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DOE OSTI2016

Finite time step and spatial grid effects in δf simulation of warm plasmas

This paper introduces a technique for analyzing time integration methods used with the particle weight equations in δf method particle-in-cell (PIC) schemes. The analysis applies to the simulation of warm, uniform, periodic or infinite plasmas in the linear regime and considers the collective behavior similar to the analysis performed by Langdon for full-f PIC schemes [1,2]. We perform both a time integration analysis and spatial grid analysis for a kinetic ion, adiabatic electron model of ion acoustic waves. An implicit time integration scheme is studied in detail for δf simulations using our weight equation analysis and for full-f simulations using the method of Langdon. It is found that the δf method exhibits a CFL-like stability condition for low temperature ions, which is independent of the parameter characterizing the implicitness of the scheme. The accuracy of the real frequency and damping rate due to the discrete time and spatial schemes is also derived using a perturbative method. The theoretical analysis of numerical error presented here may be useful for the verification of simulations and for providing intuition for the design of new implicit time integration schemes for the δf method, as well as understanding differences between δf and full-f approaches to plasma simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1993

Modeling ice streams: Derived quantities

The model addressed is a finite-element, map-plane, time-dependent, column-averaged continuity equation solver. The key to the fitting process involves the balance between ice motion dominated by flow in internal layers, and ice motion dominated by sliding at the bed. The fitting process involves an iterative process carried out in the time domain. Beginning with the portion of the ice sheet being modeled identical to the present ice sheet with uniform flow, sliding, and fraction specified at nominal values, the model monitors each nodal point surface elevation. As the calculated surface elevation deviates from the present surface, a correction proportional to the difference is applied to selected parameter sets. This correction is in a sense that would tend to improve the fit at the particular nodal point. A calculated surface elevation that was higher than the present surface would result in an increased fraction, which would tend to lower the calculated surface (if the flow or sliding constant were being used as the fitting parameter, they would be lowered to improve the fit). This process is allowed to proceed as long as is necessary for the situation to stabilize. Typically, this takes tens of thousands of model years, but the rate is dependent on other external forcings such as the accumulation rate. The primary result is that while a typical sample of ice streams from around Antarctica can be fitted quite reasonably using only the fraction of the velocity due to sliding, a different mechanism seems to be in play along the Siple Coast, where reduced sliding constants are required to attain a reasonable fit. Flow is more strongly channelized in this region, and velocities are, in general, higher than are observed in other regions. It is unlikely that the mechanism that controls the ice movement along the Siple Coast is exactly similar to the mechanisms in the other ice streams. The concept of deformable sediments and their contribution to the fast flow along the Siple Coast may have limited applicability to other Antarctic ice streams.

Fastook, James↗

NASA NTRS2014

High-Energy Pulsar Models: Developments and New Questions

The past few years have seen a major advance in observational knowledge of high-energy (HE) pulsars. The Fermi Large Area Telescope (LAT) and AGILE have increased the number of known gamma-ray pulsars by an order of magnitude, its members being divided roughly equally among millisecond pulsars (MSPs), young radio-loud pulsars, and young radio-quiet pulsars. Many new and diverse emission characteristics are being measured, while radio and X-ray follow-up observations increase the pulsar detection rate and enrich our multiwavelength picture of these extreme sources. The wealth of new data has provided impetus for further development and improvement of existing theoretical pulsar models. Geometric light curve (LC) modelling has uncovered three broad classes into which HE pulsars fall: those where the radio profile leads, is aligned with, or lags the gamma-ray profile. For example, the original MSP and original black widow system are members of the second class, requiring co-located emission regions and thereby breaking with traditional notions of radio emission origin. These models imply narrow accelerator gaps in the outer magnetosphere, indicating copious pair production even in MSP magnetospheres that were previously thought to be pair-starved. The increased quality and variety of the LCs necessitate construction of ever more sophisticated models. We will review progress in global magnetosphere solutions which specify a finite conductivity on field lines above the stellar surface, filling the gap between the standard vacuum and force-free (FF; plasma-filled) models. The possibility of deriving phase-resolved spectra for the brightest pulsars, coupled with the fact that the HE pulsar population is sizable enough to allow sampling of various pulsar geometries, will enable much more stringent testing of future radiation models. Reproduction of the observed phase-resolved behavior of this disparate group will be one of the next frontiers in pulsar science, impacting on our understanding of particle acceleration, emission, and magnetosphere geometry. One may now also study evolutionary trends of the measured or inferred quantities, and probe pulsar visibility and population properties such as radiation beam sizes of different pulsar classes, as well as the distribution of spin-down power, gamma-ray luminosity, conversion efficiency, spectral index, and cutoff energy across the population. Lastly, the recent detection of very-high-energy (VHE) pulsations from the Crab pulsar generated quite a few ideas to explain this emission, leading to an extension of standard models and possibly even a bridge between the physics of pulsars and pulsar wind nebulae (PWNe).

