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DOE OSTI2017

Demonstration of MAMMOTH Strongly-Coupled Multiphysics Simulation with the Godiva Benchmark Problem

This paper provides a detailed description of the Godiva benchmark problem suitable for multiphysics code verification. Multigroup transport weak forms for general curvilinear coordinates are derived using SAAF (self-adjoint angular flux) formulation. A new scheme based on spherical harmonics expansion for evaluating the angular derivative terms using the SN method are presented and tested. A one-dimensional spherical coordinate system is used by MAMMOTH for modeling the Godiva benchmark. Strongly-coupled multiphysics simulation mode of MAMMOTH is exercised and numerical results are given.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2012

Evaluation of accuracy of calculations of VVER-1000 core states with incomplete covering of fuel by the absorber

An additional verification of bundled software (BS) SAPFIR-95 and amp;RC [1] and code KORSAR/GP [2] was performed. Both software products were developed in A.P. Alexandrov NITI and certified by ROSTEKHNADZOR of RF for numeric simulation of stationary, transitional and emergency conditions of VVER reactors. A benchmark model for neutronics calculations was created within the limits of this work. The cold subcritical state of VVER - 1000 reactor stationary fuelling was simulated on the basis of FA with an increased height of the fuel column (TVS-2M) considering detailed presentation of radial and front neutron reflectors. A case of passing of pure condensate slug through the core in initially deep subcritical state during start of the first RCP set after refueling was considered as an examined condition of reactor operation. A relatively small size of the slug, its spatial position near the reflectors (lower and lateral), as well as failure of the inserted control rods of the control and protection system (CPS CR) to reach the lower limit of the fuel column stipulate for methodical complexity of a correct calculation of the neutron multiplication constant (K{sub eff}) using engineering codes. Code RC was used as a test program in the process of reactor calculated 3-D modeling. Code MCNP5 [3] was used as the precision program, which solves the equation of neutrons transfer by Monte-Carlo method and which was developed in the US (Los-Alamos). As a result of comparative calculations dependency of K{sub eff} on two parameters was evaluated - boron acid concentration (Cb) and CPS CR position. Reactivity effect was evaluated, which is implemented as a result of failure of all CPS control rods to reach the lower fuel limit calculated using the engineering codes mentioned above. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2015

Code Comparison Study Fosters Confidence in the Numerical Simulation of Enhanced Geothermal Systems

Numerical simulation has become a standard analytical tool for scientists and engineers to evaluate the potential and performance of enhanced geothermal systems. A variety of numerical simulators developed by industry, universities, and national laboratories are currently available and being applied to better understand enhanced geothermal systems at the field scale. To yield credible predictions and be of value to site operators, numerical simulators must be able to accurately represent the complex coupled processes induced by producing geothermal systems, such as fracture aperture changes due to thermal stimulation, fracture shear displacement with fluid injection, rate of thermal depletion of reservoir rocks, and permeability alteration with mineral precipitation or dissolution. A suite of numerical simulators was exercised on a series of test problems that considered coupled thermal, hydraulic, geomechanical, and geochemical (THMC) processes. Problems were selected and designed to isolate selected coupled processes, to be executed on workstation class computers, and have simple but illustrative metrics for result comparisons. This paper summarizes the initial suite of seven benchmark problems, describes the code comparison activities, provides example results for problems and documents the capabilities of currently available numerical simulation codes to represent coupled processes that occur during the production of geothermal resources. Code comparisons described in this paper use the ISO (International Organization for Standardization) standard ISO-13538 for proficiency testing of numerical simulators. This approach was adopted for a recent code comparison study within the radiation transfer-modeling field of atmospheric sciences, which was focused on canopy reflectance models. This standard specifies statistical methods for analyzing laboratory data from proficiency testing schemes to demonstrate that the measurement results do not exhibit evidence of an unacceptable level of bias.

benchmark problems↗

DOE OSTI2013

Verification & Validation of High-Order Short-Characteristics-Based Deterministic Transport Methodology on Unstructured Grids

The research team has developed a practical, high-order, discrete-ordinates, short characteristics neutron transport code for three-dimensional configurations represented on unstructured tetrahedral grids that can be used for realistic reactor physics applications at both the assembly and core levels. This project will perform a comprehensive verification and validation of this new computational tool against both a continuous-energy Monte Carlo simulation (e.g. MCNP) and experimentally measured data, an essential prerequisite for its deployment in reactor core modeling. Verification is divided into three phases. The team will first conduct spatial mesh and expansion order refinement studies to monitor convergence of the numerical solution to reference solutions. This is quantified by convergence rates that are based on integral error norms computed from the cell-by-cell difference between the code’s numerical solution and its reference counterpart. The latter is either analytic or very fine- mesh numerical solutions from independent computational tools. For the second phase, the team will create a suite of code-independent benchmark configurations to enable testing the theoretical order of accuracy of any particular discretization of the discrete ordinates approximation of the transport equation. For each tested case (i.e. mesh and spatial approximation order), researchers will execute the code and compare the resulting numerical solution to the exact solution on a per cell basis to determine the distribution of the numerical error. The final activity comprises a comparison to continuous-energy Monte Carlo solutions for zero-power critical configuration measurements at Idaho National Laboratory’s Advanced Test Reactor (ATR). Results of this comparison will allow the investigators to distinguish between modeling errors and the above-listed discretization errors introduced by the deterministic method, and to separate the sources of uncertainty.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1997

