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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Method for Coupled Electromagnetic and Circuit Simulations to Evaluate Surge Arrester Performance in Protecting Equipment Against E1 HEMP

Surge arrester behavioral modeling for realistic systems embedded in an E1 high-altitude electromagnetic pulse environment inherently encompasses three interconnected complications: (1) the need to account for signal propagation across two domains, electromagnetics and electrical; (2) the need to include both linear and nonlinear circuit components in the analysis; and (3) the need to understand that the over-current and over-voltage mitigation performance is dependent not only on the properties of the surge arrester and protected load but also on the topology of the overall electrical network. This study presents a framework to address these challenges in a systematic manner to consider the effectiveness of protective measures for a common class of equipment in power generation facilities. Full-wave simulations were carried out to derive circuit-domain (i.e., lumped element–based) equivalent models for the excitation waveform and the physical components of the system. Then, these equivalent models were imported to a circuit solver and combined with a high-frequency surge arrester model to evaluate mitigation performance. The methodology outlined is general enough such that it can be applied for other electromagnetic interference problems that involve E2/E3 HEMP or microwave emissions.

42 ENGINEERING↗
NASA NTRS1999

Computational Assessment of Aft-Body Closure for the HSR Reference H Configuration

A study has been conducted to determine how well the USM3D unstructured Euler solver can be utilized to predict the flow over the High Speed Research (HSR) Reference H configuration with an ultimate goal of prediction of Sting interference so after body closure effects may be evaluated. This study has shown that the code can be used to predict the interference effects of a lower mounted blade sting with a high degree of confidence. It has been shown that wing and fuselage pressures, both levels and trends, can be predicted well. Force and moment levels are not predicted well but experimental trends are predicted. Based upon this, predicted force and moment increments are assumed to be predicted accurately. Deflection of the horizontal tail was found to cause a non-linear increment from the non-deflected sting interference effects.

Londenberg, W. Kelly↗
DOE OSTI2021

Nonlinear convergence in contact mechanics: Immersed boundary finite volume

In this report we present an immersed boundary finite volume (IBM) method for simulating quasistatic contact mechanics of linearly elastic domains at small strains. In IBM, all external boundaries and internal contacts of an object are represented by embedded surfaces inside a Cartesian mesh, which need not conform to the grid lines. The contact constraints consist of the non-penetrability condition and Coulomb’s friction law, which are discretized using special interpolation stencils and enforced via penalty parameters. The resulting nonlinear system depends on displacement unknowns only. To solve it, we use the Newton method but find that it diverges frequently. To understand the divergence pattern, we analyze a simplified 2-cell problem and show that the global convergence of Newton cannot be ensured for any choice of penalty parameters. We thus propose a modified Newton solver, which guarantees convergence for the 2-cell problem and is numerically verified to converge for all the challenging simulations considered herein. While both 1 st - and 2 nd -order variants of IBM, in displacement unknowns, are proposed, the modified Newton solver applies only to the 1 st -order variant.

42 ENGINEERING↗
DOE OSTI2026

Benchmarking core turbulence and transport predictions for an inductive compact tokamak reactor plasma

Motivated by the need for accurate, timely, and efficient calculations of plasma transport, predictions of plasma turbulence properties made using different TGLF saturation rules are benchmarked against corresponding predictions from linear and nonlinear gyrokinetic CGYRO simulations. This benchmarking is carried out using parameters taken from an inductive burning plasma scenario in a hypothetical compact high-field (R maj = 4 m, B T = 8 T) tokamak, lying in a much different regime of parameter space than either the TGLF calibration regime or current-day experiments. The core turbulent transport in this scenario is predicted to be dominated by ion temperature gradient (ITG) turbulence. In general, the ITG critical gradients predicted by various TGLF saturation rules are quite close to the CGYRO predictions. Both codes predict similar linear ITG growth rates and frequency spectra, as well as their scaling with R/L T i = −Rd ln(T i )/dr. However, TGLF systematically predicts unstable trapped-electron modes (TEMs) above k y ρ s ≃ 0.5 not seen by CGYRO for the same parameters, due to TGLF predicting a lower threshold in R/L T e than CGYRO for TEM onset. It is shown that for this scenario, nonlinear CGYRO simulations predict stiffer ITG turbulence than the TGLF SAT0 and SAT1 saturation rules, with energy fluxes close in magnitude and scaling with R/L T i to what is predicted by the SAT2 saturation rule. Self-consistent core profiles calculated using nonlinear CGYRO flux predictions and the PORTALS transport solver are shown to agree fairly well with corresponding predictions made using the TGLF SAT2 model, including a similar level of density peaking.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Spectrally Stabilized Interface Capturing Formulation and Implementation in Nek5000/NekRS

