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At least 271 records · Page 15

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NASA NTRS1972

Examination of the collision force method for analyzing the responses of simple containment/deflection structures to impact by one engine rotor blade fragment

An approximate collision analysis, termed the collision-force method, was developed for studying impact-interaction of an engine rotor blade fragment with an initially circular containment ring. This collision analysis utilizes basic mass, material property, geometry, and pre-impact velocity information for the fragment, together with any one of three postulated patterns of blade deformation behavior: (1) the elastic straight blade model, (2) the elastic-plastic straight shortening blade model, and (3) the elastic-plastic curling blade model. The collision-induced forces are used to predict the resulting motions of both the blade fragment and the containment ring. Containment ring transient responses are predicted by a finite element computer code which accommodates the large deformation, elastic-plastic planar deformation behavior of simple structures such as beams and/or rings. The effects of varying the values of certain parameters in each blade-behavior model were studied. Comparisons of predictions with experimental data indicate that of the three postulated blade-behavior models, the elastic-plastic curling blade model appears to be the most plausible and satisfactory for predicting the impact-induced motions of a ductile engine rotor blade and a containment ring against which the blade impacts.

Zirin, R. M.↗

NASA NTRS2008

Evaluation of Recent Upgrades to the NESS (Nuclear Engine System Simulation) Code

The Nuclear Thermal Rocket (NTR) concept is being evaluated as a potential propulsion technology for exploratory expeditions to the moon, Mars, and beyond. The need for exceptional propulsion system performance in these missions has been documented in numerous studies, and was the primary focus of a considerable effort undertaken during the Rover/NERVA program from 1955 to 1973. The NASA Glenn Research Center is leveraging this past NTR investment in their vehicle concepts and mission analysis studies with the aid of the Nuclear Engine System Simulation (NESS) code. This paper presents the additional capabilities and upgrades made to this code in order to perform higher fidelity NTR propulsion system analysis and design, and a comparison of its results to the Small Nuclear Rocket Engine (SNRE) design.

Fittje, James E.↗

NASA NTRS2015

Space Radiation Transport Code Development: 3DHZETRN

The space radiation transport code, HZETRN, has been used extensively for research, vehicle design optimization, risk analysis, and related applications. One of the simplifying features of the HZETRN transport formalism is the straight-ahead approximation, wherein all particles are assumed to travel along a common axis. This reduces the governing equation to one spatial dimension allowing enormous simplification and highly efficient computational procedures to be implemented. Despite the physical simplifications, the HZETRN code is widely used for space applications and has been found to agree well with fully 3D Monte Carlo simulations in many circumstances. Recent work has focused on the development of 3D transport corrections for neutrons and light ions (Z < 2) for which the straight-ahead approximation is known to be less accurate. Within the development of 3D corrections, well-defined convergence criteria have been considered, allowing approximation errors at each stage in model development to be quantified. The present level of development assumes the neutron cross sections have an isotropic component treated within N explicit angular directions and a forward component represented by the straight-ahead approximation. The N = 1 solution refers to the straight-ahead treatment, while N = 2 represents the bi-directional model in current use for engineering design. The figure below shows neutrons, protons, and alphas for various values of N at locations in an aluminum sphere exposed to a solar particle event (SPE) spectrum. The neutron fluence converges quickly in simple geometry with N > 14 directions. The improved code, 3DHZETRN, transports neutrons, light ions, and heavy ions under space-like boundary conditions through general geometry while maintaining a high degree of computational efficiency. A brief overview of the 3D transport formalism for neutrons and light ions is given, and extensive benchmarking results with the Monte Carlo codes Geant4, FLUKA, and PHITS are provided for a variety of boundary conditions and geometries. Improvements provided by the 3D corrections are made clear in the comparisons. Developments needed to connect 3DHZETRN to vehicle design and optimization studies will be discussed. Future theoretical development will relax the forward plus isotropic interaction assumption to more general angular dependence.