gamma rays:↗

DOE OSTI2021

Chiral Topological Surface States on a Finite Square Photonic Crystal Bounded by Air

Chiral, topologically protected, photonic surface states can be found at the boundary between gyrotropic photonic crystals where a changing magnetic field induces different topology across the interface. Typically, photonic crystals with either a suitable band structure on both sides of the interface to provide a band gap and evanescent decay of the surface states away from the interface, or an outer layer with engineered material properties is required. In this paper, we show the emergence of topological, unidirectional surface states at the termination of finite gyrotropic photonic crystals with a simple square lattice and C 4 rotational symmetry bounded by a vacuum, eliminating the need for an outside layer to enable chiral surface modes. Here, we start from an infinite, time-reversal-symmetry-breaking photonic crystal with a band gap associated with bands with nonzero Chern numbers, different from all-zero Chern numbers in air. We then modify the photonic crystal to move this band gap below the light line, while maintaining the Chern-number discontinuities. Band-structure calculations for a supercell approximating a photonic crystal finite in the direction normal to the surface demonstrate the existence, dispersion, and chirality of the surface mode. Extensive direct scattering calculations for a point source and spatial Fourier analysis further reveal a unidirectional free-space topological surface state, which propagates counterclockwise around the surface of a finite photonic crystal, providing a nearly foolproof way to cross-check the surface-mode band structure unaffected by backscattering from local defects. Additionally, scattering simulations allow an independent characterization of the state dispersion and unveil the robustness of the topological plasmonic mode propagation around the 90° bends of the structure, being due to only radiation leakage. In contrast to buried topological surface states, the observed surface modes at the photonic crystal–air interface have the advantage of being accessible to the outside world, allowing one to take advantage of the defect-tolerant backscattering-free surface modes to engineer emission from photonic crystal surfaces into arbitrary free-space beam shapes and directions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Performance analysis of a finite radon transform in OFDM system under different channel models

In this paper, a class of discrete Radon transforms namely Finite Radon Transform (FRAT) was proposed as a modulation technique in the realization of Orthogonal Frequency Division Multiplexing (OFDM). The proposed FRAT operates as a data mapper in the OFDM transceiver instead of the conventional phase shift mapping and quadrature amplitude mapping that are usually used with the standard OFDM based on Fast Fourier Transform (FFT), by the way that ensure increasing the orthogonality of the system. The Fourier domain approach was found here to be the more suitable way for obtaining the forward and inverse FRAT. This structure resulted in a more suitable realization of conventional FFT- OFDM. It was shown that this application increases the orthogonality significantly in this case due to the use of Inverse Fast Fourier Transform (IFFT) twice, namely, in the data mapping and in the sub-carrier modulation also due to the use of an efficient algorithm in determining the FRAT coefficients called the optimal ordering method. The proposed approach was tested and compared with conventional OFDM, for additive white Gaussian noise (AWGN) channel, flat fading channel, and multi-path frequency selective fading channel. The obtained results showed that the proposed system has improved the bit error rate (BER) performance by reducing inter-symbol interference (ISI) and inter-carrier interference (ICI), comparing with conventional OFDM system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Impact of Control Blade Insertion on the Deformation Behavior of SiC-SiC Channel Boxes in Boiling Water Reactors