This report documents the formulation of a novel level-set method for incompressible two-phase flows in the continuous Galerkin (CG) high order spectral element framework. The overall method hinges on a novel implementation of the spectral vanishing viscosity (SVV) operator for the stabilization of linear/non-linear hyperbolic problems. The multidimensional SVV convolution kernels, which in essence, have a similar effect as a high pass filter applied to the derivatives, are formulated by exploiting the tensor product form, analogous to the construction of the usual stiffness matrix system. The resulting kernels are directionally decoupled and ensure a linear, symmetric positive definite, elliptic matrix operator. The SVV formulation is demonstrated to provide a robust stabilizing mechanism through challenging linear and non-linear hyperbolic problems, including problems pertinent to the level-set formulation. The two-phase framework conceptualized herein is based on the conservative level-set (CLS) method which represents the interface between the fluids by the 0.5 iso-contour of the smoothed Heaviside function. The CLS method is augmented with a preconditioning procedure for interface normals using the signed distance function which precludes the manifestation of spurious oscillations in the vicinty of the interface. Further, the existing mixed explicit-implicit approach for the solution of Navier-Stokes equations in Nek5000, as described in Tomboulides et al, is augmented with a pressure coefficient splitting approach for the Poisson equation, which greatly accelerated the convergence of pressure solver for two-phase systems with large density ratio. The robustness and accuracy of the overall two-phase method is demonstrated through canonical challenging problems involving high density and viscosity ratios, with and without surface tension. The two-phase formulation is wholly implemented in Nek5000 and the SVV stabilization method is implemented in NekRS, which is the essential precursor to the two-phase framework, undergoing active development.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Hardware-Efficient Quantum Optimization Layered Algorithms and Experiments

Quantum optimization algorithms, such as QAOA, that implement parametrized stochastic optimization solvers attempt to identify low-energy solutions of Ising systems by exploiting available quantum effects in noisy-intermediate scale machines. Engineering a well-performing parametrized quantum optimization circuit is indeed an exercise in balancing the trade-off between expressivity and implementation complexity. We show that, for MaxCut QAOA circuits defined on native hardware topology (Rigetti’s Aspen Quantum Processors), error-mitigation techniques recover simulated features of the noiseless theory. Moreover, we explore a design space for QAOA-like ansatze that perform well in theory as well as in hardware for fully-connected problems. We also discuss how efficient coherence and entanglement detection methods that could be coupled with quantum optimization experiments require only linear overhead in benchmarking time.

quantum computing↗
NASA NTRS1987

A generalized procedure for constructing an upwind based TVD scheme

A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some linear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to scalar nonlinear equations and a constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance in numerical experiments. The formulation is extended to the nonlinear system. It is demonstrated that the present procedure can easily convert existing central or upwind, and second- or higher-order differencing schemes to preserve monotonicity and yield physically admissible solutions. The formulation is simple mathematically as well as numerically; both matrix-vector multiplication and Riemann solver are avoided. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made.

Liou, Meng-Sing↗
NASA NTRS1990

Domain decomposition methods in aerodynamics

Compressible Euler equations are solved for two-dimensional problems by a preconditioned conjugate gradient-like technique. An approximate Riemann solver is used to compute the numerical fluxes to second order accuracy in space. Two ways to achieve parallelism are tested, one which makes use of parallelism inherent in triangular solves and the other which employs domain decomposition techniques. The vectorization/parallelism in triangular solves is realized by the use of a recording technique called wavefront ordering. This process involves the interpretation of the triangular matrix as a directed graph and the analysis of the data dependencies. It is noted that the factorization can also be done in parallel with the wave front ordering. The performances of two ways of partitioning the domain, strips and slabs, are compared. Results on Cray YMP are reported for an inviscid transonic test case. The performances of linear algebra kernels are also reported.

