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DOE OSTI2017

SAM Theory Manual

The System Analysis Module (SAM) is an advanced and modern system analysis tool being developed at Argonne National Laboratory under the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. SAM development aims for advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability for reactor transient analyses. To facilitate the code development, SAM utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage modern advanced software environments and numerical methods. SAM focuses on modeling advanced reactor concepts such as SFRs (sodium fast reactors), LFRs (lead-cooled fast reactors), and FHRs (fluoride-salt-cooled high temperature reactors) or MSRs (molten salt reactors). These advanced concepts are distinguished from light-water reactors in their use of single-phase, low-pressure, high-temperature, and low Prandtl number (sodium and lead) coolants. As a new code development, the initial effort has been focused on modeling and simulation capabilities of heat transfer and single-phase fluid dynamics responses in Sodium-cooled Fast Reactor (SFR) systems. The system-level simulation capabilities of fluid flow and heat transfer in general engineering systems and typical SFRs have been verified and validated. This document provides the theoretical and technical basis of the code to help users understand the underlying physical models (such as governing equations, closure models, and component models), system modeling approaches, numerical discretization and solution methods, and the overall capabilities in SAM. As the code is still under ongoing development, this SAM Theory Manual will be updated periodically to keep it consistent with the state of the development.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2017

Development of Geomechanical Screening Tools to Identify Risk: An Experimental and Modeling Approach for Secure CO 2 Storage Final Technical Report

CO 2 injection in the subsurface introduces additional complexity in terms of interactions of the reservoir host pore fluid with natural heterogeneity of hydro-mechanical properties of the rock. Natural heterogeneity of the reservoir rock and caprock formations includes spatial variation of hydro-mechanical properties as well as the presence of natural fractures. We developed a coupled mathematical modeling and experimental framework that takes into account the effect of rock heterogeneity on effective mechanical properties of the rock in contact with CO 2 . We performed accurate laboratory experiments to determine the changes in rock mechanical properties due to mineral dissolution in the presence of carbonic acid generated by CO 2 injection. A two-scale adaptive homogenization framework was then developed to consistently upscale petrophysical and geomechanical properties to the field scale. Further, we also developed high-fidelity, numerical solution schemes, non-linear and linear solvers and preconditioners to solve the coupled flow, reactive transport and geomechanical system. The numerical model was then used to study field scale CO 2 sequestration problems for the two selected field sites: (1) Frio formation and (2) Cranfield site. We also developed robust schemes for field data assimilation, model calibration such that the residual uncertainty at the end of the data assimilation procedures can be faithfully represented while taking into account the coupled geochemical and geomechanical processes.

42 ENGINEERING↗

DOE OSTI2018

Exploring Deep Learning and Sparse Matrix Format Selection

We proposed to explore the use of Deep Neural Networks (DNN) for addressing the longstanding barriers. The recent rapid progress of DNN technology has created a large impact in many fields, which has significantly improved the prediction accuracy over traditional machine learning techniques in image classifications, speech recognitions, machine translations, and so on. To some degree, these tasks resemble the decision makings in many HPC tasks, including the aforementioned format selection for SpMV and linear solver selection. For instance, sparse matrix format selection is akin to image classification—such as, to tell whether an image contains a dog or a cat; in both problems, the right decisions are primarily determined by the spatial patterns of the elements in an input. For image classification, the patterns are of pixels, and for sparse matrix format selection, they are of non-zero elements. DNN could be naturally applied if we regard a sparse matrix as an image and the format selection or solver selection as classification problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

SAM User's Guide

The System Analysis Module (SAM) is a modern system analysis tool being developed at Argonne National Laboratory for advanced non-LWR safety analysis. It aims to provide fast-running, whole-plant transient analyses capability with improved-fidelity for Sodium-cooled Fast Reactors (SFR), Lead-cooled Fast Reactors (LFR), and Molten Salt Reactors (MSR) or Fluoride-cooled High-temperature Reactors (FHR). SAM takes advantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage the modern advanced software environments and numerical methods. This document provides a user’s guide, which will help users understand the input description and core capabilities of the SAM code. A brief overview of the code is presented, as well as how to obtain and run it. The input syntax for various parts of the code is provided. Additionally, a number of example problems, starting with simple unit component problems to problems with increasing complexity, are provided. Because the code is still under active development, this SAM User’s Guide will evolve with periodic updates.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2020

PETSc Users Manual (Rev. 3.13)

