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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

The Role and Value of Interregional Transmission in a Decarbonized U.S. Electricity System

Decarbonizing the U.S. energy system entails a significant expansion of wind and solar power and electrification of end-use applications. Achieving both is more efficient and less costly when interregional transmission capacity is expanded, but the fractured nature of grid planning in the United States is often a barrier to such expansion. Here, we explore the role of interregional transmission under a variety of decarbonization scenarios, using a capacity-expansion model to generate co-optimized portfolios of generation, storage, and transmission that meet decarbonization targets and electrification-driven demand. We explore portfolio and cost differences across 92 scenarios, from scenarios with limited transmission expansion to those that include a meshed high-voltage direct current (HVDC) network. In the core decarbonization scenarios, wind capacity expands by ~10x and solar by ~20x compared to 2020, hundreds of gigawatts of battery storage are deployed, and interregional transmission expands by 3-6x. Transmission expansion occurs nationwide but is concentrated between the central "wind belt" and eastern load centers. The HVDC scenarios result in hundreds of billions of dollars of savings in total system cost, demonstrating the economic benefits of interregional transmission in support of rapid decarbonization.

capacity expansion↗
NASA NTRS1997

Reduced Navier Stokes Relaxation Procedures for Internal Flows

In spite of significant advancement in the field of high speed computing, flow calculations involving complex geometries and/or flow behavior still require large amounts of CPU time and memory. In order to predict such flows without sacrificing grid convergence and accuracy, adaptive gridding techniques that provide optimal resolution are highly desirable. The present work combines multigrid techniques and domain decomposition concepts to provide local, solution adaptive, grid refinement. Several viscous compressible and incompressible, two and three-dimensional, flows with strong inviscid interaction and/or axial flow reversal, are considered with a segmented multigrid domain decomposition (SMGDD) procedure for which uniform meshes result in each domain. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable non-staggered grid computation. The SMGDD technique presented herein has previously been applied for incompressible two dimensional flows. The present work offers improvement in the gridding strategy, by allowing for disjoint subdomains that provide optimal resolution of disparate flow features. It also extends the SMGDD technique to three dimensional compressible flows. Laminar and turbulent flow in a backward facing step channel is considered; although the procedure is applicable to more severe geometries. The standard K-epsilon model is applied for turbulence closure. For Re greater than 400, differences between two-dimensional theory and experiment are resolved through a three dimensional simulation, which confirms the experimentally observed three dimensionality of the recirculation patterns on the upper and lower surfaces.

Rubin, Stanley G.↗
DOE OSTI2020

On the Derivation of Quasi-Newton Formulas for Optimization in Function Spaces

Newton’s method is usually preferred when solving optimization problems due to its superior convergence properties compared to gradient-based or derivative-free optimization algorithms. However, deriving and computing second-order derivatives needed by Newton’s method often is not trivial and, in some cases, not possible. In such cases quasi-Newton algorithms are a great alternative. In this paper, we provide a new derivation of well-known quasi-Newton formulas in an infinite-dimensional Hilbert space setting. Furthermore, it is known that quasi-Newton update formulas are solutions to certain variational problems over the space of symmetric matrices. In this paper, we formulate similar variational problems over the space of bounded symmetric operators in Hilbert spaces. By changing the constraints of the variational problem we obtain updates (for the Hessian and Hessian inverse) not only for the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method but also for Davidon–Fletcher–Powell (DFP), Symmetric Rank One (SR1), and Powell-Symmetric-Broyden (PSB). In addition, for an inverse problem governed by a partial differential equation (PDE), we derive DFP and BFGS “structured” secant formulas that explicitly use the derivative of the regularization and only approximates the second derivative of the misfit term. We show numerical results that demonstrate the desired mesh-independence property and superior performance of the resulting quasi-Newton methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Improvements to MOOSE user workflow through polyhedral elements, automation, and concise physics syntax

The MOOSE framework is a foundational capability used by the NEAMS program to create over 15 different simulation tools for advanced nuclear reactors. Due to MOOSE's broad use, improvements to the framework in support of modeling and simulation goals are critical to the program. Such improvements can take many forms, including optimization, improved user experience, streamlined application programming interfaces (APIs), parallelism, and new capabilities. The work described in this report was conducted in direct support of NEAMS tools and includes: addition of support for polyhedral elements, incorporation of mesh smoothers for mesh repair, integration of the Physics and ActionComponents systems, expansion of the Convergence system, and exploration of automated input file generation. These five areas of development are fundamental capabilities that will be leveraged by many NEAMS applications.