Wilson, John W.↗

DOE OSTI2020

The EGS Collab Project: Learnings from Experiment 1

The primary objective of the EGS Collab Project sponsored by DOE is to increase the understanding needed to efficiently implement enhanced geothermal systems (EGS). One goal of the EGS Collab project is to create a collaborative research environment in which to study stimulation of crystalline rock at the 10 meter scale. Key to this effort is the collection of high quality data to allow comparison to numerical coupled process models in an effort to build confidence in the codes and modeling techniques used. In response to this, the EGS Collab team has created an underground test bed at the Sanford Underground Research Facility (SURF) in Lead SD at a depth of approximately 1.5 km to examine hydraulic fracturing (Experiment 1). We are currently designing a second test bed aimed at investigating shear stimulation (Experiment 2). At the Experiment 1 location, we have characterized our host rock using laboratory testing and numerous field-based geophysical and geological techniques, and created a well-instrumented test bed to allow us to carefully monitor stimulation events and flow tests. In addition to the installed geophysical sensors, we have used tracer tests, differences in the ambient microbial communities at flow collection locations, and cold water injection to inform us about dynamic flow pathways. In Experiment 1, we have hydraulically stimulated the host rock in a number times at several locations in one well, creating new fractures that connect to existing fractures between the injection and production boreholes. We have performed long-term ambient and chilled water injection tests as an analog to EGS, and have monitored system changes resulting from these water injections through geophysical monitoring, flow and pressure measurements, tracer tests, and microbiology. Here, we summarize the tests performed, issues identified including poroelastic and thermoelastic effects, Joule-Thomson effects, restarting effects, indications of flow channeling, and the primary learnings from Experiment 1.

Enhanced Geothermal Systems, EGS Collab, stimulati↗

DOE OSTI2023

Evaluation of Irradiation Creep Effects in HT9 Cladding for FAST Experiments

The push for advanced reactor fuels for improved reactor safety and efficiency had led to a renewed interest in metallic fuel for nuclear reactor applications. Experimental investigation is necessary to ensure a robust understanding of the thermomechanical properties of new metallic fuel designs. Unfortunately, with the current experimental facilities, thoroughly investigating the responses of metallic fuel burnup would take a prohibitively long time. To alleviate this, the Fission Accelerated Steady State Test (FAST) was developed to accelerate the irradiation testing while simultaneously decreasing the sensitivity to fabrication tolerances by reducing the fuel diameter and scaling the experiment. This method successfully scales the radiation effects on the fuel, but the HT9 cladding is not exposed to prototypic radiation conditions. This raises questions on whether the FAST experiment results are truly indicative of the HT9 cladding performance due to radiation induced creep effects not being appropriately accounted for. Using BISON fuel performance code, the simulated FAST cladding strain is compared to simulated EBR-II cladding strain. This is done through a sensitivity study of input parameters and scaling of neutron fluence on the cladding. This allows a parametric comparison of physical phenomena on the effective difference between cladding strains between FAST and equivalent burnup EBR-II fuel pins. The results show that the irradiation induced deformation (creep or swelling) is insignificant compared to the thermal-mechanical deformation. Therefore, the difference between the FAST experiment cladding and the EBR-II experiment cladding is negligible and comparison of fuel system performance between the two experiments is appropriate.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1988

Configuration trade and code validation study on a conical hypersonic vehicle

A study has been conducted on a generic wing-cone transatmospheric vehicle at Mach numbers form 2.5 to 4.5. The objectives of the study were to experimentally define the aerodynamic characteristics of the vehicle and evaluate several computational aerodynamic prediction methods through comparison with the experimental results. The baseline wing-cone configuration fuselage consisted of a 5 deg half-angle cone forebody, cylindrical midbody, and 9 deg truncated cone afterbody. The 4-percent-thick diamond airfoil wing had an aspect ratio of 1. Several configuration variables were investigated to provide trade information on canard, wing-position and incidence, vertical tail, and nose bluntness effects. Results of the study show that wing-position and wing-incidence effects on the longitudinal aerodynamic characteristics can be significantly influenced by wing-body interference. The use of positive wing incidence to provide favorable forebody orientation for possible inlet performance improvement is accompanied by trim drag and lift-drag ratio penalties. The lateral-directional stability characteristics were strongly influenced by the location of the vertical tails. The higher-order full-potential method provided better estimates of the aerodynamic characteristics than either the linearized supersonic potential method or the tangent-cone/tangent-wedge/shock-expansion on method.

