab. (INL), Idaho Falls, ID (United States)

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S_N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form is based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.

• Research Organization: Idaho National Lab. (INL), Idaho Falls, ID (United States)
• Sponsoring Organization: USDOE Office of Nuclear Energy (NE)
• Grant/Contract Number: AC07-05ID14517
• OSTI ID: 1363728
• Alternate ID(s): OSTI ID: 1397847
• Report Number(s): INL/JOU-16-37745; PII: S0021999117301286
• Journal Information: Journal of Computational Physics, Vol. 338; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
neutron transport equation
nonlinear diffusion acceleration
discontinuous finite element method