This report describes the analysis of distortion of a Silicon carbide fiber-reinforced silicon carbide matrix (SiC-SiC) composite channel box under in-reactor conditions of a boiling water reactor (BWR). The BWR core has significant gradients in the fast neutron flux across the channel box due to the presence of water rods within the fuel assemblies, and these gradients increase further with the insertion of control blades. As a result of temperature and neutron flux dependent irradiation induced swelling of SiC, the SiC-SiC composite channel box can undergo significant distortion. In this work, we evaluate the SiC-SiC channel box distortion for three different control blade positions. This analysis is based on the neutron flux and temperature distributions in the BWR core calculated using the neutronics code MPACT and thermalhydraulics code CTF. This calculation is coupled through temperature feedback. Subsequently, we have performed structural analysis based on the calculated neutron flux and temperature distributions, to determine the deformation and stress development in the channel box. The structural analysis was performed using the fuel performance modeling code BISON and the commercial finite element analysis software Abaqus. The results indicate that the channel box will undergo time dependent lateral bowing for all the control blade positions in the assembly. The bowing behavior is dominated by the swelling of SiC-SiC material under non-uniform neutron flux, and changes with variation in the control blade position. The lateral bending will cause a temporary interference between the channel box and the control blade. The developed stresses exceed the proportional limit stress of the material, which may cause matrix microcracking in the channel box. However, the stresses remain below the ultimate tensile strength of the material, and therefore, development of a full, through thickness crack in the channel box is not expected.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2015

Simulation of nonlinear propagation of biomedical ultrasound using PZFlex and the KZK Texas code

In biomedical ultrasound nonlinear acoustics can be important in both diagnostic and therapeutic applications and robust simulations tools are needed in the design process but also for day-to-day use such as treatment planning. For most biomedical application the ultrasound sources generate focused sound beams of finite amplitude. The KZK equation is a common model as it accounts for nonlinearity, absorption and paraxial diffraction and there are a number of solvers available, primarily developed by research groups. We compare the predictions of the KZK Texas code (a finite-difference time-domain algorithm) to an FEM-based commercial software, PZFlex. PZFlex solves the continuity equation and momentum conservation equation with a correction for nonlinearity in the equation of state incorporated using an incrementally linear, 2nd order accurate, explicit algorithm in time domain. Nonlinear ultrasound beams from two transducers driven at 1 MHz and 3.3 MHz respectively were simulated by both the KZK Texas code and PZFlex, and the pressure field was also measured by a fibre-optic hydrophone to validate the models. Further simulations were carried out a wide range of frequencies. The comparisons showed good agreement for the fundamental frequency for PZFlex, the KZK Texas code and the experiments. For the harmonic components, the KZK Texas code was in good agreement with measurements but PZFlex underestimated the amplitude: 32% for the 2nd harmonic and 66% for the 3rd harmonic. The underestimation of harmonics by PZFlex was more significant when the fundamental frequency increased. Furthermore non-physical oscillations in the axial profile of harmonics occurred in the PZFlex results when the amplitudes were relatively low. These results suggest that careful benchmarking of nonlinear simulations is important.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

Highly skewed current–phase relation in superconductor–topological insulator–superconductor Josephson junctions

Three-dimensional topological insulators (TIs) in proximity with superconductors are expected to exhibit exotic phenomena, such as topological superconductivity (TSC) and Majorana-bound states (MBS), which may have applications in topological quantum computation. In superconductor–TI–superconductor Josephson junctions, the supercurrent versus the phase difference between the superconductors, referred to as the current–phase relation (CPR), reveals important information including the nature of the superconducting transport. Here, we study the induced superconductivity in gate-tunable Josephson junctions (JJs) made from topological insulator BiSbTeSe 2 with superconducting Nb electrodes. We observe highly skewed (non-sinusoidal) CPR in these junctions. The critical current, or the magnitude of the CPR, increases with decreasing temperature down to the lowest accessible temperature ( T ~ 20 mK), revealing the existence of low-energy modes in our junctions. The gate dependence shows that close to the Dirac point the CPR becomes less skewed, indicating the transport is more diffusive, most likely due to the presence of electron/hole puddles and charge inhomogeneity. Our experiments provide strong evidence that superconductivity is induced in the highly ballistic topological surface states (TSS) in our gate-tunable TI-based JJs. Furthermore, the measured CPR is in good agreement with the prediction of a model which calculates the phase-dependent eigenstate energies in our system, considering the finite width of the electrodes, as well as the TSS wave functions extending over the entire circumference of the TI.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

A stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented herein. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Gibbs Measures Over Locally Tree-Like Graphs and Percolative Entropy Over Infinite Regular Trees

Consider a statistical physical model on the d-regular infinite tree T{sub d} described by a set of interactions Φ. Let {G_n} be a sequence of finite graphs with vertex sets V{sub n} that locally converge to T{sub d}. From Φ one can construct a sequence of corresponding models on the graphs G{sub n}. Let {μ_n} be the resulting Gibbs measures. Here we assume that {μ_n} converges to some limiting Gibbs measure μ on T{sub d} in the local weak{sup ∗} sense, and study the consequences of this convergence for the specific entropies |V{sub n}|{sup −1}H(μ{sub n}). We show that the limit supremum of |V{sub n}|{sup −1}H(μ{sub n}) is bounded above by the percolative entropyH{sub perc}(μ), a function of μ itself, and that |V{sub n}|{sup −1}H(μ{sub n}) actually converges to H{sub perc}(μ) in case Φ exhibits strong spatial mixing on T{sub d}. When it is known to exist, the limit of |V{sub n}|{sup −1}H(μ{sub n}) is most commonly shown to be given by the Bethe ansatz. Percolative entropy gives a different formula, and we do not know how to connect it to the Bethe ansatz directly. We discuss a few examples of well-known models for which the latter result holds in the high temperature regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Preface to the Special Issue on TOUGH Symposium 2015

The TOUGH Symposium 2015 was held in Berkeley, California, September 28-30, 2015. The TOUGH family of codes, developed at the Energy Geosciences Division of Lawrence Berkeley National Laboratory (LBNL), is a suite of computer programs for the simulation of multiphase and multicomponent fluid and heat flows in porous and fractured media with applications in many geosciences fields, such as geothermal reservoir engineering, nuclear waste disposal, geological carbon sequestration, oil and gas reservoirs, gas hydrate research, vadose zone hydrology and environmental remediation. Since the first release in the 1980s, many modifications and enhancements have been continuously made to TOUGH and its various descendants (iTOUGH2, TOUGH+, TOUGH-MP, TOUGHREACT, TOUGH+HYDRATE, TMVOC...), at LBNL and elsewhere. Today, these codes are used worldwide in academia, government organizations and private companies in problems involving coupled hydrological, thermal, biogeochemical and geomechanical processes. The Symposia, organized every 2-3 years, bring together developers and users for an open exchange on recent code enhancements and applications. In 2015, the Symposium was attended by one hundred participants, representing thirty-four nationalities. This Special Issue in Computers & Geosciences gathers extended versions of selected Symposium proceedings related to (i) recent enhancements to the TOUGH family of codes and (ii) coupled flow and geomechanics processes modeling. In this special issue, a paper by Jung et al. provides a new base version of TOUGH, TOUGH3. This latest version addresses the computational robustness and efficiency needed for the increasing complexity of the simulated processes and the growing size of model domains. Moreover, it consolidates the serial and parallel versions into a single code, hence, inconsistencies between different versions are less likely to occur, and code maintenance and development become more efficient. Finsterle et al. present a review of the capabilities of iTOUGH2 and illustrate the workflow of an integrated simulation-optimization framework. Liu et al. present an approach to reduce the computational cost of performing Bayesian inverse modeling and demonstrate their approach using a synthetic experiment simulated with TOUGH2. Regarding the mesh generation process, the paper by Doughty presents a generalization of the grid-generation algorithm embedded in TOUGH2 (MESHMAKER) to create one-column grids with fractal dimension, useful for representing flow through fractures or highly heterogeneous media with fractal geometry, and also for inverse methods. Sentís and Gable present a module to interface the open source code Lagrit with TOUGH2, that assists in the processes of mesh generation and model setup, and that can be particularly useful for complex geometries and large models. Bonduà et al. present a pre-processing tool (VORO2MESH) that features a full 3D Voronoi approach for structured and unstructured grids, and an enhanced post-processor (TOUGH2Viewer) for the visualization of 3D Voronoi grids. The literature review shows that coupled fluid flow and geomechanics has gained increasing attention in the last years in many geosciences fields. In this context, several codes of the TOUGH family have been successfully coupled with geomechanics software. The paper by Rutqvist presents a review of some of these TOUGH-based geomechanics models, of which the TOUGH-FLAC simulator – presented for the first time in the TOUGH Symposium 2003 – is well-known worldwide and has been used in a large variety of applications, encompassing the application domains of the TOUGH codes. Blanco-Martín et al. present an extension of TOUGH-FLAC to the finite strain framework, motivated by the existence of large strains associated with rock salt deformation in the context of heat-generating nuclear waste disposal. Following a paper published in the Special Issue of the TOUGH Symposium 2012 in this journal, Kim et al. present the current status of the TOUGH-RSBN simulator for coupled hydro-mechanical modeling of hydraulic fracturing using a discrete fracture network approach, and present some validation and demonstration cases. Rinaldi and Nespoli present TOUGH-SEED, an injection-induced seismicity modeling approach using TOUGH2 and a geomechanics stochastic model, and apply it to the Basel EGS project. Finally, Rinaldi et al. use the PEST protocol implemented in iTOUGH2, combined with TOUGH-FLAC as the forward model, to perform inverse modeling for the In Salah CO2 demonstration site in Algeria. Using pore pressures and InSAR displacements as observations, this approach allows for a multi-physics joint inversion and takes advantage of the inverse capabilities of iTOUGH2 (parameter estimation, sensitivity analysis, uncertainty estimation …), applied to coupled fluid flow and geomechanics. On behalf of the members of the TOUGH Symposium 2015 Organizing Committee, I hope that this collection of papers will provide the readers of Computers & Geosciences with a recent view of the capabilities of the TOUGH family of codes, as well as with current modeling research domains in the geosciences. Last but not least, I would like to express my gratitude to all the reviewers who kindly contributed to this Special Issue, as well as the Journal staff who have made this publication possible.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2017

