Comparison of Spatial Discretization Methods for Solving the SN Equations Using a Three-Dimensional Method of Manufactured Solutions Benchmark Suite with Escalating Order of Nonsmoothness
Journal Article
·
· Nuclear Science and Engineering
- North Carolina State Univ., Raleigh, NC (United States). Department of Nuclear Engineering; CNEC/NC State
- North Carolina State Univ., Raleigh, NC (United States). Department of Nuclear Engineering
For this study, a comparison of the accuracy and computational efficiency of spatial discretization methods of the three-dimensional SN equations is conducted, including discontinuous Galerkin finite element methods, the arbitrarily high-order transport method of nodal type (AHOTN), the linear-linear method, the linear-nodal (LN) method, and the higher-order diamond difference method. For this purpose, we have developed a suite of method of manufactured solutions benchmarks that provides an exact solution of the SN equations even in the presence of scattering. Most importantly, our benchmark suite permits the user to set an arbitrary level of smoothness of the exact solution across the singular characteristics. Our study focuses on the computational efficiency of the considered spatial discretization methods. Numerical results indicate that the best-performing method depends on the norm used to measure the discretization error. We employ discrete Lp norms and integral error norms in this work. For configurations with continuous exact angular flux, high-order AHOTNs perform best under Lp error norms, while the LN method performs best when measured by integral error norms. Lastly, when the angular flux is discontinuous, a new singular-characteristic tracking method for three-dimensional geometries performs best among the considered methods.
- Research Organization:
- North Carolina State University, Raleigh, NC (United States). Consortium for Nonproliferation Enabling Capabilities (CNEC)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA), Office of Nonproliferation and Verification Research and Development (NA-22)
- DOE Contract Number:
- NA0002576
- OSTI ID:
- 1437425
- Journal Information:
- Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 1 Vol. 180; ISSN 0029-5639
- Publisher:
- Taylor & Francis
- Country of Publication:
- United States
- Language:
- English
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