Single Grid Error Estimation for Neutron Transport Solvers

Whewell, Ben Joseph; McClarren, Ryan G.

doi:10.1115/1.4069426

Single Grid Error Estimation for Neutron Transport Solvers

Journal Article · Tue Sep 02 00:00:00 EDT 2025 · Journal of Verification, Validation and Uncertainty Quantification

DOI:https://doi.org/10.1115/1.4069426· OSTI ID:2998253

^[1]; McClarren, Ryan G. ^[2]

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
University of Notre Dame, IN (United States)

The method of nearby problems (MNP) is a solution verification technique that does not require the use of multiple spatial grids. To estimate spatial discretization error without requiring a high-fidelity spatial grid, an analytical curve fit is interpolated from the numerical solution. The residual between the curve fit solution and numerical solution is calculated and added as an additional source term to the governing equation. The nearby solution is estimated using the updated source term and boundary conditions to remain consistent with the curve fit interpolation. The nearby solution can be compared to the curve fit solution as a discretization error estimation while using a single spatial grid. Without the use of higher fidelity spatial grids, the MNP is able to approximate the spatial discretization error, a facet of solution verification. The application of the method of nearby problems is presented for one- and two-dimensional neutron transport problems for both fixed source and criticality problems on the spatial variable. The fixed source results demonstrate the effectiveness of nearby problems for spatial error identification using the discrete ordinates method. Criticality results are shown to identify area of high spatial error for the C5G7 problem as well as for the discrete ordinates solver. A novel approach of combining the capabilities of Monte Carlo with the discrete ordinates nearby problems is presented for one- and two-dimensional fixed source problems. In conclusion, the MNP demonstrates its effectiveness at identifying spatial error on a single structured grid with a wide variety of neutron transport problems.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2998253

Report Number(s):: LA-UR--25-23253; 10.1115/1.4069426; 2377-2166

Journal Information:: Journal of Verification, Validation and Uncertainty Quantification, Journal Name: Journal of Verification, Validation and Uncertainty Quantification Journal Issue: 2 Vol. 10; ISSN 2377-2158; ISSN 2377-2166

Publisher:: ASME InternationalCopyright Statement

Country of Publication:: United States

Language:: English

References (15)

General Principles of Neutron Transport Prinja, Anil K.; Larsen, Edward W. Handbook of Nuclear Engineering https://doi.org/10.1007/978-0-387-98149-9_5	book	December 2009
Filtered Discrete Ordinates Equations for Radiative Transport Hauck, Cory; Heningburg, Vincent Journal of Scientific Computing, Vol. 80, Issue 1 https://doi.org/10.1007/s10915-019-00950-1	journal	May 2019
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes Larsen, Edward W.; Morel, J. E.; Miller, Warren F. Journal of Computational Physics, Vol. 69, Issue 2 https://doi.org/10.1016/0021-9991(87)90170-7	journal	April 1987
The application of Method of Manufactured Solutions to method of characteristics in planar geometry Wang, Jipu; Martin, William; Collins, Benjamin Annals of Nuclear Energy, Vol. 121 https://doi.org/10.1016/j.anucene.2018.07.041	journal	November 2018
Review of code and solution verification procedures for computational simulation Roy, Christopher J. Journal of Computational Physics, Vol. 205, Issue 1 https://doi.org/10.1016/j.jcp.2004.10.036	journal	May 2005
A high-order/low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations Peng, Zhuogang; McClarren, Ryan G. Journal of Computational Physics, Vol. 447 https://doi.org/10.1016/j.jcp.2021.110672	journal	December 2021
Generalized Nuclear Data: A New Structure (with Supporting Infrastructure) for Handling Nuclear Data Mattoon, C. M.; Beck, B. R.; Patel, N. R. Nuclear Data Sheets, Vol. 113, Issue 12 https://doi.org/10.1016/j.nds.2012.11.008	journal	December 2012
Ray Effect Mitigation for the Discrete Ordinates Method Using Artificial Scattering Frank, Martin; Kusch, Jonas; Camminady, Thomas Nuclear Science and Engineering, Vol. 194, Issue 11 https://doi.org/10.1080/00295639.2020.1730665	journal	March 2020
Fully-discrete numerical transfer in diffusive regimes Jin, Shi; Levermore, C. David Transport Theory and Statistical Physics, Vol. 22, Issue 6 https://doi.org/10.1080/00411459308203842	journal	October 1993
The Monte Carlo Method Metropolis, Nicholas; Ulam, S. Journal of the American Statistical Association, Vol. 44, Issue 247 https://doi.org/10.1080/01621459.1949.10483310	journal	September 1949
Unstructured grid Techniques Mavriplis, D. J. Annual Review of Fluid Mechanics, Vol. 29, Issue 1 https://doi.org/10.1146/annurev.fluid.29.1.473	journal	January 1997
New Difference Schemes for the Neutron Transport Equation Reed, William H. Nuclear Science and Engineering, Vol. 46, Issue 2 https://doi.org/10.13182/NSE46-309	journal	November 1971
On Numerical Solutions of Transport Problems in the Diffusion Limit Larsen, Edward W. Nuclear Science and Engineering, Vol. 83, Issue 1 https://doi.org/10.13182/NSE83-A17992	journal	January 1983
Monte Carlo / Dynamic Code (MC/DC): An accelerated Python package for fully transient neutron transport and rapid methods development Morgan, Joanna Piper; Variansyah, Ilham; Pasmann, Samuel L. Journal of Open Source Software, Vol. 9, Issue 96 https://doi.org/10.21105/joss.06415	journal	April 2024
Estimation of Discretization Errors Using the Method of Nearby Problems Roy, Christopher J.; Raju, Anil; Hopkins, Matthew M. AIAA Journal, Vol. 45, Issue 6 https://doi.org/10.2514/1.24282	journal	June 2007

Similar Records

Discretization error estimation and exact solution generation using the method of nearby problems.

Technical Report · Sat Oct 01 00:00:00 EDT 2011 · OSTI ID:1029791

CFD-DEM solution verification: Fixed-bed studies

Journal Article · Mon Aug 20 20:00:00 EDT 2018 · Powder Technology · OSTI ID:1509722

Verification & Validation of High-Order Short-Characteristics-Based Deterministic Transport Methodology on Unstructured Grids

Technical Report · Thu Dec 19 23:00:00 EST 2013 · OSTI ID:1111549

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Discrete Ordinates
Monte Carlo
Nearby Problems
Neutron Transport
Solution Verification

Single Grid Error Estimation for Neutron Transport Solvers

Citation Formats

References (15)

Similar Records

Related Subjects