Implementation of CMFD Acceleration Scheme in PROTEUS-MOC

The PROTEUS-MOC code is a three-dimensional (3D) transport code, which is being developed at Argonne National Laboratory under the DOE-NE's Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. It provides a fully consistent 3D discretization of the transport equation by combining the two-dimensional (2D) method of characteristics (MOC) for the planar direction with the discontinuous Galerkin method for the treatment of the axial variable. PROTEUS-MOC uses the unstructured finite element method (FEM) and thus allows the explicit representation of any extruded geometries. It also has a capability of massively parallel computation in energy group, angle, plane, and space using a top-level GMRES linear algebra solver. For parallel computation in space, it uses an unstructured domain decomposition by adapting METIS. The computational burden for direct heterogeneous core calculations based on unstructured geometries is excessive for practical reactor problems, and hence it is essential to implement an efficient acceleration scheme in PROTEUS-MOC. Recently, the coarse mesh finite difference (CMFD) method, which was originally applied to the nodal diffusion methods, has been successfully applied to the MOC transport solvers, resulting in a remarkable reduction in the number of fission source iterations. In addition, a modified CMFD method has been developed to overcome the limitation of the conventional CMFD that is applicable only to neutronics solvers with a conservative discretization. This CMFD method was derived to be consistent with the FEM, which is based on a nonconservative discretization. In this method, the neutron balance in each coarse mesh is enforced by introducing a pseudo absorption cross section (PAXS), and the well-established alternating solution process of CMFD and transport calculations is employed to accelerate source convergence. This modified CMFD acceleration scheme was adopted in PROTEUS-MOC to accelerate the fission source iteration. Pin-cell and assembly based CMFD schemes have been implemented by defining individual pin cells or assemblies as a coarse mesh. For this, an algorithm to map the finite elements to coarse meshes was developed, and the routines were developed to determine the coupling coefficients and PAXS of the CMFD equations from the transport solution. Preliminary performance tests were carried out using the C5G7 benchmark problem. This paper presents the main features of this CMFD acceleration scheme and the preliminary test results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