Covell, Peter F.↗

NASA NTRS1998

Combined Numerical/Analytical Perturbation Solutions of the Navier-Stokes Equations for Aerodynamic Ejector/Mixer Nozzle Flows

In spite of rapid advances in both scalar and parallel computational tools, the large number of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical, With this restriction, it is concluded that an important family of methods for mathematical/computational development are reduced or approximate fluid flow models. In this study a combined perturbation/numerical modeling methodology is developed which provides a rigorously derived family of solutions. The mathematical model is computationally more efficient than classical boundary layer but provides important two-dimensional information not available using quasi-1-d approaches. An additional strength of the current methodology is its ability to locally predict static pressure fields in a manner analogous to more sophisticated parabolized Navier Stokes (PNS) formulations. To resolve singular behavior, the model utilizes classical analytical solution techniques. Hence, analytical methods have been combined with efficient numerical methods to yield an efficient hybrid fluid flow model. In particular, the main objective of this research has been to develop a system of analytical and numerical ejector/mixer nozzle models, which require minimal empirical input. A computer code, DREA Differential Reduced Ejector/mixer Analysis has been developed with the ability to run sufficiently fast so that it may be used either as a subroutine or called by an design optimization routine. Models are of direct use to the High Speed Civil Transport Program (a joint government/industry project seeking to develop an economically.viable U.S. commercial supersonic transport vehicle) and are currently being adopted by both NASA and industry. Experimental validation of these models is provided by comparison to results obtained from open literature and Limited Exclusive Right Distribution (LERD) sources, as well as dedicated experiments performed at Texas A&M. These experiments have been performed using a hydraulic/gas flow analog. Results of comparisons of DREA computations with experimental data, which include entrainment, thrust, and local profile information, are overall good. Computational time studies indicate that DREA provides considerably more information at a lower computational cost than contemporary ejector nozzle design models. Finally. physical limitations of the method, deviations from experimental data, potential improvements and alternative formulations are described. This report represents closure to the NASA Graduate Researchers Program. Versions of the DREA code and a user's guide may be obtained from the NASA Lewis Research Center.

DeChant, Lawrence Justin↗

DOE OSTI2021

3D simulations of vertical displacement events in tokamaks: A benchmark of M3D-C 1 , NIMROD, and JOREK

In recent years, the nonlinear 3D magnetohydrodynamic codes JOREK, M3D-C1, and NIMROD developed the capability of modeling realistic 3D vertical displacement events (VDEs) including resistive walls. In this paper, a comprehensive 3D VDE benchmark is presented between these state-of-the-art codes. The simulated case is based on an experimental NSTX plasma but with a simplified rectangular wall. There are differences between the physics models and numerical methods, and the VDE evolution leads to sensitivities on the initial conditions that cannot be avoided as can be done in edge localized modes (ELM) and sawtooth simulations (due to the non-cyclical nature of VDEs). Nonetheless, the comparison serves to quantify the level of agreement in the relevant quantities used to characterize disruptions, such as the 3D wall forces and energy decay. The results bring confidence regarding the use of the mentioned codes for disruption studies, and they distinguish aspects that are specific to the models used (e.g., reduced vs full MHD models). Here, the simulations show important 3D fea- tures for a NSTX plasma, such as the self-consistent evolution of the halo current and the origin of the wall forces. In contrast to other reduced MHD models based on an ordering in the aspect ratio, the ansatz-based JOREK reduced MHD model allows capturing many aspects of the 3D dynamics even in the spherical tokamak limit considered here.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2010

Comparison of DAC and MONACO DSMC Codes with Flat Plate Simulation

Various implementations of the direct simulation Monte Carlo (DSMC) method exist in academia, government and industry. By comparing implementations, deficiencies and merits of each can be discovered. This document reports comparisons between DSMC Analysis Code (DAC) and MONACO. DAC is NASA's standard DSMC production code and MONACO is a research DSMC code developed in academia. These codes have various differences; in particular, they employ distinct computational grid definitions. In this study, DAC and MONACO are compared by having each simulate a blunted flat plate wind tunnel test, using an identical volume mesh. Simulation expense and DSMC metrics are compared. In addition, flow results are compared with available laboratory data. Overall, this study revealed that both codes, excluding grid adaptation, performed similarly. For parallel processing, DAC was generally more efficient. As expected, code accuracy was mainly dependent on physical models employed.