Venkatakrishnan, V.↗
DOE OSTI2024

Pressure stability in explicitly coupled simulations of poromechanics with application to CO 2 sequestration

We study in detail the pressure stabilizing effects of the non-iterated fixed-stress splitting in poromechanical problems which are nearly undrained and incompressible. When applied in conjunction with a spatial discretization which does not satisfy the discrete inf–sup condition, namely a mixed piecewise linear–piecewise constant spatial discretization, the explicit fixed-stress scheme can have a pressure stabilizing effect in transient problems. This effect disappears, however, upon time step refinement or the attainment of steady state. The interpretation of the scheme as an Augmented Lagrangian method similar to Uzawa iteration for incompressible flow helps explain these results. Moreover, due to the slowly evolving solution within undrained seal regions, we show that the explicit fixed-stress scheme requires very large time steps to reveal its pressure stabilizing effect in examples of geologic CO 2 sequestration. We note that large time steps can result in large errors in drained regions, such as the aquifer or reservoir regions of these examples, and can prevent convergence of nonlinear solvers in the case of multiphase flows, which can make the explicit scheme an unreliable source of pressure stabilization. We conclude by demonstrating that pressure jump stabilization is as effective in the explicit fixed-stress setting as in the fully implicit setting for undrained problems, while maintaining the stability and convergence of the fixed-stress split for drained problems.

58 GEOSCIENCES↗
DOE OSTI2017

Initial CEED API (CEED-MS10)

Key components of CEED software development involve fast finite element operator storage and evaluation, architecture optimizations, performant algorithms for all orders, global kernels for finite element operators, efficient use of the memory sub-system, optimal data locality and motion, enhanced scalability and parallelism, and fast tensor contractions. As ultimate goals of the project, CEED is exploring and identifying the best algorithms for the full range of discretizations and applying algorithmic and software development to support ECP applications’ needs. In this milestone, we initiated the development and implementation of a common CEED API consisting of two main components: low-level and high-level APIs. We accomplished the goal of having the low-level component ready for the release of CEED v1.0 in the next quarter, see CEED-MS13. In this report we also provide a highlight from CEED’s integration with the MARBL app and the corresponding Laghos miniapp. A main theme in this work has been the systematic transition of advanced algorithms, developed and tested in Laghos, to the large-scale multi-physics settings of the MARBL code. The low-level CEED API provides a set of FE kernels and components for writing new low-level kernels. Examples include: vector and sparse linear algebra, element matrix assembly over a batch of elements, partial assembly and action for efficient high-order operators like mass, diffusion, advection, etc. The main goal of the low-level API is to establish the basis for the high-level API. Also, identifying such low-level kernels and providing a reference implementation for them serves as the basis for collaboration with vendors and STs. Another goal for the low-level API is to make it easy for applications with their own discretization infrastructure, who do not want to switch directly to using the high-level CEED API, to still evaluate and use the core operations provided by the low-level API. One of the challenges with high-order methods is that a global sparse matrix is no longer a good representation of a high-order linear operator, both with respect to the FLOPs needed for its evaluation, as well as the memory transfer needed for a matvec. Thus, another important question we tried to address while developing the low-level API is: is it possible to abstract out in a natural and efficient way the different implementations and data structures that arise when dealing with various computational device types: CPUs, GPUs, etc. Fully answering this question is beyond the scope of this particular milestone, since that requires longer time as we develop and expand the devices we support. The future high-level API will be the frontend provided by CEED consisting of high-level abstractions such as meshes, finite element spaces and solutions, bilinear forms, solvers, etc. At this high-level, an important aspect of the API will be to provide a uniform abstraction layer for writing code in a portable manner. To achieve that, we plan to utilize the MPI programming model combined with a device abstraction layer (DAL) for finite element computations that we will develop. The DAL will serve as the bridge between the low- and the high-level APIs, allowing a variety of programming models to be used for the low-level kernel implementations. The software artifacts delivered as part of this milestone include an initial CEED API software implementation (libCEED) provided through the CEED website, http://ceed.exascaleproject.org and the CEED GitHub organization, http://github.com/ceed. In addition to details and results from the above R&D efforts, in this document we are also reporting on other project-wide activities performed in Q1 of FY18, including: the Nek5000 v17.0 MFEM v3.3.2 and PETSc v3.8 releases, collaborations with ECP/ST and SciDAC projects, the inaugural Nek5000 hackathon and various outreach activities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Single classical field description of interacting scalar fields

