Publications

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A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier-Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.

The Next Generation Global Atmosphere Model LDRD project developed a suite of atmosphere models: a shallow water model, an x-z hydrostatic model, and a 3D hydrostatic model, by using Albany, a finite element code. Albany provides access to a large suite of leading-edge Sandia high-performance computing technologies enabled by Trilinos, Dakota, and Sierra. The next-generation capabilities most relevant to a global atmosphere model are performance portability and embedded uncertainty quantification (UQ). Performance portability is the capability for a single code base to run efficiently on diverse set of advanced computing architectures, such as multi-core threading or GPUs. Embedded UQ refers to simulation algorithms that have been modified to aid in the quantifying of uncertainties. In our case, this means running multiple samples for an ensemble concurrently, and reaping certain performance benefits. We demonstrate the effectiveness of these approaches here as a prelude to introducing them into ACME.

The need to better represent the material properties within the earth's interior has driven the development of higherfidelity physics, e.g., visco-tilted-transversely-isotropic (visco- TTI) elastic media and material interfaces, such as the ocean bottom and salt boundaries. This is especially true for full waveform inversion (FWI), where one would like to reproduce the real-world effects and invert on unprocessed raw data. Here we present a numerical formulation using a Discontinuous Galerkin (DG) finite-element (FE) method, which incorporates the desired high-fidelity physics and material interfaces. To offset the additional costs of this material representation, we include a variety of techniques (e.g., non-conformal meshing, and local polynomial refinement), which reduce the overall costs with little effect on the solution accuracy.

We present a synthetic study investigating the resolution limits of Full Wavefield Inversion (FWI) when applied to data generated from a visco-TTI-elastic (VTE) model. We compare VTE inversion having fixed Q and TTI, with acoustic inversion of acoustically generated data and elastic inversion of elastically generated data.

The purpose of this report is to document a multi-year plan for enhancing turbulence modeling in Hydra-TH for the Consortium for Advanced Simulation of Light Water Reactors (CASL) program. Hydra-TH is being developed to the meet the high- fidelity, high-Reynolds number CFD based thermal hydraulic simulation needs of the program. This work is being conducted within the thermal hydraulics methods (THM) focus area. This report is an extension of THM CASL milestone L3:THM.CFD.P10.02 [33] (March, 2015) and picks up where it left off. It will also serve to meet the requirements of CASL THM level three milestone, L3:THM.CFD.P11.04, scheduled for completion September 30, 2015. The objectives of this plan will be met by: maturation of recently added turbulence models, strategic design/development of new models and systematic and rigorous testing of existing and new models and model extensions. While multi-phase turbulent flow simulations are important to the program, only single-phase modeling will be considered in this report. Large Eddy Simulation (LES) is also an important modeling methodology. However, at least in the first year, the focus is on steady-state Reynolds Averaged Navier-Stokes (RANS) turbulence modeling.

New large eddy simulation (LES) turbulence models for incompressible magnetohydrodynamics (MHD) derived from the variational multiscale (VMS) formulation for finite element simulations are introduced. The new models include the variational multiscale formulation, a residual-based eddy viscosity model, and a mixed model that combines both of these component models. Each model contains terms that are proportional to the residual of the incompressible MHD equations and is therefore numerically consistent. Moreover, each model is also dynamic, in that its effect vanishes when this residual is small. The new models are tested on the decaying MHD Taylor Green vortex at low and high Reynolds numbers. The evaluation of the models is based on comparisons with available data from direct numerical simulations (DNS) of the time evolution of energies as well as energy spectra at various discrete times. A numerical study, on a sequence of meshes, is presented that demonstrates that the large eddy simulation approaches the DNS solution for these quantities with spatial mesh refinement.

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Accurate simulation of turbulence remains one of the most challenging problems in nuclear reactor analysis and design. Due to limitations in computing resources, Reynolds averaged Navier Stokes models (RANS) continue to play an important role in reactor simulations. The Consortium for advanced simulations of light water reactors (CASL) is a Department of Energy technology hub that is investing in research and development of a state-of-the-art computational fluid dynamics capability to meet the challenges of turbulent simulation of nuclear reactors. In this presentation, we assess several RANS eddy viscosity models appropriate for single-phase incompressible turbulent flows. Specifically, we compare the single equation Splalart-Allmaras to several variations of the k − ε model. The assessment takes into consideration elements of full system reactor cores such as complex geometries, heterogeneous meshes, swirling flow, near wall flow behavior, heat transfer and robustness issues. The goal of this strategically oriented assessment is to provide an accurate and robust turbulent simulation capability for the CASL community. Metrics of performance will be constructed by comparing different models on a strategically chosen set of problems that represent reactor core sub-systems.

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This document summarizes the results from a level 3 milestone study within the CASL VUQ effort. We compare the adjoint-based a posteriori error estimation approach with a recent variant of a data-centric verification technique. We provide a brief overview of each technique and then we discuss their relative advantages and disadvantages. We use Drekar::CFD to produce numerical results for steady-state Navier Stokes and SARANS approximations. 3

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An analytical expression for the pressure wavefield radiated from an explosion seismic source with an amplitude distribution in the form of a 3D Gaussian function is developed. This expression provides a useful reference solution for validating various numerical seismic wave propagation algorithms. © 2011 Society of Exploration Geophysicists.