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At least 1,297 records · Page 72
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

On numerical errors to the fields surrounding a relativistically moving particle in PIC codes

The particle-in-cell (PIC) method is widely used to model the self-consistent interaction between discrete particles and electromagnetic fields. It has been successfully applied to problems across plasma physics including plasma based acceleration, inertial confinement fusion, magnetically confined fusion, space physics, astrophysics, high energy density plasmas. In many cases the physics involves how relativistic particles (those with high relativistic γ factors) are generated and interact with plasmas. However, when relativistic particles stream across the grid, both in “vacuum” and in plasma, many numerical issues may arise which can lead to unphysical results. We present a detailed analysis of how discretized Maxwell solvers used in PIC codes can lead to numerical errors to the fields that surround particles that move at relativistic speeds across the grid. Expressions for the axial electric field as integrals in k space are presented that reveal two types of errors. The first arises from errors to the numerator of the integrand and leads to unphysical fields that are antisymmetric about the particle. Furthermore, the second arises from errors to the denominator of the integrand and lead to Cherenkov like radiation in “vacuum”. These fields are not anti-symmetric, extend behind the particle, and cause the particle to accelerate or decelerate depending on the solver and parameters. The unphysical fields are studied in detail for two representative solvers - the Yee solver and the FFT based solver. Although the Cherenkov fields are absent, the space charge fields are still present in the fundamental Brillouin zone for the FFT based solvers. In addition, the Cherenkov fields are present in higher order zones for the FFT based solvers. Comparison between the analytical solutions and PIC simulation results are presented. A solution for eliminating these unphysical fields by modifying the k operator in the axial direction is also presented. Using a customized finite difference solver, this solution was successfully implemented into OSIRIS [1]. Results from the customized solver are also presented. Additionally, this solution will be useful for a beam of particles that all move in one direction with a small angular divergence.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks

We develop a weakly intrusive framework to simulate the propagation of uncertainty in solutions of generic hyperbolic partial differential equation systems on graph-connected domains with nodal coupling and boundary conditions. The method is based on the Stochastic Finite Volume (SFV) approach and can be applied for uncertainty quantification (UQ) of the dynamical state of fluid flow over actuated transport networks. The numerical scheme has specific advantages for modeling intertemporal uncertainty in time-varying boundary parameters, which cannot be characterized by strict upper and lower (interval) bounds. We describe the scheme for a single pipe, and then formulate the controlled junction Riemann problem (JRP) that enables the extension to general network structures. In conclusion, we demonstrate the method's capabilities and performance characteristics using a standard benchmark test network.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems

Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been successfully employed to solve diverse forward and inverse PDE problems. However, one disadvantage of the first generation of PINNs is that they usually have limited accuracy even with many training points. Here, we propose a new method, gradient-enhanced physics-informed neural networks (gPINNs), for improving the accuracy of PINNs. gPINNs leverage gradient information of the PDE residual and embed the gradient into the loss function. We tested gPINNs extensively and demonstrated the effectiveness of gPINNs in both forward and inverse PDE problems. Our numerical results show that gPINN performs better than PINN with fewer training points. Additionally, we combined gPINN with the method of residual-based adaptive refinement (RAR), a method for improving the distribution of training points adaptively during training, to further improve the performance of gPINN, especially in PDEs with solutions that have steep gradients.

42 ENGINEERING↗
DOE OSTI2022

General solution to the Kohn–Luttinger nonconvergence problem

A simple, but general solution is proposed for the Kohn–Luttinger problem, i.e., the nonconvergence of the finite-temperature many-body perturbation theory with its zero-temperature counterpart as temperature is lowered to zero under some circumstances. How this nonconvergence can be avoided by altering the reference wave function is illustrated numerically by using up to the fifth order of the perturbation theory.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Toward a scalable robust security-constrained optimal power flow using a proximal projection bundle method

Robust security-constrained optimal power flow (rSCOPF) aims to find the worst-case contingencies of alternating current optimal power flow (ACOPF) in power systems. With the rise of GPU architectures on the upcoming supercomputer architectures, optimization algorithms that rely on sparse linear algebra and indefinite linear systems are becoming increasingly hard to solve efficiently (e.g. interior-point method). To address this we revisit a maximin optimization formulation of the rSCOPF and the single-level mixed-integer semidefinite programming (MISDP) reformulation, which is obtained by taking the Lagrangian relaxation of the inner minimization ACOPF problem. In this paper, we focus on the development of a proximal projection bundle method (PPBM) for solving continuous relaxation node subproblems of the MISDP problem, based primarily on the well-known alternating direction method of multipliers. Cutting planes reminiscent of bundle method ideas are also applied in coordination with updates of the proximal parameter. The cutting-plane method can generate a large number of linear inequalities, leading to a large scale but decomposable quadratic programming (QP) subproblem that is amenable to GPUs. We present the numerical results on the IEEE 30, 57, 118, and 300-bus systems by using our PBMM method. We discuss the main computational bottleneck of our method, which is the time taken to solve each iteration of a QP subproblem instance of the PPBM, and how GPU architectures can accelerate this solution process.