This manual describes the use of PETSc for the numerical solution of partial differential equations and related problems on high-performance computers. The Portable, Extensible Toolkit for Scientific Computation (PETSc) is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all message-passing communication. PETSc includes an expanding suite of parallel linear solvers, nonlinear solvers, and time integrators that may be used in application codes written in Fortran, C, C++, and Python. PETSc provides many of the mechanisms needed within parallel application codes, such as parallel matrix and vector assembly routines. The library is organized hierarchically, enabling users to employ the level of abstraction that is most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users. PETSc is a sophisticated set of software tools; as such, for some users it initially has a much steeper learning curve than a simple subroutine library. In particular, for individuals without some computer science background, experience programming in C, C++, python, or Fortran and experience using a debugger such as gdb or dbx, it may require a significant amount of time to take full advantage of the features that enable efficient software use. However, the power of the PETSc design and the algorithms it incorporates may make the efficient implementation of many application codes simpler than \rolling them" yourself.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

SAM Plug-in Development (Phase I Final Report)

The DOE Office of Nuclear Energy (NE) has created an extensive set of advanced modeling and simulation tools for nuclear engineering analysis. The advanced capabilities of these newer analysis codes require more in-depth training, skills, and knowledge in order to effectively utilize them for the design, analysis, and licensing of advanced nuclear systems and experiments. A high learning curve for inexperienced users may deter organizations from incorporating these tools into their internal processes. This project involved development of a plug-in to the Symbolic Nuclear Analysis Package (SNAP) for the System Analysis Module (SAM) tool. SAM is an advanced system analysis tool for reactor transient analyses being developed at Argonne National Laboratory under the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. SAM utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage modern advanced software environments and numerical methods. SNAP provides a highly flexible framework for creating, modifying and documenting input for engineering analysis codes such as SAM as well as extensive functionality for submitting, monitoring, and interacting with the codes through an intuitive graphical user interface (GUI). The common user interface provided by SNAP minimizes the learning curve for engineers starting with a new analysis code and provides an intuitive framework for transitioning between different analysis codes. SNAP provides a powerful but intuitive interface to facilitate access to advanced modeling and simulation tools for inexperienced users. Unlike many “form based” GUI’s, SNAP maps each engineering code’s component input to an internal database which manages all component input parameters along with component interconnections. This level of abstraction permits SNAP to support several advanced capabilities such as renodalization, model validation and consistency checks, embedded documentation, model notebook generation, data ownership and reviewer tracking, and variable assignment for inputs to name a few. SNAP includes a built-in Python interpreter and is interfaced to several commercial and open source packages including CPython, MATLAB/OCTAVE, Microsoft Office, Open Office, and SANDIA’s DAKOTA package which provides Uncertainty Quantification analysis through the SNAP plug-ins. Phase I of this project involved development a fully functional basic SAM plug-in to SNAP. This plug-in provides the ability to import existing models, graphically construct, edit and submit models using SNAP’s extensive functionality.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2021

SAM Theory Manual

The System Analysis Module (SAM) is an advanced and modern system analysis tool under development at Argonne National Laboratory for advanced non-LWR reactor safety analysis. It aims to provide fast-running, modest-fidelity, whole-plant transient analyses capabilities, which are essential for fast turnaround design scoping and engineering analyses of advanced reactor concepts. While SAM is being developed as a system-level modeling and simulation tool, advanced modeling techniques being implemented include a reduced-order three-dimensional module, pseudo 3-D conjugate heat transfer modeling in reactor core, flexible and multi-scale modeling of heat transfer between fluid and structures, in addition to the advances in software environments and design, and numerical methods. SAM aims to be a generic system-level safety analysis tool for advanced non-LWRs, including Liquid-Metal-cooled fast Reactors (LMR), Molten Salt Reactors (MSR), Fluoride-salt-cooled High- temperature Reactors (FHR), and High-Temperature Gas-cooled Reactors (HTGR). SAM takes ad- vantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented computational framework (MOOSE), and its underlying meshing and finite-element library and linear and non-linear solvers, to leverage the modern advanced software environments and numerical methods. This document provides the theoretical and technical basis of the code to help users understand the underlying physical models (such as governing equations, closure models, and component models), system modeling approaches, numerical discretization and solution methods, and the overall capabilities in SAM. As new code capabilities and features are added, the SAM Theory Manual will be updated periodically to keep it consistent with the state of the development.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

