Publications

Abstract not provided.

Abstract not provided.

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.

Abstract not provided.

Abstract not provided.

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.

Abstract not provided.

Abstract not provided.

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

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Sensitivity analysis is critically important to numerous analysis algorithms, including large scale optimization, uncertainty quantification,reduced order modeling, and error estimation. Our research focused on developing tools, algorithms and standard interfaces to facilitate the implementation of sensitivity type analysis into existing code and equally important, the work was focused on ways to increase the visibility of sensitivity analysis. We attempt to accomplish the first objective through the development of hybrid automatic differentiation tools, standard linear algebra interfaces for numerical algorithms, time domain decomposition algorithms and two level Newton methods. We attempt to accomplish the second goal by presenting the results of several case studies in which direct sensitivities and adjoint methods have been effectively applied, in addition to an investigation of h-p adaptivity using adjoint based a posteriori error estimation. A mathematical overview is provided of direct sensitivities and adjoint methods for both steady state and transient simulations. Two case studies are presented to demonstrate the utility of these methods. A direct sensitivity method is implemented to solve a source inversion problem for steady state internal flows subject to convection diffusion. Real time performance is achieved using novel decomposition into offline and online calculations. Adjoint methods are used to reconstruct initial conditions of a contamination event in an external flow. We demonstrate an adjoint based transient solution. In addition, we investigated time domain decomposition algorithms in an attempt to improve the efficiency of transient simulations. Because derivative calculations are at the root of sensitivity calculations, we have developed hybrid automatic differentiation methods and implemented this approach for shape optimization for gas dynamics using the Euler equations. The hybrid automatic differentiation method was applied to a first order approximation of the Euler equations and used as a preconditioner. In comparison to other methods, the AD preconditioner showed better convergence behavior. Our ultimate target is to perform shape optimization and hp adaptivity using adjoint formulations in the Premo compressible fluid flow simulator. A mathematical formulation for mixed-level simulation algorithms has been developed where different physics interact at potentially different spatial resolutions in a single domain. To minimize the implementation effort, explicit solution methods can be considered, however, implicit methods are preferred if computational efficiency is of high priority. We present the use of a partial elimination nonlinear solver technique to solve these mixed level problems and show how these formulation are closely coupled to intrusive optimization approaches and sensitivity analyses. Production codes are typically not designed for sensitivity analysis or large scale optimization. The implementation of our optimization libraries into multiple production simulation codes in which each code has their own linear algebra interface becomes an intractable problem. In an attempt to streamline this task, we have developed a standard interface between the numerical algorithm (such as optimization) and the underlying linear algebra. These interfaces (TSFCore and TSFCoreNonlin) have been adopted by the Trilinos framework and the goal is to promote the use of these interfaces especially with new developments. Finally, an adjoint based a posteriori error estimator has been developed for discontinuous Galerkin discretization of Poisson's equation. The goal is to investigate other ways to leverage the adjoint calculations and we show how the convergence of the forward problem can be improved by adapting the grid using adjoint-based error estimates. Error estimation is usually conducted with continuous adjoints but if discrete adjoints are available it may be possible to reuse the discrete version for error estimation. We investigate the advantages and disadvantages of continuous and discrete adjoints through a simple example.

This report describes research and development of the large eddy simulation (LES) turbulence modeling approach conducted as part of Sandia's laboratory directed research and development (LDRD) program. The emphasis of the work described here has been toward developing the capability to perform accurate and computationally affordable LES calculations of engineering problems using unstructured-grid codes, in wall-bounded geometries and for problems with coupled physics. Specific contributions documented here include (1) the implementation and testing of LES models in Sandia codes, including tests of a new conserved scalar--laminar flamelet SGS combustion model that does not assume statistical independence between the mixture fraction and the scalar dissipation rate, (2) the development and testing of statistical analysis and visualization utility software developed for Exodus II unstructured grid LES, and (3) the development and testing of a novel new LES near-wall subgrid model based on the one-dimensional Turbulence (ODT) model.