In this report we test the degree to which interacting Bosonic systems can be approximated by a classical field as total occupation number is increased. This is done with our publicly available code repository, QIBS, a new massively parallel solver for these systems. We use a number of toy models well studied in the literature and track when the classical field description admits quantum corrections, called the quantum breaktime. This allows us to test claims in the literature regarding the rate of convergence of these systems to the classical evolution. We test a number of initial conditions, including coherent states, number eigenstates, and field number states. We find that of these initial conditions, only number eigenstates do not converge to the classical evolution as occupation number is increased. We find that systems most similar to scalar field dark matter exhibit a logarithmic enhancement in the quantum breaktime with total occupation number. Systems with contact interactions or with field number state initial conditions, and linear dispersions, exhibit a power law enhancement. Finally, we find that the breaktime scaling depends on both model interactions and initial conditions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Investigation of Microbunching Instabilities in Modern Recirculating Accelerators

Particle accelerators are machines to accelerate and store charged particles, such as electrons or protons, to the energy levels for various scientific applications. A collection of charged particles usually forms a particle beam. There are three basic types of particle accelerators: linear accelerators (linac), storage-ring (or circular) accelerators, and recirculating accelerators. In a linac, particles are accelerated and pass through once along a linear or straight beamline. Storage-ring accelerators propel particles around a circular track and repetitively append the energy to the stored beam. The third type, also the most recent one in chronology, the recirculating accelerator, is designed to accelerate the particle beam in a short section of linac, circulate the beam, and then either continue to accelerate for energy boost or decelerate it for energy recovery. The beam properties of a linac machine are set at best by the initial particle sources. For storage rings, the beam equilibria are instead determined by the overall machine design. The modern recirculating machines share with linacs the advantages to both accelerate and preserve the beam with high beam quality, as well as efficiently reuse the accelerating components. The beamline design in such a machine configuration can however be much more complicated than that of linacs. As modern accelerators push toward the high-brightness or high-intensity frontier by demanding particles in a highly charged bunch (about nano-Coulomb per bunch) to concentrate in an ever-decreasing beam phase space (transverse normalized emittance about 1 μm and relative energy spread of the order of 10^-5 in GeV beam energy), the interaction amongst particles via their self-generated electromagnetic fields can potentially lead to coherent instabilities of the beam and thus pose significant challenges to the machine design and operation. In the past decade and a half, microbunching instability (MBI) has been one of the most challenging issues for such high-brightness or high-intensity beam transport, as it would degrade lasing performance in the fourth-generation light sources, reduce cooling efficiency in electron cooling facilities, and compromise the luminosity of colliding beams in lepton or lepton-hadron colliders. The dissertation work will focus on the MBI in modern recirculating electron accelerators. It has been known that the collective interactions, the coherent synchrotron radiation (CSR) and the longitudinal space charge (LSC) forces, can drive MBI. The CSR effect is a collective phenomenon in which the electrons in a curved motion, e.g. a bending dipole, emit radiation at a scale comparable to the micro-bunched structure of the bunch distribution. The LSC effect stems from non-uniformity of the charge distribution, acts as plasma oscillation, and can eventually accumulate an amount of energy modulation when the beam traverses a long section of a beamline. MBI can be seeded by non-uniformity or shot noise of the beam, which originates from granularity of the elementary charge. Through the aforementioned collective effects, the modulation of the bunch sub-structure can be amplified and, once the beam-wave interaction formed a positive feedback, can result in MBI. The problem of MBI has been intensively studied for linac-based facilities and for storage-ring accelerators. However, systematic studies for recirculation machines are still very limited and form a knowledge gap. Because of the much more complicated machine configuration of the recirculating accelerators than that of linacs, the existing MBI analysis needs to be extended to accommodate the high-brightness particle beam transport in modern recirculating accelerators. This dissertation is focused on theoretical investigation of MBI in such machine configuration in the following seven themes: (1) Development and generalization of MBI theory The theoretical formulation has been extended so as to be applicable to a general linear beamline lattice including horizontal and vertical transport bending elements, and beam acceleration or deceleration. These featured generalizations are required for MBI analysis in recirculation accelerators. (2) Construction of CSR impedance models In addition to the steady-state CSR interaction, it has been found that the exit transient effect (or CSR drift) can even result in more serious MBI in high-brightness recirculation arcs. The onedimensional free-space CSR impedances, especially the exit transients, are derived. The steady-state CSR impedance is also extended to non-ultrarelativistic beam energy for MBI analysis of low-energy merger sections in recirculating accelerators. (3) Numerical implementation of the derived semi-analytical formulation This includes the development of a semi-analytical Vlasov solver for MBI analysis, and also benchmarking of the solver against massive particle tracking simulations. (4) Exploration of multistage amplification behavior of CSR microbunching development The CSR-induced MBI acts as an amplifier, which amplifies the sub-bunch modulation of a beam. The amplification is commonly quantified by the amplification gain. A beam transport system can be considered as a cascaded amplifier. Unlike the two-stage amplification of four-dipole bunch compressor chicanes employed in linacs, the recirculation arcs, which are usually constituted by several tens of bending magnets, show a distinguishing feature of up to six-stage microbunching amplification for our example arc lattices. That is, the maximal CSR amplification gain can be proportional to the peak bunch current up to sixth power. A method to compare lattice performance has been developed in terms of gain coefficients, which nearly depend on the lattice properties only. This method has also proven to be an effective way to quantify the current dependence of the maximal (5) Control of CSR MBI in multibend transport or recirculation arcs The existing mitigation schemes of MBI mostly aim to linac-based accelerators and may not be practical to the recirculating accelerator facilities. Thus a set of conditions for suppression of CSR MBI was proposed and examined for example lattices from low (~100 MeV) to high (~1 GeV) energies. (6) Study of more aspects of microbunched structures in beam phase spaces For a cascaded amplifier in circuit electronics, the total amplification gain can be estimated as the product of individual gains. In a beam transport line of an accelerator, the (scalar) gain multiplication was examined and found to under-estimate the overall microbunching amplification. The concept of gain matrix was developed, which includes the density, energy and transverse-longitudinal modulations in a beam phase space, and used to analyze MBI for a proposed recirculating machine. Throughout the gain matrix approach, it reasonably gives the upper limit of spectral MBI gain curves. This extended analysis can be employed to study multi-pass recirculation. (7) Study of MBI for magnetized beams Driven by a recent energy-recovery-linac based cooler design for electron cooling at Jefferson Lab Electron-Ion Collider Project, the generalized theoretical formulation for MBI to a transversely coupled beam has been developed and applied to this study. A magnetized beam in general features non-zero canonical angular momentum, thus considered to be a transversely coupled beam. A novel idea of utilizing magnetized beam transport was proposed for improvement of cooling efficiency and possible mitigation of collective effects. A concern of MBI regarding this design was studied and excluded. The large transverse beam size associated with the beam magnetization is found to help suppress MBI via the transverse-longitudinal correlation.