bundle method↗
DOE OSTI2023

Advancements in Development and Testing of Thermal Power Dispatch Simulators

Flexible plant operations and generation (FPOG) offer nuclear power plants (NPPs) the chance to leverage alternative, non-electric revenue streams while ensuring their continued role as reliable, clean, and constant sources of baseload electrical power. The excess thermal energy generated from NPPs during periods of low electricity demand can be channeled as raw materials to numerous industrial processes via a thermal power dispatch (TPD) system. Hydrogen production via high-temperature steam electrolysis (HTSE) is an optimal use case based on technical and economic feasibility. Researchers at Idaho National Laboratory (INL) have conducted previous works that developed and implemented TPD system models within the GSE Solutions Generic Pressurized Water Reactor (GPWR) simulator to support human-in-the-loop (HITL) scenario-based evaluations. The first part of this report documents modifications made to the GPWR TPD model and HMI from the previous iteration in line with a new Sargent and Lundy (S&L) TPD design with an automatic control system. The was done in collaboration with Westinghouse using their three-loop pressurizer water reactor (W3LPWR) simulator which contains an industrial grade automatic control system for the TPD. This was installed in the Human Systems Simulation Laboratory (HSSL) at INL. The second part of the report documents findings from an all-hands-on-deck integration and verification workshop that was conducted in the HSSL over several days. The research team comprised INL human factors and TPD experts, a nuclear engineer from GSE Solutions who implemented the revised TPD model for GPWR, the human-machine interface (HMI) prototyping and human factors team from the University of Idaho, and personnel with operations experience with pressurized water reactors. The workshop provided time and expertise to conduct the final activities to bring the operations, HMI, and simulator into a functional state. The goals of the integration and verification workshop were: 1. to install the revised GPWR TPD model into the HSSL 2. verify the TPD HMI prototype was functional 3. integrate the HTSE Simulink model to GPWR. 3. Issues were identified for resolution, but overall the workshop accomplished its goal to integrated and verify the majority of the intended functional. Future work will resolve the identified issues and use the integrated simulation to support an evaluation and demonstration in the next fiscal year.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Resolution requirements for high-speed droplet impact along a rigid wall

The mechanical and thermal loads that are produced on high-speed projectiles from a droplet are key in the projectile development.To accurately predict the pressure produced along the wall surface during impact, it is important to correctly model the air/water interface of the droplet. Novel modeling approaches such as the Phase-Field enable control of the (numerical) interface thickness. However, the interplay between the grid resolution (including potential adaptive mesh refinement) and the interface thickness is unclear. In this work, the resolution requirements for numerical simulations of a two-dimensional cylindrical water droplet impacting a rigid wall at Mach four are computationally investigated. Numerical simulations are performed using a second-order accurate scheme with adaptive mesh refinement and a Phase-Field interface model. The choice of numerical interface thickness and resolution parameters affects the maximum pressure and location of the maximum pressure along the wall. The overall maximum pressure does not converge even at high resolutions. The number of levels and thickness (number of cells across the interface) play a role in obtaining a well behaved solution.

Burrell, E.↗
DOE OSTI2020

Strings in Ramond-Ramond backgrounds from the Neveu-Schwarz-Ramond formalism

We treat RR flux backgrounds of type II string theory in the framework of closed superstring field theory based on the NSR formalism, focusing on two examples: (1) the pp-wave background supported by 5-form flux, and (2) AdS 3 × S 3 × M 4 supported by mixed 3-form fluxes. In both cases, we analyze the classical string field solution perturbatively, and compute the correction to the dispersion relation of string states to quadratic order in the RR flux. In the first example, our result is in a delicate way consistent with that obtained from lightcone quantization of the Green-Schwarz string. In the second example, we will obtain numerically the mass corrections to pulsating type IIB strings in AdS 3 × S 3 × M 4 . Our results, valid at finite AdS radius, agree with previously known answers in the semiclassical limit and in the BMN limit respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