Padilla, Jose F.↗

DOE OSTI2023

High-Fidelity Numerical Investigation on Elucidating Sodium Heat Transfer Characteristics for 37-Pin Wire-Wrapped Fuel Bundle in the PLANDTL Facility

This study involved a Reynolds-averaged Navier-Stokes- (RANS-) based computational fluid dynamics (CFD) analysis of the 37-pin wire-wrapped fuel bundle of the PNC Plant dynamics test loop (PLANDTL) facility. Previously, mainly the hydrodynamic phenomena of the wire-wrapped fuel bundle were analyzed, but the present study additionally included heat transfer analysis through conjugate heat transfer. The main purpose of the study was to benchmark the experimental data of the PLANDTL 37-pin wire-wrapped fuel bundle to investigate the heat transfer phenomena. In addition, the aim was to verify the accuracy of the RANS-based CFD analysis method using the STAR-CCM+ simulation software in comparison with the experimental data. The grid used for verification was an innovative grid system consisting of hexahedra using Fortran-based code. The development of the RANS-based CFD methodology included grid sensitivity analysis, turbulence model sensitivity analysis, and turbulent Prandtl number sensitivity analysis. Information on the temperature, mass flow rate, and area of the CFD results for each subchannel was provided for the top of the heated section and is expected to serve as a reference for future studies aiming to perform the validation and verification of a PLANDTL facility. In addition, the dependence of the peak temperature on the azimuth angle of each pin was analyzed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

The AGORA High-resolution Galaxy Simulations Comparison Project. IV. Halo and Galaxy Mass Assembly in a Cosmological Zoom-in Simulation at z ≤ 2

In this fourth paper from the AGORA Collaboration, we study the evolution down to redshift z = 2 and below of a set of cosmological zoom-in simulations of a Milky Way mass galaxy by eight of the leading hydrodynamic simulation codes. We also compare this CosmoRun suite of simulations with dark matter-only simulations by the same eight codes. We analyze general properties of the halo and galaxy at z = 4 and 3, and before the last major merger, focusing on the formation of well-defined rotationally supported disks, the mass–metallicity relation, the specific star formation rate, the gas metallicity gradients, and the nonaxisymmetric structures in the stellar disks. Codes generally converge well to the stellar-to-halo mass ratios predicted by semianalytic models at z ~ 2. We see that almost all the hydro codes develop rotationally supported structures at low redshifts. Most agree within 0.5 dex with the observed mass–metallicity relation at high and intermediate redshifts, and reproduce the gas metallicity gradients obtained from analytical models and low-redshift observations. We confirm that the intercode differences in the halo assembly history reported in the first paper of the collaboration also exist in CosmoRun, making the code-to-code comparison more difficult. We show that such differences are mainly due to variations in code-dependent parameters that control the time stepping strategy of the gravity solver. We find that variations in the early stellar feedback can also result in differences in the timing of the low-redshift mergers. All the simulation data down to z = 2 and the auxiliary data will be made publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

SCALE 6.2.4 Validation: Radiation Shielding

For safe and reliable use of computer codes by the community, accuracy must be clearly evaluated. In particular, the nuclear reactor engineering and licensing field needs accurate tools for radiation shielding modeling. Monaco with Automated Variance Reduction using Importance Calculations (MAVRIC) is one such tool, with built-in variance reduction methods distributed within the SCALE code, and its validity is demonstrated in this report for the released version 6.2.4. Representative benchmarks corresponding to shielding analysis are selected for the validation study. Typical experimental results analyzed from those benchmarks include neutron fluxes, detector count rates, detector energy response functions, neutron and gamma doses, foil neutron activation rates and activities, neutron leakage fluxes, and skyshine dose rates. Thousands of points of comparison between experiment and calculation are presented in this work. Other than rare outliers typically explained by either a lack of information or large uncertainties in the experiment conditions, material, or dimensions, MAVRIC agrees well with the experiment results. MAVRIC is also compared to Monte Carlo N-Particle (MCNP) calculations when available, and both codes generally produce good agreements within estimated uncertainties. The selected benchmarks are obtained from reliable sources such as the International Criticality Safety Benchmark Evaluation Project Handbook (ICSBEP Handbook), the Shielding Integral Benchmark Archive & Database (SINBAD), and other shielding validation work found in the literature. Additional datapoints and benchmarks will be added to future versions of this report to incrementally expand the shielding validation suite incrementally.

