Publications

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Consortium for Advance Simulation of Light Water Reactors (CASL) is a Department of Energy Innovation Hub whose mission is the following, "CASL is a collaboration of the nation's leading scientists, institutions, and supercomputers, with an aggressive 10-year mission to confidently predict the performance of existing and next-generation commercial nuclear reactors through comprehensive, science-based modeling and simulation." The CASL program to date has focused on developing the necessary predictive capability. Rightly so, it is characterized by many as a research project. As a matter of intent, the first 6 years of CASL focused on developing and demonstrating the prediction capability of a suite of independent physics codes: MPACT (neutronics), CTH (thermal hydraulics in the core), BISON (fuel performance), and MAMBA (CRUD and boron uptake on fuel rod surfaces) The last 4 years focused on initial attempts to couple the codes and to demonstrate those capabilities through a series of challenge problems aligned to 3 key issues of interest to the nuclear power industry.

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The simplified spherical harmonics (SPn) approximation to the radiative transport equation (RTE) is a computationally efficient deterministic solution method that may be derived either as an asymptotic correction to the diffusion approximation or as a 3D analog to the 1D spherical harmonics (Pn) or discrete ordinates (Sn) approximations. It is used to approximate the effects of participating media radiation. In order to trust the output of a given implementation for a high consequence application, code verification activities must be undertaken to build confidence in the results generated. The method of manufactured solutions is a widely accepted code verification technique in which a solution is assumed and arbitrary source terms are derived such that the code should converge to the prescribed solution. This convergence rate is then confirmed. In this paper we consider the set of coupled PDEs representative of radiation/conduction problems. The RTE is approximated using the “canonical” SPn equations with Mark boundary conditions. All boundaries are diffuse and emissivities range from 0 to 1. A set of manufactured solutions are presented for 1D-planar, 2D-planar, 2D-axisymmetric, and 3D-radially symmetric geometries. These manufactured solutions are used to verify the convergence rate of the conduction and simplified spherical harmonics approximations implemented in Sierra Aria, a highly scalable thermal analysis code.

The use of computational models to simulate the behavior of complex mechanical systems is ubiquitous in many high consequence applications such as aerospace systems. Results from these simulations are being used, among other things, to inform decisions regarding system reliability and margin assessment. In order to properly support these decisions, uncertainty needs to be accounted for. To this end, it is necessary to identify, quantify and propagate different sources of uncertainty as they relate to these modeling efforts. Some sources of uncertainty arise from the following: (1) modeling assumptions and approximations, (2) solution convergence, (3) differences between model predictions and experiments, (4) physical variability, (5) the coupling of various components and (6) and unknown unknowns. An additional aspect of the problem is the limited information available at the full system level in the application space. This is offset, in some instances, by information on individual components at testable conditions. In this paper, we focus on the quantification of uncertainty due to differences in model prediction and experiments, and present a technique to aggregate and propagate uncertainty from the component level to the full system in the applications space. A numerical example based on a structural dynamics application is used to demonstrate the technique.

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