The Bayesian reconstruction of the in-medium heavy quark potential from lattice QCD and its stability

We report recent results of a non-perturbative determination of the static heavy-quark potential in quenched and dynamical lattice QCD at finite temperature. The real and imaginary part of this complex quantity are extracted from the spectral function of Wilson line correlators in Coulomb gauge. To obtain spectral information from Euclidean time numerical data, our study relies on a novel Bayesian prescription that differs from the Maximum Entropy Method. We perform simulations on quenched 32{sup 3} × N{sub τ} (β = 7.0, ξ = 3.5) lattices with N{sub τ} = 24, …, 96, which cover 839MeV ≥ T ≥ 210MeV. To investigate the potential in a quark-gluon plasma with light u,d and s quarks we utilize N{sub f} = 2 + 1 ASQTAD lattices with m{sub l} = m{sub s}/20 by the HotQCD collaboration, giving access to temperatures between 286MeV ≥ T ≥ 148MeV. The real part of the potential exhibits a clean transition from a linear, confining behavior in the hadronic phase to a Debye screened form above deconfinement. Interestingly its values lie close to the color singlet free energies in Coulomb gauge at all temperatures. We estimate the imaginary part on quenched lattices and find that it is of the same order of magnitude as in hard-thermal loop perturbation theory. From among all the systematic checks carried out in our study, we discuss explicitly the dependence of the result on the default model and the number of datapoints.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Thermal-Mechanical Elastic-Plastic and Ductile Failure Model Calibrations for 304L Stainless Steel Alloy

Numerical simulations of metallic structures undergoing rapid loading into the plastic range require material models that accurately represent the response. In general, the material response can be seen as having four interrelated parts: the baseline response under slow loading, the effect of strain rate, the conversion of plastic work into heat and the effect of temperature. In essence, the material behaves in a thermal-mechanical manner if the loading is fast enough so when heat is generated by plastic deformation it raises the temperature and therefore influences the mechanical response. In these cases, appropriate models that can capture the aspects listed above are necessary. The material of interest here is 304L stainless steel, and the objective of this work is to calibrate thermal-mechanical models: one for the constitutive behavior and another for failure. The work was accomplished by first designing and conducting a material test program to provide data for the calibration of the models. The test program included uniaxial tension tests conducted at room temperature, 150 and 300 C and at strain rates between 10 –4 and 10 3 1/s. It also included notched tension and shear-dominated compression hat tests specifically designed to calibrate the failure model. All test specimens were extracted from a single piece of plate to maintain consistency. The constitutive model adopted was a modular $J_2$ plasticity model with isotropic hardening that included rate and temperature dependence. A criterion for failure initiation based on a critical value of equivalent plastic strain fitted the failure data appropriately and was adopted. Possible ranges of the values of the parameters of the models were determined partially on historical data from calibrations of the same alloy from other lots and are given here. The calibration of the parameters of the models were based on finite element simulations of the various material tests using relatively ne meshes and hexahedral elements. When using the model in structural finite element calculations, however, element formulations and sizes different from those in the calibration are likely to be used. A brief investigation demonstrated that the failure initiation predictions can be particularly sensitive to the element selection and provided an initial guide to compensate for the effect of element size in a specific example.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Signatures of deconfined quark phases in binary neutron star mergers

We investigate the quark deconfinement phase transition in the context of binary neutron star (BNS) mergers. We employ a new finite-temperature composition-dependent equation of state (EOS) with a first order phase transition between hadrons and deconfined quarks to perform numerical relativity simulations of BNS mergers. Here, the softening of the EOS due to the phase transition causes the merger remnants to be more compact and to collapse to a black hole (BH) at earlier times. The phase transition is imprinted on the postmerger gravitational wave (GW) signal duration, amplitude, and peak frequency. However, this imprint is only detectable for binaries with sufficiently long-lived remnants. Moreover, the phase transition does not result in significant deviations from quasi-universal relations for the postmerger GW peak frequency. We also study the impact of the phase transition on dynamical ejecta, remnant accretion disk masses, r-process nucleosynthetic yields and associated electromagnetic (EM) counterparts. While there are differences in the EM counterparts and nucleosynthesis yields between the purely hadronic models and the models with phase transitions, these can be primarily ascribed to the difference in remnant collapse time between the two. An exception is the non-thermal afterglow caused by the interaction of the fastest component of the dynamical ejecta and the interstellar medium, which is systematically boosted in the binaries with phase transition as a consequence of the more violent merger they experience.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