Computations of Complex Three-Dimensional Turbulent Free Jets

Three-dimensional, incompressible turbulent jets with rectangular and elliptical cross-sections are simulated with a finite-difference numerical method. The full Navier- Stokes equations are solved at low Reynolds numbers, whereas at high Reynolds numbers filtered forms of the equations are solved along with a sub-grid scale model to approximate the effects of the unresolved scales. A 2-N storage, third-order Runge-Kutta scheme is used for temporary discretization and a fourth-order compact scheme is used for spatial discretization. Although such methods are widely used in the simulation of compressible flows, the lack of an evolution equation for pressure or density presents particular difficulty in incompressible flows. The pressure-velocity coupling must be established indirectly. It is achieved, in this study, through a Poisson equation which is solved by a compact scheme of the same order of accuracy. The numerical formulation is validated and the dispersion and dissipation errors are documented by the solution of a wide range of benchmark problems. Three-dimensional computations are performed for different inlet conditions which model the naturally developing and forced jets. The experimentally observed phenomenon of axis-switching is captured in the numerical simulation, and it is confirmed through flow visualization that this is based on self-induction of the vorticity field. Statistical quantities such as mean velocity, mean pressure, two-point velocity spatial correlations and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stress equations are presented to aid in the turbulence modeling of complex jets. Simulations of circular jets are used to quantify the effect of the non-uniform curvature of the non-circular jets.

Wilson, Robert V.↗

DOE OSTI2023

Wind Turbine Noise Code Benchmark: A Comparison and Verification Exercise: Preprint

In a number of institutions and companies, researchers and engineers are developing modeling numerical frameworks that are used to predict the aerodynamic noise emission from a wind turbine rotor. The simulation codes vary from empirically-tuned engineering models to high-fidelity computational ones. Their common feature is the fact that they all specifically model the main aerodynamic noise mechanisms occurring at the rotating blades, namely trailing edge noise and turbulent inflow noise. Nevertheless, it can be expected that these different modeling frameworks will produce different results for a same given rotor design, and identical operating conditions. Trailing edge noise is put at the forefront of the study as it is recognized as the main audible source of noise from wind turbines. The present benchmark aims at comparing the results from the different modeling approaches, and drawing some conclusions from these comparisons. This effort, denoted as Wind Turbine Noise Code benchmark, was initiated in 2019 as a joint-activity between the IEA Wind Task 39 (Quiet Wind Turbine Technology) and Task 29 (Detailed Aerodynamics of Wind Turbines, now Task 47). In addition to the investigation of the noise emissions themselves, the rotor aerodynamic characteristics are investigated as they have a significant impact on the noise generation mechanisms. A number of test cases are defined and the aerodynamic and aeroacoustic predictions from the various models are compared. There exist some discrepancies between the different methods, but it is difficult to conclude if one methodology is better than another in order to design a wind turbine with noise as a constraint.

aeroacoustics↗

NASA NTRS2002

Effect of Melt Convection and Solid Transport on Macrosegregation and Grain Structure in Equiaxed Al-Cu Alloys

Macrosegregation in metal casting can be caused by thermal and solutal melt convection, and the transport of unattached solid crystals. These free grains can be a result of, for example, nucleation in the bulk liquid or dendrite fragmentation. In an effort to develop a comprehensive numerical model for the casting of alloys, an experimental study has been conducted to generate benchmark data with which such a solidification model could be tested. The specific goal of the experiments was to examine equiaxed solidification in situations where sinking of grains is (and is not) expected. The objectives were: 1) experimentally study the effects of solid transport and thermosolutal convection on macrosegregation and grain size distribution patterns; and 2) provide a complete set of controlled thermal boundary conditions, temperature data, segregation data, and grain size data, to validate numerical codes. The alloys used were Al-1 wt. pct. Cu, and Al-10 wt. pct. Cu with various amounts of the grain refiner TiB2 added. Cylindrical samples were either cooled from the top, or the bottom. Several trends in the data stand out. In attempting to model these experiments, concentrating on experiments that show clear trends or differences is recommended.

