Enabling solution verification and efficient, high-accuracy simulations through spline-based adaptivity in MOOSE

While the Nuclear Regulatory Commission has targeted uncertainty quantification as a key desirable in nuclear software, as of this submission, no major nuclear solver has included this capability. All computer simulation processes include an element of uncertainty; these include mathematical errors in the process, but also include the unknowable variations always present in physical systems. The demands on the nuclear energy industry are such that knowing there is “always some uncertainty” in the results is not good enough. Competitive pressures, safety concerns, and regulatory demands all coalesce to create a need for simulation results that include a mathematical representation of exactly what is uncertain, and by how much. Since the major nuclear codes are also generally so complex they are inaccessible to inexperienced users, these factors have combined to create a situation where the most powerful government modeling and simulation codes are significantly under-utilized. Uncertainty quantification in nuclear energy promises two significant benefits: improved decision making, and improved ease of use. Producing a numerical quantification of the level of confidence in simulation results would improve nuclear industry decision making and ease regulatory uncertainty; adding this to a key government simulation code promises to increase its value. Improved ease of use is a collateral benefit. Uncertainty quantification requires adaptivity, essentially a reduction in model error, which makes complex simulations faster and easier for non-expert users, and consequently will further improve access to government simulation codes. Complex issues make it difficult to implement uncertainty quantification in traditional finite element analysis, which is why no current nuclear codes offer it. However, the mathematical properties of the smooth splines central to this proposal avoid many of these issues, suggesting that this work is likely to lead to a commercial solution that has long evaded others. Today, Idaho National Laboratory’s open-source nuclear simulation software MOOSE is the recommended platform for next-generation non-light-water nuclear reactors. The proposer’s robust meshing software is of- ten used along with MOOSE. Both software have recently been enhanced to handle smooth splines and Bézier elements, enabling MOOSE to work with spline elements in addition to traditional linear elements. This project will build on these recent enhancements to successfully equip MOOSE with uncertainty quantifica- tion. In Phase I, the foundational adaptivity, or error-reduction, schemes will be developed and uncertainty quantification methods will be prototyped. In Phase II, the adaptivity schemes will be automated, and uncertainty quantification methods will be added to the preprocessor for use with MOOSE. The competitive benefits of uncertainty quantification include reduced development time and cost, improved designs, better understanding of risk, and quantifiable confidence in analysis results and engineering decisions. MOOSE is a well-developed, targeted nuclear energy simulation code rapidly growing in usage, and our enhancements will prove invaluable in the private nuclear marketplace. Broad commercial applications and benefits to other segments of the modeling and simulation industry are also possible. Others face many of the same problems as nuclear energy when it comes to quantifying uncertainty, particularly in the areas of automotive, defense, climate and environmental modeling, energy generation, control and manufacturing, and process and system design. They will experience the same ben- efits of faster development, better decision-making, and higher confidence through the technology developed in this proposal.