In the last 50 years there has been a tremendous progress in solving numerically the Navier-Stokes equations using finite differences, finite elements, spectral, and even meshless methods. Yet, in many real cases, we still cannot incorporate seamlessly (multi-fidelity) data into existing algorithms, and for industrial-complexity applications the mesh generation is time consuming and still an art. Moreover, solving ill-posed problems (e.g., lacking boundary conditions) or inverse problems is often prohibitively expensive and requires different formulations and new computer codes. Here, we employ physics-informed neural networks (PINNs), encoding the governing equations directly into the deep neural network via automatic differentiation, to overcome some of the aforementioned limitations for simulating incompressible laminar and turbulent flows. We develop the Navier-Stokes flow nets (NSFnets) by considering two different mathematical formulations of the Navier-Stokes equations: the velocity-pressure (VP) formulation and the vorticity-velocity (VV) formulation. Since this is a new approach, we first select some standard benchmark problems to assess the accuracy, convergence rate, computational cost and flexibility of NSFnets; analytical solutions and direct numerical simulation (DNS) databases provide proper initial and boundary conditions for the NSFnet simulations. The spatial and temporal coordinates are the inputs of the NSFnets, while the instantaneous velocity and pressure fields are the outputs for the VP-NSFnet, and the instantaneous velocity and vorticity fields are the outputs for the VV-NSFnet. This is unsupervised learning and, hence, no labeled data are required beyond boundary and initial conditions and the fluid properties. The residuals of the VP or VV governing equations, together with the initial and boundary conditions, are embedded into the loss function of the NSFnets. No data is provided for the pressure to the VP-NSFnet, which is a hidden state and is obtained via the incompressibility constraint without extra computational cost. Unlike the traditional numerical methods, NSFnets inherit the properties of neural networks (NNs), hence the total error is composed of the approximation, the optimization, and the generalization errors. Here, we empirically attempt to quantify these errors by varying the sampling (“residual”) points, the iterative solvers, and the size of the NN architecture. For the laminar flow solutions, we show that both the VP and the VV formulations are comparable in accuracy but their best performance corresponds to different NN architectures. The initial convergence rate is fast but the error eventually saturates to a plateau due to the dominance of the optimization error. For the turbulent channel flow, we show that NSFnets can sustain turbulence at , but due to expensive training we only consider part of the channel domain and enforce velocity boundary conditions on the subdomain boundaries provided by the DNS data base. We also perform a systematic study on the weights used in the loss function for balancing the data and physics components, and investigate a new way of computing the weights dynamically to accelerate training and enhance accuracy. In the last part, we demonstrate how NSFnets should be used in practice, namely for ill-posed problems with incomplete or noisy boundary conditions as well as for inverse problems. We obtain reasonably accurate solutions for such cases as well without the need to change the NSFnets and at the same computational cost as in the forward well-posed problems. As a result, we also present a simple example of transfer learning that will aid in accelerating the training of NSFnets for different parameter settings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Development and Validation of SAM Multi-dimensional Flow Model for Thermal Mixing and Stratification Modeling