Rerko, Rodney S.↗

DOE OSTI2019

Benchmarking the extraction of statistical neutron capture cross sections on short-lived nuclei for applications using the β -Oslo method

Numerous scientific fields including astrophysics, nuclear power, and nuclear forensics require a knowledge of basic nuclear properties for large numbers of short-lived, radioactive isotopes far removed from stable nuclei. Neutron-capture cross sections are one such piece of nuclear data where direct measurements are not possible and theoretical predictions can vary by orders of magnitude. A recently developed indirect technique for inferring neutron capture rates, the β-Oslo method, has been introduced but not compared against a known, directly measured neutron capture cross section. To provide this benchmark, two indirect methods based on β decay and charged-particle reactions were used to extract the nuclear level density and γ-ray strength function of 51 Ti. The nuclear level density and γ-ray strength function from the two data sets were found to be equivalent and were used to extract the neutron capture cross section of 50 Ti which agrees with previous direct measurements at high neutron energies. Here, the results demonstrate the validity of the β-Oslo method for extracting neutron capture cross sections of short-lived nuclei and provide a sufficiently small uncertainty to be used in various applications.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Calibrating the Classical Hardness of the Quantum Approximate Optimization Algorithm

The trading of fidelity for scale enables approximate classical simulators such as matrix product states (MPSs) to run quantum circuits beyond exact methods. A control parameter, the so-called bond dimension $\mathcal{χ}$ for MPSs, governs the allocated computational resources and the output fidelity. Here, we characterize the fidelity for the quantum approximate optimization algorithm by the expectation value of the cost function that it seeks to minimize and find that it follows a scaling law $\mathscr{F}$(ln $\mathcal{χ}$/N), where N is the number of qubits. With ln $\mathcal{χ}$ amounting to the entanglement that a MPS can encode, we show that the relevant variable for investigating the fidelity is the entanglement per qubit. Importantly, our results calibrate the classical computational power required to achieve the desired fidelity and benchmark the performance of quantum hardware in a realistic setup. For instance, we quantify the hardness of performing better classically than a noisy superconducting quantum processor by readily matching its output to the scaling function. Moreover, we relate the global fidelity to that of individual operations and establish its relationship with $\mathcal{χ}$ and N. We sharpen the requirements for noisy quantum computers to outperform classical techniques at running a quantum optimization algorithm in speed, size, and fidelity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2012

Development and benchmarking of codes for simulation of beam-beam effects at the LHC

Beam dynamics in modern hadron colliders is strongly affected by effects of beam-beam interactions, which are complex phenomena and generally require extensive numerical simulations for accurate evaluation. In this note we describe the development of codes used for simulations of beam-beam effects at the LHC. We benchmark the codes on several test cases and report the results of this comparison.

43 PARTICLE ACCELERATORS↗

DOE OSTI2012

Development and Benchmarking of Codes for Simulation of Beam-Beam Effects at the LHC

43 PARTICLE ACCELERATORS↗

DOE OSTI2017

Graphics processing unit accelerated phase field dislocation dynamics: Application to bi-metallic interfaces

We present the first high-performance computing implementation of the meso-scale phase field dislocation dynamics (PFDD) model on a graphics processing unit (GPU)-based platform. The implementation takes advantage of the portable OpenACC standard directive pragmas along with Nvidia's compute unified device architecture (CUDA) fast Fourier transform (FFT) library called CUFFT to execute the FFT computations within the PFDD formulation on the same GPU platform. The overall implementation is termed ACCPFDD-CUFFT. The package is entirely performance portable due to the use of OPENACC-CUDA inter-operability, in which calls to CUDA functions are replaced with the OPENACC data regions for a host central processing unit (CPU) and device (GPU). A comprehensive benchmark study has been conducted, which compares a number of FFT routines, the Numerical Recipes FFT (FOURN), Fastest Fourier Transform in the West (FFTW), and the CUFFT. The last one exploits the advantages of the GPU hardware for FFT calculations. The novel ACCPFDD-CUFFT implementation is verified using the analytical solutions for the stress field around an infinite edge dislocation and subsequently applied to simulate the interaction and motion of dislocations through a bi-phase copper-nickel (Cu–Ni) interface. It is demonstrated that the ACCPFDD-CUFFT implementation on a single TESLA K80 GPU offers a 27.6X speedup relative to the serial version and a 5X speedup relative to the 22-multicore Intel Xeon CPU E5-2699 v4 @ 2.20 GHz version of the code.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Scalable DPG multigrid solver for Helmholtz problems: A study on convergence