NESSi : The N on- E quilibrium S ystems S imulation package

The nonequilibrium dynamics of correlated many-particle systems is of interest in connection with pump–probe experiments on molecular systems and solids, as well as theoretical investigations of transport properties and relaxation processes. Nonequilibrium Green’s functions are a powerful tool to study interaction effects in quantum many-particle systems out of equilibrium, and to extract physically relevant information for the interpretation of experiments. Here, we present the open-source software package NESSi (The Non-Equilibrium Systems Simulation package) which allows to perform many-body dynamics simulations based on Green’s functions on the L-shaped Kadanoff–Baym contour. NESSi contains the library libcntr which implements tools for basic operations on these nonequilibrium Green’s functions, for constructing Feynman diagrams, and for the solution of integral and integro-differential equations involving contour Green’s functions. The library employs a discretization of the Kadanoff–Baym contour into time points and a high-order implementation of integration routines. The total integrated error scales up to $\mathcal{O}(N^{-7})$, which is important since the numerical effort increases at least cubically with the simulation time. A distributed-memory parallelization over reciprocal space allows large-scale simulations of lattice systems. We provide a collection of example programs ranging from dynamics in simple two-level systems to problems relevant in contemporary condensed matter physics, including Hubbard clusters and Hubbard or Holstein lattice models. The libcntr library is the basis of a follow-up software package for nonequilibrium dynamical mean-field theory calculations based on strong-coupling perturbative impurity solvers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Multimode turbulent flow measurements using magnetic resonance imaging- and laser-based techniques and computational fluid dynamics simulations

We studied the flow field characteristics of a turbulent flow over a regularized cube array with a perpendicular injection flow through the floor between the second and third cubical elements, representing the complex flow interactions of a 3D jet and the wake flows behind cubical obstacles. Four different experimental measurements were performed: two magnetic resonance imaging-based measurements for three-dimensional three-component velocity (MRV) and concentration (MRC) and two laser-based techniques, particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF), for two-dimensional two-component velocity and concentration measurement, respectively. The mainstream Reynolds number is Re = 15 000⁠, based on the primary inlet velocity U m and channel height D H ⁠, whereas the injector Reynolds number is Re j = 3400⁠, based on the injector velocity U j and the injector's exit width D j ⁠. Numerical simulations were performed for the studied flow configuration of turbulent flow over a regularized cube array using Reynolds-averaged Navier–Stokes (RANS) and large-eddy simulation (LES) approaches. Results obtained from experimental measurements—including MRV, MRC, PIV, and PLIF—as well as RANS and LES simulations are discussed and compared along several horizontal and vertical planes of the studied configuration. In addition, 3D turbulent flow structures, such as leading-edge vortex, horseshoe vortex, and jet shear-layer vortex, and the isosurfaces of scalar concentration successfully revealed by MRV and MRC techniques were found to be in very good agreement with those 3D features extracted from RANS and LES simulations. In conclusion, the high-resolution experimental and numerical database obtained from this study could be useful for validation and verification of numerical codes.

Computational fluid dynamics↗
DOE OSTI2022

Near-field radiative heat transfer between irregularly shaped dielectric particles modeled with the discrete system Green's function method

Near-field radiative heat transfer (NFRHT) between irregularly shaped dielectric particles made of SiO 2 and morphology characterized by Gaussian random spheres is studied. Particles are modeled using the discrete system Green's function (DSGF) approach, which is a volume integral numerical method based on fluctuational electrodynamics. This method is applicable to finite, three-dimensional objects, and all system interactions are defined independent of thermal excitation by a generalized system Green's function. The DSGF method is deemed suitable to model NFRHT between irregularly shaped particles after verification against the analytical solution for chains of two and three SiO 2 spheres. The NFRHT results reveal that geometric irregularity in particles leads to a reduction of the total conductance from that of comparable perfect spheres at vacuum separation distances smaller than the particle size, a regime in which NFRHT is a surface phenomenon. At vacuum separation distances larger than the particle size, NFRHT becomes a volumetric process, and the total conductance between irregularly shaped particles converges to that of comparable perfect spheres. Spectral analysis reveals, however, that particle irregularity leads to damping and broadening of resonances at all separation distances, thereby highlighting the importance of the DSGF method for spectral engineering in the near field. The reduced spectral coherence when particle size is larger than the vacuum separation distance is attributed to coupling of surface phonon-polaritons within the randomly generated, distorted particle features. For particle size smaller than the vacuum separation distance, resonance broadening and damping are linked with the multiple localized surface phonon modes supported by the composite spherical harmonic morphologies of the Gaussian random spheres. In conclusion, this paper has direct implications for thermal management of packed particle systems, with applications in radiative property control, electronics, energy conversion, and nanomanufacturing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Revealing Decision Conservativeness Through Inverse Distributionally Robust Optimization