97 - MATHEMATICS AND COMPUTING↗
NASA NTRS2000

High Performance Fortran for Aerospace Applications

This paper focuses on the use of High Performance Fortran (HPF) for important classes of algorithms employed in aerospace applications. HPF is a set of Fortran extensions designed to provide users with a high-level interface for programming data parallel scientific applications, while delegating to the compiler/runtime system the task of generating explicitly parallel message-passing programs. We begin by providing a short overview of the HPF language. This is followed by a detailed discussion of the efficient use of HPF for applications involving multiple structured grids such as multiblock and adaptive mesh refinement (AMR) codes as well as unstructured grid codes. We focus on the data structures and computational structures used in these codes and on the high-level strategies that can be expressed in HPF to optimally exploit the parallelism in these algorithms.

Mehrotra, Piyush↗
DOE OSTI2021

Hexagonal Geometries in MPACT

The MPACT code is a high-fidelity light-water reactor analysis code using whole-core pin-resolved neutron transport calculations on modern parallel-computing hardware. MPACT uses the 2D/1D method to solve 3D neutron transport problems by decomposing the problem into a stack of 2D slices, each of which is solved independently using the method of characteristics (MOC). The slices are then coupled axially using the P3 nodal expansion method (NEM-P3) for the 1D axial calculations. MPACT also employs the coarse mesh finite difference (CMFD) method to accelerate calculations. This manuscript details work supporting advanced reactor designs using hexagonal pins and hexagonal assemblies such as the VVER-1000. If performed correctly, MOC is geometry agnostic. However, MPACT previously had optimizations in place for Cartesian geometries, specifically in the modularization and current calculations. Sections 2 and 3 detail the changes made to MPACT to support MOC and CMFD calculations on hexagonal geometries. Section 4 reports results demonstrating solution consistency for problems run with and without CMFD acceleration, results demonstrating solution consistency when run in serial and parallel, and pincell results using the Monte Carlo code, McCard’s benchmark results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS2023

Optimizing the Resolution of Hydrodynamic Simulations for MCRaT Radiative Transfer Calculations

Despite their discovery about half a century ago, the Gamma-ray burst (GRB) prompt emission mechanism is still not well understood. Theoretical modeling of the prompt emission has advanced considerably due to new computational tools and techniques. One such tool is the PLUTO hydro dynamics code, which is used to numerically simulate GRB outflows. PLUTO uses Adaptive Mesh Refinement to focus computational efforts on the portion of the grid that contains the simulated jet. Another tool is the Monte Carlo Radiation Transfer (MCRaT) code, which predicts electromagnetic signatures of GRBs by conducting photon scatterings within a jet using PLUTO. The effects of the underlying resolution of a PLUTO simulation with respect to MCRaT post-processing radiative transfer results have not yet been quantified. We analyze an analytic spherical outflow and a hydrodynamically simulated GRB jet with MCRaT at varying spatial and temporal resolutions and quantify how decreasing both resolutions affect the resulting mock observations. We find that changing the spatial resolution changes the hydrodynamic properties of the jet, which directly affect the MCRaT mock observable peak energies. We also find that decreasing the temporal resolution artificially decreases the high energy slope of the mock observed spectrum, which increases both the spectral peak energy and the luminosity. We show that the effects are additive when both spatial and temporal resolutions are modified. Our results allow us to understand how decreased hydrodynamic temporal and spatial resolutions affect the results of post-processing radiative transfer calculations, allowing for the optimization of hydrodynamic simulations for radiative transfer codes.