61 RADIATION PROTECTION AND DOSIMETRY↗

NASA NTRS2012

Plume-Free Stream Interaction Heating Effects During Orion Crew Module Reentry

During reentry of the Orion Crew Module (CM), vehicle attitude control will be performed by firing reaction control system (RCS) thrusters. Simulation of RCS plumes and their interaction with the oncoming flow has been difficult for the analysis community due to the large scarf angles of the RCS thrusters and the unsteady nature of the Orion capsule backshell environments. The model for the aerothermal database has thus relied on wind tunnel test data to capture the heating effects of thruster plume interactions with the freestream. These data are only valid for the continuum flow regime of the reentry trajectory. A Direct Simulation Monte Carlo (DSMC) analysis was performed to study the vehicle heating effects that result from the RCS thruster plume interaction with the oncoming freestream flow at high altitudes during Orion CM reentry. The study was performed with the DSMC Analysis Code (DAC). The inflow boundary conditions for the jets were obtained from Data Parallel Line Relaxation (DPLR) computational fluid dynamics (CFD) solutions. Simulations were performed for the roll, yaw, pitch-up and pitch-down jets at altitudes of 105 km, 125 km and 160 km as well as vacuum conditions. For comparison purposes (see Figure 1), the freestream conditions were based on previous DAC simulations performed without active RCS to populate the aerodynamic database for the Orion CM. Other inputs to the analysis included a constant Orbital reentry velocity of 7.5 km/s and angle of attack of 160 degrees. The results of the study showed that the interaction effects decrease quickly with increasing altitude. Also, jets with highly scarfed nozzles cause more severe heating compared to the nozzles with lower scarf angles. The difficulty of performing these simulations was based on the maximum number density and the ratio of number densities between the freestream and the plume for each simulation. The lowest altitude solutions required a substantial amount of computational resources (up to 1800 processors) to simulate approximately 2 billion molecules for the refined (adapted) solutions.

Marichalar, J.↗

NASA NTRS1999

A Comparison of Single-Cycle Versus Multiple-Cycle Proof Testing Strategies

Single-cycle and multiple-cycle proof testing (SCPT and MCPT) strategies for reusable aerospace propulsion system components are critically evaluated and compared from a rigorous elastic-plastic fracture mechanics perspective. Earlier MCPT studies are briefly reviewed. New J-integral estimation methods for semielliptical surface cracks and cracks at notches are derived and validated. Engineering methods are developed to characterize crack growth rates during elastic-plastic fatigue crack growth (FCG) and the tear-fatigue interaction near instability. Surface crack growth experiments are conducted with Inconel 718 to characterize tearing resistance, FCG under small-scale yielding and elastic-plastic conditions, and crack growth during simulated MCPT. Fractography and acoustic emission studies provide additional insight. The relative merits of SCPT and MCPT are directly compared using a probabilistic analysis linked with an elastic-plastic crack growth computer code. The conditional probability of failure in service is computed for a population of components that have survived a previous proof test, based on an assumed distribution of initial crack depths. Parameter studies investigate the influence of proof factor, tearing resistance, crack shape, initial crack depth distribution, and notches on the MCPT versus SCPT comparison. The parameter studies provide a rational basis to formulate conclusions about the relative advantages and disadvantages of SCPT and MCPT. Practical engineering guidelines are proposed to help select the optimum proof test protocol in a given application.

McClung, R. C.↗

NASA NTRS1996

A Comparison of Single-Cycle Versus Multiple-Cycle Proof Testing Strategies

Single-cycle and multiple-cycle proof testing (SCPT and MCPT) strategies for reusable aerospace propulsion system components are critically evaluated and compared from a rigorous elastic-plastic fracture mechanics perspective. Earlier MCPT studies are briefly reviewed. New J-integral estimation methods for semi-elliptical surface cracks and cracks at notches are derived and validated. Engineering methods are developed to characterize crack growth rates during elastic-plastic fatigue crack growth (FCG) and the tear-fatigue interaction near instability. Surface crack growth experiments are conducted with Inconel 718 to characterize tearing resistance, FCG under small-scale yielding and elastic-plastic conditions, and crack growth during simulated MCPT. Fractography and acoustic emission studies provide additional insight. The relative merits of SCPT and MCPT are directly compared using a probabilistic analysis linked with an elastic-plastic crack growth computer code. The conditional probability of failure in service is computed for a population of components that have survived a previous proof test, based on an assumed distribution of initial crack depths. Parameter studies investigate the influence of proof factor, tearing resistance, crack shape, initial crack depth distribution, and notches on the MCPT vs. SCPT comparison. The parameter studies provide a rational basis to formulate conclusions about the relative advantages and disadvantages of SCPT and MCPT. Practical engineering guidelines are proposed to help select the optimum proof test protocol in a given application.