This paper introduces Inverse Distributionally Robust Optimization (I-DRO) as a method to infer the conservativeness level of a decision-maker, represented by the size of a Wasserstein metric-based ambiguity set, from the optimal decisions made using Forward Distributionally Robust Optimization (F-DRO). By leveraging the Karush-Kuhn-Tucker (KKT) conditions of the convex F-DRO model, we formulate I-DRO as a bi-linear program, which can be solved using off-the-shelf optimization solvers. Additionally, this formulation exhibits several advantageous properties. We demonstrate that I-DRO not only guarantees the existence and uniqueness of an optimal solution but also establishes the necessary and sufficient conditions for this optimal solution to accurately match the actual conservativeness level in F-DRO. Furthermore, we identify three extreme scenarios that may impact I-DRO effectiveness. Our case study applies F-DRO for power system scheduling under uncertainty and employs I-DRO to recover the conservativeness level of system operators. Numerical experiments based on an IEEE 5-bus system and a realistic NYISO 11-zone system demonstrate I-DRO performance in both normal and extreme scenarios. An extended version of this paper with additional analyses is available at li2024revealing.

distributionally robust optimization↗
DOE OSTI2023

Adaptive Time Step Control for Multirate Infinitesimal Methods

Multirate methods have been used for decades to temporally evolve initial-value problems in which different components evolve on distinct time scales, and thus use of different step sizes for these components can result in increased computational efficiency. Generally, such methods select these different step sizes based on experimentation or stability considerations. For problems that evolve on a single time scale, adaptivity approaches that strive to control local temporal error are widely used to achieve numerical results of a desired accuracy with minimal computational effort, while alleviating the need for manual experimentation with different time step sizes. However, there is a notable gap in the publication record on the development of adaptive time step controllers for multirate methods. In this paper, we extend the single-rate controller work of Gustafsson [ACM Trans. Math. Software, 20 (1994), pp. 496-517] to the multirate method setting. Specifically, we develop controllers based on polynomial approximations to the principal error functions for both the "fast" and "slow" time scales within multirate infinitesimal (MRI) methods. We additionally investigate a variety of approaches for estimating the errors arising from each time scale within MRI methods. We then numerically evaluate the proposed multirate controllers and error estimation strategies on a range of multirate test problems, comparing their performance against an estimated optimal performance. Through this work, we combine the most performant of these approaches to arrive at a set of multirate adaptive time step controllers that robustly achieve desired solution accuracy with minimal computational effort.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

hypredrive: high-level interface for solving linear systems with hypre

This software introduces a high-level interface designed to simplify solving linear systems using hypre, a renowned library for such computational challenges. It is crafted to be accessible and user-friendly, making the powerful capabilities of hypre available to a broader audience without requiring in-depth technical knowledge. The interface is characterized by its use of YAML for input, a format celebrated for its structured yet straightforward readability. This choice ensures that users can easily configure the software to meet their specific needs. Additionally, the software boasts an intuitive API that encapsulates hypre's functionalities, making it easier for users to interact with the process of solving linear systems. It is particularly beneficial for prototyping, offering a quick and efficient means to test various solver and preconditioner configurations. Furthermore, the software allows for the creation of an offline testing framework in which predefined linear systems are read from files and benchmarked with user-defined solution strategies. This makes it an invaluable tool for developers and researchers exploring and validating their computational models. Overall, the software serves as a bridge, bringing the advanced computational capabilities of hypre closer to users who may need more specialized technical expertise, thereby facilitating innovation and exploration in the field of numerical linear algebra.

Paludetto Magri, Victor↗
DOE OSTI2020

Edge ICRF simulations in 3D geometry: From MHD equilibrium to coupling determination

We present in this work a consistent numerical scheme that allows the computation of 3D magnetic fields a nd 3D density profiles and their usage in ion cyclotron range of frequencies (ICRF) coupling simulations. We first utilize the PARVMEC code to compute the 3D free-boundary plasma equilibrium in the ideal magnetohydrodynamic (MHD) approximation. Since the PARVMEC solution is only defined within the last closed flux surface (LCFS), the magnetic field domain is extended to the scrape-off layer (SOL) via the BMW code, which computes a divergence-free magnetic field solution arising from the external conductors’ vacuum field a nd t he PARVMEC flux surface currents. This magnetic reconstruction is then used in the EMC3-EIRENE transport code in order to compute 3D density profiles. In the last step, the RAPLICASOL code is utilized to compute the ICRF antenna S-matrices resulting from the 3D density profiles. We exemplify this scheme for the ASDEX Upgrade tokamak. A new implementation of a curved model for the ASDEX Upgrade ICRF 2-strap antenna in RAPLICASOL allows simulations in realistic geometry, without any coordinate transformations.