This paper presents a scalable multigrid preconditioner targeting large-scale systems arising from discontinuous Petrov–Galerkin (DPG) discretizations of high-frequency wave operators. This work is built on previously developed multigrid preconditioning techniques of Petrides and Demkowicz (Comput. Math. Appl. 87 (2021) pp. 12–26) and extends the convergence results from $\mathscr{O}$(10 7 ) degrees of freedom (DOFs) to $\mathscr{O}$(10 9 ) DOFs using a new scalable parallel MPI/OpenMP implementation. Novel contributions of this paper include an alternative definition of coarse-grid systems based on restriction of fine-grid operators, yielding superior convergence results. In the uniform refinement setting, a detailed convergence study is provided, demonstrating h and p robust convergence and linear scaling with respect to the wave frequency. Finally, the paper concludes with numerical results on hp -adaptive simulations including a large-scale seismic modeling benchmark problem with high material contrast.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Upgrades for the CMS simulation

Over the past several years, the CMS experiment has made significant changes to its detector simulation application. The geometry has been generalized to include modifications being made to the CMS detector for 2015 operations, as well as model improvements to the simulation geometry of the current CMS detector and the implementation of a number of approved and possible future detector configurations. These include both completely new tracker and calorimetry systems. We have completed the transition to Geant4 version 10, we have made significant progress in reducing the CPU resources required to run our Geant4 simulation. These have been achieved through both technical improvements and through numerical techniques. Substantial speed improvements have been achieved without changing the physics validation benchmarks that the experiment uses to validate our simulation application for use in production. As a result, we will discuss the methods that we implemented and the corresponding demonstrated performance improvements deployed for our 2015 simulation application.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Resilience-Motivated Distribution System Restoration Considering Electricity-Water-Gas Interdependency

A major outage in the electricity distribution system may affect the operation of water and natural gas supply systems, leading to an interruption of multiple services to critical customers. Therefore, enhancing resilience of critical infrastructures requires joint efforts of multiple sectors. In this paper, a distribution system service restoration method considering the electricity-water-gas interdependency is proposed. The objective is maximizing the supply of electricity, water, and gas to critical customers after an extreme event. The operational constraints of electricity, water, and natural gas networks are considered. Additionally, the characteristics of electricity-driven coupling components, including water pumps and gas compressors, are also modeled. Relaxation techniques are applied to non convex constraints posed by physical laws of those networks. Consequently, the restoration problem is formulated as a mixed-integer second-order cone program, which can readily be solved by the off-the-shelf solvers. The proposed method is validated by numerical simulations on an electricity-water-gas integrated system, developed based on benchmark models of the subsystems. The results indicate that considering the interdependency refines the allocation of limited generation resources and demonstrate the exactness of the proposed convex relaxation

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2012

Reactor Engineering: Experimental Investigation of Alpha Convection

This report summarizes the progress on DE-FG07-07ID14806 project funded by the US Department of Energy under Nuclear Engineering Education Research (NEER) program. During the project a test apparatus was designed and manufactured for experimental investigation of Alpha Convection. Benchmark testing of the new apparatus without the neutron radiation was performed and numerical simulations were conducted to validate the experimental results on natural convection. These results were reported in a journal publication. Subsequently, we conducted the experiment at Missouri S&T research reactor in the beam port to investigate the phenomenon of Alpha Convection. Unfortunately, these experiments were inconclusive. No observable effect of neutron beam was noticed. Insufficient neutron flux as it passes through the borated water is responsible for the unsuccessful experiments. A number of new experiments are designed and manufactured to investigate the phenomenon. A new experiment using shadowgraphy is designed and manufactured to investigate and visualize the natural convection and the impact of neutron on the phenomenon. Moreover, to continue with the original and newly designed experiments a neutron generator was needed to supply a vertical beam of neutrons. This new source of neutron is acquired using DOE NEUP General Scientific Infrastructure number DE-FOA-0000321. The new facility is installed and tested but is yet to be licensed by NRC for regular use and continuation of the experiments.

Conduction convection transition.↗

NASA NTRS1986

Multiply scaled constrained nonlinear equation solvers

To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original solvers. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled solvers, results are presented for several benchmark examples.

Padovan, Joe↗

NASA NTRS1988

First-principle and empirical modelling of the global-scale ionosphere

The SUNDIAL program offers a unique opportunity to study ionospheric behavior on a global scale. As part of this program, data pertaining to solar, interplanetary, magnetospheric, ionospheric, and thermospheric conditions are collected simultaneously from a large number of satellite and ground-based sites spread around the world. In the coming years, these data should lead to a major improvement in both empirical and first-principle ionospheric models. As a benchmark against which to compare future progress, the present state of empirical and numerical ionospheric modeling is discussed. The discussion covers the capabilities and limitations of the existing models as well as the direction of future modeling efforts.

Schunk, R. W.↗