McClung, R. C.↗

NASA NTRS1996

A Comparison of Single-Cycle Versus Multiple-Cycle Proof Testing Strategies

Single-cycle and multiple-cycle proof testing (SCPT and MCPT) strategies for reusable aerospace propulsion system components are critically evaluated and compared from a rigorous elastic-plastic fracture mechanics perspective. Earlier MCPT studies are briefly reviewed. New J-integral estimation methods for semi-elliptical surface cracks and cracks at notches are derived and validated. Engineering methods are developed to characterize crack growth rates during elastic-plastic fatigue crack growth (FCG) and the tear-fatigue interaction near instability. Surface crack growth experiments are conducted with Inconel 718 to characterize tearing resistance, FCG under small-scale yielding and elastic-plastic conditions, and crack growth during simulated MCPT. Fractography and acoustic emission studies provide additional insight. The relative merits of SCPT and MCPT are directly compared using a probabilistic analysis linked with an elastic-plastic crack growth computer code. The conditional probability of failure in service is computed for a population of components that have survived a previous proof test, based on an assumed distribution of initial crack depths. Parameter studies investigate the influence of proof factor, tearing resistance, crack shape, initial crack depth distribution, and notches on the MCPT vs. SCPT comparison. The parameter studies provide a rational basis to formulate conclusions about the relative advantages and disadvantages of SCPT and MCPT. Practical engineering guidelines are proposed to help select the optimum proof test protocol in a given application.

McClung, R. C.↗

DOE OSTI2023

Fuel performance uncertainty quantification and sensitivity analysis in the presence of epistemic and aleatoric sources of uncertainties

Fuel performance modeling and simulation includes many uncertain parameters from models to boundary conditions, manufacturing parameters and material properties. These parameters exhibit large uncertainties and can have an epistemic or aleatoric nature, something that renders fuel performance code-to-code and code-to-measurements comparisons for complex phenomena such as the pellet cladding mechanical interaction (PCMI) very challenging. Additionally, PCMI and other complex phenomena found in fuel performance modeling and simulation induce strong discontinuities and non-linearities that can render difficult to extract meaningful conclusions form uncertainty quantification (UQ) and sensitivity analysis (SA) studies. In this work, we develop and apply a consistent treatment of epistemic and aleatoric uncertainties for both UQ and SA in fuel performance calculations and use historical benchmark-quality measurement data to demonstrate it. More specifically, the developed methodology is applied to the OECD/NEA Multi-physics Pellet Cladding Mechanical Interaction Validation benchmark. A cold ramp test leading to PCMI is modeled. Two measured quantities of interest are considered: the cladding axial elongation during the irradiations and the cladding outer diameter after the cold ramp. The fuel performance code used to perform the simulation is FAST. The developed methodology involves various steps including a Morris screening to decrease the number of uncertain inputs, a nested loop approach for propagating the epistemic and aleatoric sources of uncertainties, and a global SA using Sobol indices. The obtained results indicate that the fuel and cladding thermal conductivities as well as the cladding outer diameter uncertainties are the three inputs having the largest impact on the measured quantities. More importantly, it was found that the epistemic uncertainties can have a significant impact on the measured quantities and can affect the outcome of the global sensitivity analysis.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Efficient real space formalism for hybrid density functionals

We present an efficient real space formalism for hybrid exchange-correlation functionals in generalized Kohn–Sham density functional theory (DFT). In particular, we develop an efficient representation for any function of the real space finite-difference Laplacian matrix by leveraging its Kronecker product structure, thereby enabling the time to solution of associated linear systems to be highly competitive with the fast Fourier transform scheme while not imposing any restrictions on the boundary conditions. We implement this formalism for both the unscreened and range-separated variants of hybrid functionals. We verify its accuracy and efficiency through comparisons with established planewave codes for isolated as well as bulk systems. In particular, we demonstrate up to an order-of-magnitude speedup in time to solution for the real space method. We also apply the framework to study the structure of liquid water using ab initio molecular dynamics, where we find good agreement with the literature. Overall, the current formalism provides an avenue for efficient real-space DFT calculations with hybrid density functionals.

Chemistry↗