Thermal mixing and stratification in large pools or enclosures are very important phenomena that are critical to nuclear reactor safety. Because of the wide ranges of time and length scales associated with such phenomena, accurate modeling and simulation of thermal mixing and stratification remain as the key unresolved, challenging problems for reactor transient analyses. In traditional system analysis codes, simplified zero-dimensional (0-D) models are widely used for their high numerical efficiency, but they generally suffer from very limited prediction accuracies or range of applicability. Like traditional system analysis codes, the current version of the SAM code has implemented such simplified 0-D and one-dimensional mixing models. On the other hand, high-resolution Computational Fluid Dynamics (CFD) tools are often used to model complex thermal mixing and stratification phenomena. They are, however, generally numerically expensive, and they require large amounts of computational resources. It is therefore desirable to implement advanced and efficient thermal mixing and stratification modeling capabilities embedded in a system analysis code. This approach will improve the accuracy of reactor safety analyses when thermal mixing and stratification are involved, and also avoid using the large computational resources needed for high-resolution CFD analysis. Currently, with the support of the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation program, an effort has been launched to develop and implement a multi-dimensional flow model in the system analysis code SAM, and demonstrate its applications to model thermal mixing and stratification phenomena in large enclosures. The main outcomes of this research and development activity are summarized in this report, which presents an attempt to include a built-in advanced multi-dimensional flow model in a system analysis code with the focus on overcoming the simulation challenges of thermal mixing and stratification phenomena. In this report, we start with the introduction of existing SAM code capabilities to simulate thermal mixing and stratification phenomena, which is followed by a short summary of the multi-dimensional model implemented in the SAM code, including both the physical model and the Finite Element Method code implementation. In this study, two options were implemented in the SAM code to model turbulent flows: a relatively simple built-in turbulence model and an interface to accept externally computed turbulent viscosities (e.g., from a high- resolution CFD simulation). Code validation studies on this newly added capability were then carried out to compare SAM simulation results with experimental data from the SUPERCAVNA facility, which was designed to study the complex flow recirculation and thermal stratification phenomena relevant to sodium fast reactor designs. In this study, one transient and two steady-state test cases were used for code validation. Different approaches have been used to model the complex turbulence flow fields in the SUPERCAVNA facility. A highly simplified zero-equation turbulence model was first used, but it was determined that it is too simple to capture the complex turbulence flow fields in these test cases. Subsequently, the code validation continued with the use of turbulent viscosity data from high-resolution STAR-CCM+ CFD simulations to improve the accuracy of the results. Using this approach, the SAM simulation results showed very good agreement with both the SUPERCAVNA experimental data and STAR-CCM+ simulation results. In this report, we demonstrate the development, implementation, and successful validation of a multi-dimensional flow model in the SAM code, which aims to improve the simulation accuracy for complex thermal mixing and stratification phenomena. Lessons have also been learned, including that in cases where the flow fields are not well predicted by the zero-equation model, the iinput of turbulent viscosities from an external source can enhance the overall predictive capabilities needed to accurately capture complex thermal-hydraulic phenomena. Therefore, future research will be needed to further improve the code’s capabilities, such as by developing a more efficient and robust approach to capture the turbulence effects in the SAM code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1999

A Critical Examination of Wind-Wave Spectral Functional Form

Traditionally, data from random ocean waves are presented in spectral functions. The spectra are the result of Fourier analysis. Fourier spectral analysis has dominated data analysis for, at least, the last hundred years. It has been the standard method for is examining the global amplitude-frequency distributions. Although Fourier transform valid under extremely general conditions, there are some crucial restrictions for the Fourier spectral analysis. The system must be linear, and the data must be stationary- otherwise, the resulting spectrum will make little physical sense. The stationarity requirement is also a common required criterion for most of other available data analysis methods. Nevertheless, few, if any, natural phenomena are linear and stationary. To compound these complications is the imperfection of our probes or numerical schemes the interactions of the imperfect probes even with a perfect linear system can make the final data nonlinear. Furthermore, all the available data are usually of finite duration. Under these conditions, Fourier analysis is of limited use, For lack of alternatives, however, Fourier analysis is still used to process such data. The loose application of Fourier analysis and the insouciant adoption of the stationary and linear assumptions may lead to misleading conclusions. Ocean waves are know to be nonlinear, and the wind system generating the wave field are seldom stationary- As a result, the traditional examination of the spectral form hardly made physical sense. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data, This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. The spectral forms of the ocean waves are very different. This new method offers the first physical meaningful view of the wave spectrum. Data from laboratory and field will be presented to illustrate the differences.

Huang, Norden E.↗