43 PARTICLE ACCELERATORS↗
NASA NTRS1999

An Elasticity-Based Mesh Scheme Applied to the Computation of Unsteady Three-Dimensional Spoiler and Aeroelastic Problems

This paper presents a modification of the spring analogy scheme which uses axial linear spring stiffness with selective spring stiffening/relaxation. An alternate approach to solving the geometric conservation law is taken which eliminates the need for storage of metric Jacobians at previous time steps. Efficiency and verification are illustrated with several unsteady 2-D airfoil Euler computations. The method is next applied to the computation of the turbulent flow about a 2-D airfoil and wing with two and three- dimensional moving spoiler surfaces, and the results compared with Benchmark Active Controls Technology (BACT) experimental data. The aeroelastic response at low dynamic pressure of an airfoil to a single large scale oscillation of a spoiler surface is computed. This study confirms that it is possible to achieve accurate solutions with a very large time step for aeroelastic problems using the fluid solver and aeroelastic integrator as discussed in this paper.

Bartels, Robert E.↗
NASA NTRS2018

Computational Investigation of Nominally-Orthogonal Pneumatic Active Flow Control for High-Lift Systems

We explore the feasibility of using nominally-orthogonal jets as active aerodynamic load control for multi-element high-lift systems, and whether the nominally-orthogonal jets can offer a variety of performance improvements. These nominally-orthogonal jets inject momentum normal to the airfoil surface near the flap trailing edge, where they create a vortex that entrains flow from the opposing side and change the airfoil circulation. Lift-enhancement opportunities of trailing edge nominally-orthogonal jets have previously been studied by Malavard et al. and Blaylock et al. on single-element airfoils; however, their effect on drag was not thoroughly investigated. In this study, we investigate two- dimensional nominally-orthogonal jet effects on both lift and drag on a two-element airfoil, NLR7301. We utilize Chimera Grid Tools to generate structured curvilinear overset grids, and the Reynolds-averaged Navier-Stokes solver OVERFLOW-2 to solve for the flow field around the airfoil. We perform various computational sensitivity studies on the baseline airfoil without a jet to validate computational results against benchmark experimental data. Using a Chimera overset grid topology, we demonstrate a similar lift-enhancement effect between a nominally-orthogonal jet and a nominally-orthogonal physical tab employed at the same location on the studied airfoil. After we introduce the nominally-orthogonal jet concept, we investigate nominally-orthogonal jets with various momentum coefficient settings, C(sub µ) = 0.00 − 0.04 and present a lift-enhancement relationship ∆C(sub l) ≃ 3.59 (C(sub µ)) for this airfoil. We discuss that utilizing a nominally-orthogonal jet with C(sub µ) = 0.01 can shift the linear region of the lift curve by a ∆C(sub l) = 0.36 for the pressure side jet and by a ∆C(sub l) = −0.27 for the suction side jet. Employing a nominally-orthogonal jet is also shown effective in altering the drag. To study the impact, we carry out a drag decomposition study in the form of drag polars. We show for a given C(sub l) = 2.50, a nominally-orthogonal jet with C(sub µ) = 0.01 on the pressure and suction side of the airfoil results in 113 drag count decrements and 41 drag count increments, respectively, compared to the baseline airfoil with no jet. These results show that large and controllable changes in aerodynamic performance can be achieved by relatively small active flow control inputs using the nominally-orthogonal jets presented in this study.

