Verification of MOOSE/Bison's Heat Conduction Solver Using Combined Spatiotemporal Convergence Analysis

Journal Article · Fri Apr 15 00:00:00 EDT 2022 · Journal of Verification, Validation and Uncertainty Quantification

DOI:https://doi.org/10.1115/1.4054216· OSTI ID:1866212

Toptan, Aysenur ^[1]; Porter, Nathan W. ^[2]; Hales, Jason D. ^[1]; Jiang, Wen ^[1]; Spencer, Benjamin W. ^[1]; Novascone, Stephen R. ^[1]

---

1. Idaho National Lab. (INL), Idaho Falls, ID (United States)
2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Bison is a computational physics code that uses the finite element method to model the thermo-mechanical response of nuclear fuel. Since Bison is used to inform high-consequence decisions, it is important that its computational results are reliable and predictive. One important step in assessing the reliability and predictive capabilities of a simulation tool is the verification process, which quantifies numerical errors in a discrete solution relative to the exact solution of the mathematical model. One step in the verification process—called code verification—ensures that the implemented numerical algorithm is a faithful representation of the underlying mathematical model, including partial differential or integral equations, initial and boundary conditions, and auxiliary relationships. In this paper, the code verification process is applied to spatiotemporal heat conduction problems in Bison. Simultaneous refinement of the discretization in space and time is employed to reveal any potential mistakes in the numerical algorithms for the interactions between the spatial and temporal components of the solution. For each verification problem, the correct spatial and temporal order of accuracy is demonstrated for both first- and second-order accurate finite elements and a variety of time-integration schemes. Furthermore, these results provide strong evidence that the Bison numerical algorithm for solving spatiotemporal problems reliably represents the underlying mathematical model in MOOSE. The selected test problems can also be used in other simulation tools that numerically solve for conduction or diffusion.

• Research Organization: Idaho National Laboratory (INL), Idaho Falls, ID (United States); Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Nuclear Energy (NE)
• Grant/Contract Number: AC07-05ID14517; NA0003525
• OSTI ID: 1866212
• Alternate ID(s): OSTI ID: 1870462
• Report Number(s): INL/JOU-21-65209-Rev000; SAND2022-3731J
• Journal Information: Journal of Verification, Validation and Uncertainty Quantification, Journal Name: Journal of Verification, Validation and Uncertainty Quantification Journal Issue: 2 Vol. 7; ISSN 2377-2158
• Publisher: ASME
• Country of Publication: United States
• Language: English

Related Subjects

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS
42 ENGINEERING
97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
Bison
FEM
MOOSE
combined order analysis
h-convergence
heat conduction
verification