SAM User’s Guide

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2018

Performance tuning of CEED software and first wave apps

The goal of this milestone was the performance tuning of the CEED software and first wave apps. In this milestone, the CEED team developed optimization techniques and tuned for performance the CEED software. Specifically, the focus was on the following: (1) Fast finite element operator storage and evaluation using partial assembly/matrix-free algorithms that take advantage of tensor-product element structure; (2) Architecture optimizations, including the development of performant discretization libraries targeting heterogeneous systems with multi-core CPUs, GPUs, and/or many-core CPUs in single node, cluster, or large-scale ECP supercomputer configurations; and (3) Global kernels for finite element operators, including the development of algorithms and libraries for fast gather-scatter exchanges for action assembly on unstructured graphs and for components needed for global linear solvers. A main part of this milestone was the performance tuning of the CEED first-wave ECP applications. This included the ExaSMR application – Coupled Monte Carlo Neutronics and Fluid Flow Simulation of Small Modular Reactors (ORNL), and the MARBL application – Next-Gen Multi-physics Simulation Code (LLNL). The artifacts delivered include performance improvements in CEED’s 1st wave of applications, and tuned CEED software for various architectures through a number of backends, freely available in the CEED’s repository on GitHub. See the CEED website, http://ceed.exascaleproject.org and the CEED GitHub organization, http://github.com/ceed for more details. In addition to details and results from the above R&D efforts, in this document we are also reporting on other project-wide activities performed in Q4 of FY18 including: CEED’s second annual meeting, a successful minisymposium at the premier international conference on high-order methods (ICOSAHOM), making the CEED milestone reports publicly available, new Laghos release, and other outreach efforts.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Physics Basis, Optimization, and Control for Integrated 3D Edge Long-pulse Tokamak Scenarios

The aim of this project with international collaborations (PI: J.-K. Park of Princeton Plasma Physics Laboratory) is to develop a unified physics basis and predictive capability for the control of edge-localized modes (ELMs) with optimized non-axisymmetric (3D) fields, by leveraging the unique research capabilities of international KSTAR tokamak in Korea. At the University of California, Irvine, we use a fusion simulation code GTC to study the effects of the 3D magnetic fields (including both magnetic islands and stochastic magnetic field lines) on microturbulence. We focus on the effects of 3D equilibrium on turbulent and neoclassical transport that leads to ELM suppression. During the project period, the UCI team of this collaboration has made significant progress in understanding turbulent transport in 3D geometry including both tokamaks with RMP and stellarators. Four UCI postdoctoral researchers, Drs. Javier Nicolau, Gyungjin Choi, Pengfei Liu, and Xishuo Wei were partially supported by this project and collaborating with the entire project team. We have published 4 journal papers and gave several invited talks. This project advance physics understand of 3D effects on microturbulence, specially effects of magnetic islands. It will contribute to the DOE SciDAC ISEP project in the area of GTC development for general 3D geometry capability, rigorous verification and validation, and readiness for the emerging exascale computing. Through collaborations with computational scientists, the project helps to advance high performance computing in the area of GPU acceleration, linear solver, and data management.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

PETSc/TAO Users Manual V.3.21

This manual describes the use of the Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Toolkit for Advanced Optimization (TAO) for the numerical solution of partial differential equations (PDEs) and related problems on high-performance computers. PETSc/TAO is a suite of data structures and routines that provide the building blocks for implementing large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all distributed memory communication. PETSc/TAO includes a large suite of parallel linear solvers, nonlinear solvers, time integrators, and optimizers that may be used in application codes written in Fortran, C, C++, and Python (via petsc4py; see Getting Started ). The library is organized hierarchically, enabling users to employ the abstraction level most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

R-Adaptivity to Enable Compression of Elementary Computations in Extreme-Scale Finite Element Simulators

Modern computing systems are capable of exascale calculations, which are revolutionizing the development and application of high-fidelity numerical models in computational science and engineering. While these systems continue to grow in processing power, the available system memory has not increased commensurately, and electrical power consumption continues to grow. A predominant approach to limit the memory usage in large-scale applications is to exploit the abundant processing power and continually recompute many low-level simulation quantities, rather than storing them. However, this approach can adversely impact the throughput of the simulation and diminish the benefits of modern computing architectures. We present three novel contributions to reduce the memory burden while maintaining, and sometimes improving, performance in simulations based on finite element discretizations. The first contribution develops dictionary-based data compression schemes that detect and exploit the structure of the discretization, due to redundancies across the finite element mesh. While these schemes are shown to reduce memory requirements by more than 99% on meshes with large numbers of identical mesh cells, there are applications where this structure does not exist. The second contribution leverages a recently developed augmented Lagrangian optimization algorithm to enable r-adaptivity for meshes with the goal of enhancing the redundancies in the mesh. The third contribution extends these methods to patch-based linear solvers and preconditioners by compressing local matrices. Numerical results demonstrate the effectiveness of the proposed methods to detect, enhance and exploit mesh structure on a suite of examples inspired by large-scale applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