Lopez, Graham↗
DOE OSTI2021

Impact of Rheology Models on Horizontal Well Polymer Flooding in a Heavy Oil Reservoir on Alaska North Slope: A Simulation Study

Polymer rheology can have either a positive or a negative effect on polymer flooding performance under varied circumstances. Many researchers have studied the effect of polymer rheology in a vertical well, but no field scale studies have been conducted to investigate whether polymer rheology is beneficial to polymer flooding in heavy oil reservoirs developed by horizontal wells. In this paper, we conducted a numerical simulation study to examine the effect of HPAM polymer rheology on a polymer flooding pilot, which is the first-ever project conducted on a heavy oil reservoir from Alaska North Slope (ANS) developed by horizontal wells. Three rheology types were considered in the study including the apparent viscosity measured during coreflooding of using a HPAM polymer, the bulk viscosity measured with a viscometer, and a Newtonian flow model. The results suggest that using the bulk viscosity in simulation underestimates the conformance control and the water-oil-ratio reduction capability of the HPAM polymer solution. When the apparent viscosity is used, the incremental oil and sweep were largely increased, and the optimal recovery period of polymer flooding was extended greatly, especially for the heterogeneous formations. Therefore, the rheology type of polymer plays a significant role in the incremental oil recovery and injection profile of the horizontal well system given the pilot test conditions. This study has provided practical guidance to field operators for the ongoing polymer flooding pilot on ANS and will also provide valuable information for other polymer projects conducted in similar conditions.

Leng, Jianqiao↗
DOE OSTI2021

Effective kinetics driven by dynamic concentration gradients under coupled transport and reaction

Biogeochemical reaction kinetics are generally established from batch reactors where concentrations are uniform. In natural systems, many biogeochemical processes are characterized by spatially and temporally variable concentration gradients that often occur at scales which are not resolved by field measurements or biogeochemical and reactive transport models. Yet, it is not clear how these sub-scale chemical gradients affect reaction kinetics compared to batch kinetics. Here we investigate this question by studying the paradigmatic case of localized pulses of solute reacting with a solid or a dissolved species in excess. Additionally, we consider non-linear biogeochemical reactions, representative of mineral dissolution, adsorption and redox reactions, which we quantify using simplified power-law kinetics. The combined effect of diffusion and reaction leads to effective kinetics that differ quantitatively and qualitatively from the batch kinetics. Depending on the nonlinearity (reaction order) of the local kinetics, these effects lead to either enhancement or decrease of the overall reaction rate, and result in a rich variety of reaction dynamics. We derive analytical results for the effective kinetics, which are validated by comparison to direct numerical simulations for a broad range of Damköhler numbers and reaction order. Our findings provide new insights into the interpretation of imperfectly mixed lab experiments, the effective kinetics of field systems characterized by intermittent reactant release and the integration of sub-scale concentration gradients in reactive transport models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

A parallel strategy for density functional theory computations on accelerated nodes

Using the Löwdin orthonormalization of tall-skinny matrices as a proxy-app for wavefunction-based Density Functional Theory solvers, we investigate a distributed memory parallel strategy focusing on Graphics Processing Unit (GPU)-accelerated nodes as available on some of the top ranked supercomputers at the present time. Here we present numerical results in the strong limit regime, as it is particularly relevant for First-Principles Molecular Dynamics. We also examine how matrix product-based iterative solvers provide a competitive alternative to dense eigensolvers on GPUs, allowing to push the strong scaling limit of these computations to a larger number of distributed tasks. Our strategy, which relies on replicated Gram matrices and efficient collective communications using the NCCL library, leads to a time-to-solution under 0.5 s for the Löwdin orthonormalization of a tall-skinny matrix of 3000 columns on Summit at Oak Ridge Leadership Facility (OLCF). Given the similarity in computational operations between one iteration of a DFT solver and this proxy-app, this shows the possibility of solving accurately the DFT equations well under a minute for 3000 electronic wave functions, and thus perform First-Principles molecular dynamics of physical systems much larger than traditionally solved on CPU systems.

97 MATHEMATICS AND COMPUTING↗