Jose Arita-Escalante↗
NASA NTRS1987

Concurrent algorithms for transient nonlinear FE analysis

A two-parameter class of time-stepping algorithms for nonlinear structural dynamics is investigated. What sets the present method apart from other concurrent algorithms is the fact that it can be used to some advantage in sequential machines as well. Thus, substantial speed-ups are obtained on a single processor as the number of subdomains is increased. An additional O(p) speed-up is obtained when p processors are utilized. The test case discussed is being repeated for a mesh comprising four times as many elements, in an effort to understand how the large scale asymptotic speed-ups are attained. A three dimensional example involving finite deformations and free body motions is also being pursued. A code optimized for concurrency in the Alliant FX8 computer is being finalized. This will provide the means for testing the performance of the algorithm in a multiprocessor environment.

Ortiz, M.↗
NASA NTRS2010

Dynamically Evolving Sectors for Convective Weather Impact

A new strategy for altering existing sector boundaries in response to blocking convective weather is presented. This method seeks to improve the reduced capacity of sectors directly affected by weather by moving boundaries in a direction that offers the greatest capacity improvement. The boundary deformations are shared by neighboring sectors within the region in a manner that preserves their shapes and sizes as much as possible. This reduces the controller workload involved with learning new sector designs. The algorithm that produces the altered sectors is based on a force-deflection mesh model that needs only nominal traffic patterns and the shape of the blocking weather for input. It does not require weather-affected traffic patterns that would have to be predicted by simulation. When compared to an existing optimal sector design method, the sectors produced by the new algorithm are more similar to the original sector shapes, resulting in sectors that may be more suitable for operational use because the change is not as drastic. Also, preliminary results show that this method produces sectors that can equitably distribute the workload of rerouted weather-affected traffic throughout the region where inclement weather is present. This is demonstrated by sector aircraft count distributions of simulated traffic in weather-affected regions.

Drew, Michael C.↗
DOE OSTI2025

Optimized Auxiliary Functions for Robust Mitigation of Finite-Size Errors in Periodic Hybrid Density Functional Theory

When calculating properties of periodic systems at the thermodynamic limit (TDL), the dominant source of finite size error (FSE) arises from the long-range Coulomb interaction, and can manifest as a slowly converging quadrature error when approximating an integral in the reciprocal space by a finite sum. The singularity subtraction (SS) method offers a systematic approach for reducing this quadrature error and thus the FSE. Here, in this work, we first investigate the performance of the SS method in the simplest setting, aiming at reducing the FSE in exact exchange calculations by subtracting the Coulomb contribution with a single, adjustable Gaussian auxiliary function. We demonstrate that a simple fitting method can robustly estimate the optimal Gaussian width and leads to rapid convergence toward the TDL. Furthermore, we suggest new forms of the auxiliary function, whose optimal parameters could also be determined through least-squares fitting. For a range of semiconductors and insulators, the proposed auxiliary functions achieve robust, millihartree-level accuracy in hybrid density functional theory calculations, including cases with sparse k-meshes and large basis sets.

Quiton, Stephen Jon [University of California, Ber↗
DOE OSTI2018

The fully nonconforming virtual element method for biharmonic problems

Here in this paper, we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbitrary order of accuracy for biharmonic problems. The approximation space is made of possibly discontinuous functions, thus giving rise to the fully nonconforming virtual element method. We derive optimal error estimates in a suitable (broken) energy norm and present numerical results to assess the validity of the theoretical estimates.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Redundancy management for efficient fault recovery in NASA's distributed computing system

The management of redundancy in computer systems was studied and guidelines were provided for the development of NASA's fault-tolerant distributed systems. Fault recovery and reconfiguration mechanisms were examined. A theoretical foundation was laid for redundancy management by efficient reconfiguration methods and algorithmic diversity. Algorithms were developed to optimize the resources for embedding of computational graphs of tasks in the system architecture and reconfiguration of these tasks after a failure has occurred. The computational structure represented by a path and the complete binary tree was considered and the mesh and hypercube architectures were targeted for their embeddings. The innovative concept of Hybrid Algorithm Technique was introduced. This new technique provides a mechanism for obtaining fault tolerance while exhibiting improved performance.