SAM Theory Manual

The System Analysis Module (SAM) is an advanced and modern system analysis tool under development at Argonne National Laboratory for advanced non-LWR reactor safety analysis. It aims to provide fast-running, modest-fidelity, whole-plant transient analyses capabilities, which are essential for fast turnaround design scoping and engineering analyses of advanced reactor concepts. While SAM is being developed as a system-level modeling and simulation tool, advanced modeling techniques being implemented include a reduced-order three-dimensional module, pseudo 3-D conjugate heat transfer modeling in reactor core, flexible and multi-scale modeling of heat transfer between fluid and structures, in addition to the advances in software environments and design, and numerical methods. SAM aims to be a generic system-level safety analysis tool for advanced non-LWRs, including Liquid-Metal-cooled fast Reactors (LMR), Molten Salt Reactors (MSR), Fluoride-salt-cooled High-temperature Reactors (FHR), and High-Temperature Gas-cooled Reactors (HTGR). SAM takes advantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented computational framework (MOOSE), and its underlying meshing and finite-element library and linear and non-linear solvers, to leverage the modern advanced software environments and numerical methods. This document provides the theoretical and technical basis of the code to help users understand the underlying physical models (such as governing equations, closure models, and component models), system modeling approaches, numerical discretization and solution methods, and the overall capabilities in SAM. As new code capabilities and features are added, the SAM Theory Manual will be updated periodically to keep it consistent with the state of the development.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

SAM User's Guide

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Optimization with Neural Network Feasibility Surrogates: Formulations and Application to Security-Constrained Optimal Power Flow

In many areas of constrained optimization, representing all possible constraints that give rise to an accurate feasible region can be difficult and computationally prohibitive for online use. Satisfying feasibility constraints becomes more challenging in high-dimensional, non-convex regimes which are common in engineering applications. A prominent example that is explored in the manuscript is the security-constrained optimal power flow (SCOPF) problem, which minimizes power generation costs, while enforcing system feasibility under contingency failures in the transmission network. In its full form, this problem has been modeled as a nonlinear two-stage stochastic programming problem. In this work, we propose a hybrid structure that incorporates and takes advantage of both a high-fidelity physical model and fast machine learning surrogates. Neural network (NN) models have been shown to classify highly non-linear functions and can be trained offline but require large training sets. In this work, we present how model-guided sampling can efficiently create datasets that are highly informative to a NN classifier for non-convex functions. We show how the resultant NN surrogates can be integrated into a non-linear program as smooth, continuous functions to simultaneously optimize the objective function and enforce feasibility using existing non-linear solvers. Overall, this allows us to optimize instances of the SCOPF problem with an order of magnitude CPU improvement over existing methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2015

PyTrilinos

PyTrilinos is a Python interface to selected Trilinos packages. This makes Trilinos linear algebra classes, linear solvers, preconditioners, nonlinear solvers, eigensolvers, and tools available to Python programmers. This broadens the user base of Trilinos, and facilitates rapid prototyping of scientific codes and interactive manipulation of large, distributed data sets.

Source record↗

DOE OSTI2017

Futility

The Futility package contains the following: 1) Definition of the size of integers and real numbers; 2) A generic Unit test harness; 3) Definitions for some basic extensions to the Fortran language: arbitrary length strings, a parameter list construct, exception handlers, command line processor, timers; 4) Geometry definitions: point, line, plane, box, cylinder, polyhedron; 5) File wrapper functions: standard Fortran input/output files, Fortran binary files, HDF5 files; 6) Parallel wrapper functions: MPI, and Open MP abstraction layers, partitioning algorithms; 7) Math utilities: BLAS, Matrix and Vector definitions, Linear Solver methods and wrappers for other TPLs (PETSC, MKL, etc), preconditioner classes; 8) Misc: random number generator, water saturation properties, sorting algorithms.

Collins, Benjamin S.↗

DOE OSTI2016

An Assessment of Some Design Constraints on Heat Production of a 3D Conceptual EGS Model Using an Open-Source Geothermal Reservoir Simulation Code

Performance of heat production process over a 30-year period is assessed in a conceptual EGS model with a geothermal gradient of 65K per km depth in the reservoir. Water is circulated through a pair of parallel wells connected by a set of single large wing fractures. The results indicate that the desirable output electric power rate and lifespan could be obtained under suitable material properties and system parameters. A sensitivity analysis on some design constraints and operation parameters indicates that 1) the fracture horizontal spacing has profound effect on the long-term performance of heat production, 2) the downward deviation angle for the parallel doublet wells may help overcome the difficulty of vertical drilling to reach a favorable production temperature, and 3) the thermal energy production rate and lifespan has close dependence on water mass flow rate. The results also indicate that the heat production can be improved when the horizontal fracture spacing, well deviation angle, and production flow rate are under reasonable conditions. To conduct the reservoir modeling and simulations, an open-source, finite element based, fully implicit, fully coupled hydrothermal code, namely FALCON, has been developed and used in this work. Compared with most other existing codes that are either closed-source or commercially available in this area, this new open-source code has demonstrated a code development strategy that aims to provide an unparalleled easiness for user-customization and multi-physics coupling. Test results have shown that the FALCON code is able to complete the long-term tests efficiently and accurately, thanks to the state-of-the-art nonlinear and linear solver algorithms implemented in the code.

enhanced geothermal system↗