Malek, Miroslaw↗
NASA NTRS1993

Modeling and new equipment definition for the vibration isolation box equipment system

Our MSAD-funded research project is to provide numerical modeling support for the VIBES (Vibration Isolation Box Experiment System) which is an IML2 flight experiment being built by the Japanese research team of Dr. H. Azuma of the Japanese National Aerospace Laboratory. During this reporting period, the following have been accomplished: A semi-consistent mass finite element projection algorithm for 2D and 3D Boussinesq flows has been implemented on Sun, HP And Cray Platforms. The algorithm has better phase speed accuracy than similar finite difference or lumped mass finite element algorithms, an attribute which is essential for addressing realistic g-jitter effects as well as convectively-dominated transient systems. The projection algorithm has been benchmarked against solutions generated via the commercial code FIDAP. The algorithm appears to be accurate as well as computationally efficient. Optimization and potential parallelization studies are underway. Our implementation to date has focused on execution of the basic algorithm with at most a concern for vectorization. The initial time-varying gravity Boussinesq flow simulation is being set up. The mesh is being designed and the input file is being generated. Some preliminary 'small mesh' cases will be attempted on our HP9000/735 while our request to MSAD for supercomputing resources is being addressed. The Japanese research team for VIBES was visited, the current set up and status of the physical experiment was obtained and ongoing E-Mail communication link was established.

Sani, Robert L.↗
DOE OSTI2026

FIREFLY: heat load and particle exhaust approximations for rapid evaluation of divertor designs

The divertor in a magnetic confinement fusion reactor is an essential component for power dissipation and particle removal. The FIREFLY package for rapid evaluation of divertor designs is presented as an extension of the FLARE code for field line reconstruction from a flux tube mesh. First, divertor loads are approximated with a simplified heat transport model. Neutralized particles are then sampled from the resulting load distribution, and the EIRENE code is used to track molecules and atoms in a plasma background while accounting for dissociation, charge exchange and ionization. Particles are removed on pumping surfaces in order to estimate the exhaust efficiency for a given divertor geometry. Optimization of the divertor geometry for more efficient particle exhaust is explored by using W7-X as an example, and the sensitivity to model parameters for the plasma background in the proxy calculations is evaluated.

mesh generation, magnetic field lines, scrape-off ↗
NASA NTRS2011

A Generalized Framework for Constrained Design Optimization of General Supersonic Configurations Using Adjoint Based Sensitivity Derivatives

The Aeronautics Research Mission Directorate (ARMD) sent out an NASA Research Announcement (NRA) for proposals soliciting research and technical development. The proposed research program was aimed at addressing the desired milestones and outcomes of ROA (ROA-2006) Subtopic A.4.1.1 Advanced Computational Methods. The second milestone, SUP.1.06.02 Robust, validated mesh adaptation and error quantification for near field Computational Fluid Dynamics (CFD), was addressed by the proposed research. Additional research utilizing the direct links to geometry through a CAD interface enabled by this work will allow for geometric constraints to be applied and address the final milestone, SUP2.07.06 Constrained low-drag supersonic aerodynamic design capability. The original product of the proposed research program was an integrated system of tools that can be used for the mesh mechanics required for rapid high fidelity analysis and for design of supersonic cruise vehicles. These Euler and Navier-Stokes volume grid manipulation tools were proposed to efficiently use parallel processing. The mesh adaptation provides a systematic approach for achieving demonstrated levels of accuracy in the solutions. NASA chose to fund only the mesh generation/adaptation portion of the proposal. So this report describes the completion of the proposed tasks for mesh creation, manipulation and adaptation as it pertains to sonic boom prediction of supersonic configurations.

Karman, Steve L., Jr.↗
DOE OSTI2019

Camellia: A Rapid Development Framework for Finite Element Solvers

We report the discontinuous Petrov–Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan guarantees the optimality of the finite element solution in a user-controllable energy norm, and provides several features supporting adaptive schemes. The approach provides stability automatically; there is no need for carefully derived numerical fluxes (as in DG schemes) or for mesh-dependent stabilization terms (as in stabilized methods). In this paper, we focus on features of Camellia that facilitate implementation of new DPG formulations; chief among these is a rich set of features in support of symbolic manipulation, which allow, e.g., bilinear formulations in the code to appear much as they would on paper. Many of these features are general in the sense that they can also be used in the implementation of other finite element formulations. In fact, because DPG’s requirements are essentially a superset of those of other finite element methods, Camellia provides built-in support for most common methods. We believe, however, that the combination of an essentially “hands-free” finite element methodology as found in DPG with the rapid development features of Camellia are particularly winsome, so we focus on use cases in this class. In addition to the symbolic manipulation features mentioned above, Camellia offers support for one-irregular adaptive meshes in 1D, 2D, 3D, and space-time. It provides a geometric multigrid preconditioner particularly suited for DPG problems, and supports distributed parallel execution using MPI. For its load balancing and distributed data structures, Camellia relies on packages from the Trilinos project, which simplifies interfacing with other computational science packages. Camellia also allows loading of standard mesh formats through an interface with the MOAB package. Camellia includes support for static condensation to eliminate element-interior degrees of freedom locally, usually resulting in substantial reduction of the cost of the global problem. Finally, we include a discussion of the variational formulations built into Camellia, with references to those formulations in the literature, as well as an MPI performance study.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Level-set Modeling Simulations of Chemical Vapor Infiltration for Ceramic Matrix Composites Manufacturing

Silicon-carbide (SiC) reinforced ceramic matrix composites (CMCs) are a key enabling technology to reduce fuel consumption and emissions of gas turbine engines. In one manufacturing approach, chemical vapor infiltration (CVI) is limited to only coating SiC fibers. The preform is then fabricated using a lay-up of basic plys or 2-D woven sheets composed of the precoated fibers. At the other extreme, CVI is used to completely densify a 3-D woven preform shaped almost like the gas turbine component itself. The latter approach is more suitable for highly engineered components which sit directly in the gas path of the engine, for example, a high pressure turbine blade. In this case, the geometry is necessarily complex for aerodynamic, stress, and lifing (multi-physics) requirements. Presently, optimizing the CVI-dominated manufacturing approach is largely by trial-and-error. In this work, a first-principles modeling of CVI is performed to realize optimization of SiC/SiC CMC manufacturing. The modeling is based on a level-set framework to describe the interface between the vapor and solid phases. A finite-difference numerical scheme using an immersed boundary method is developed for fixed, structured meshes. Massively parallel direct numerical simulations (DNS) of CVI through fiber-woven geometries are performed using one-step chemistry, and over a range of Thiele moduli. Illustrative applications of the resulting large DNS data sets are given, including the development of fiber-weave specific infiltration models and structure functions for mean-field (porous media) Computational Fluid Dynamics (CFD) simulations of CVI.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Method and apparatus for shape-based energy analysis of solids

A method of evaluating response of a physical structure to external stimulus includes defining a mesh of finite elements, each defined by edges, for a model of the physical structure. The method includes identifying a governing differential equation and associated complementary functions, which are each associated with a scalar multiplier. The method includes generating an energy optimization model that minimizes a difference between internal and external energies of the finite elements. The internal energy is based on strain energy in a volume defined by the edges of the finite element and resulting from deformations by the complementary functions. The external energy of each finite element is based on external work done by the external stimulus acting on the finite element as deformed by the complementary functions. The method includes solving the energy optimization model for the scalar multipliers and calculating a resulting parameter of interest of the physical structure.

42 ENGINEERING↗