Nominally-Orthogonal↗
DOE OSTI2017

AMPS: An Augmented Matrix Formulation for Principal Submatrix Updates with Application to Power Grids

We present an augmented matrix approach to update the solution to a linear system of equations when the coefficient matrix is modified by a few elements within a principal submatrix. This problem arises in the dynamic security analysis of a power grid, where operators need to perform $N-x$ contingency analysis, i.e., determine the state of the system when up to $x$ links from $N$ fail. Our algorithms augment the coefficient matrix to account for the changes in it, and then compute the solution to the augmented system without refactoring the modified matrix. We provide two algorithms, a direct method, and a hybrid direct-iterative method for solving the augmented system. We also exploit the sparsity of the matrices and vectors to accelerate the overall computation. Our algorithms are compared on three power grids with PARDISO, a parallel direct solver, and CHOLMOD, a direct solver with the ability to modify the Cholesky factors of the coefficient matrix. We show that our augmented algorithms outperform PARDISO (by two orders of magnitude), and CHOLMOD (by a factor of up to 5). Further, our algorithms scale better than CHOLMOD as the number of elements updated increases. The solutions are computed with high accuracy. Our algorithms are capable of computing $N-x$ contingency analysis on a $778K$ bus grid, updating a solution with $x=20$ elements in $1.6 \times 10^{-2}$ seconds on an Intel Xeon processor.

Yeung, Yu-Hong↗
DOE OSTI2025

Computational Algorithms for Unit Commitment with AC Power Flows (Final Report)

Security-constrained unit commitment (SCUC) is a key component in power system operations. When AC power flow constraints are considered in the SCUC model (AC-SCUC), the problem becomes extremely difficult due to its discrete and non-convex nature, as described in “Grid Optimization Competition Challenge 3 Problem Formulation (GOCC)”. There are four main challenges: (i) Discrete decisions regarding unit online/offline status and start-up/shut-down procedures for every single unit. The number of discrete decision variables increases considerably when a system integrates multiple generators; (ii) Configuration-based combined-cycle formulations, and multi-commodity models that include ramping products, spin/non-spin products, and regulation up/down products. The combined-cycle units introduce additional discrete decision variables and auxiliary service products further complicate the model by connecting multi-commodity products’ continuous and discrete variables; (iii) SCUC models with AC power flow constraints are far more complex due to massive bilinear terms in the large-scale nonlinear power balance equations. The nonlinear power balance equations are further complicated by the discrete step control variables of shunts; (iv) N − 1 contingency analysis. The size of the model increases linearly with the number of contingencies considered, greatly increasing the size of the optimization model. Accordingly, there is an emergent need to develop a robust algorithm capable of deriving a high-quality solution in a short time and passing through contingency tests simultaneously. In this project, we explore innovative techniques to address this challenging problem by integrating advanced polyhedral theory, approximation methods, relaxation strategies, decomposition techniques, and parallel computing. Each technique approaches the problem from a different perspective, leveraging its specific strengths to tackle distinct challenges. Each individual method has demonstrated its effectiveness in the PI’s previous research. Their integration is expected to significantly reduce the computational time required to solve the proposed complex problem. Successful completion of this project has the potential to transform the industry by enhancing optimization solvers capable of handling large-scale day-ahead energy market clearing models within strict time constraints, while incorporating AC power flow constraints. This advancement will lead to reduced overall generation costs and, consequently, increased social welfare.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

Time-periodic steady-state solution of fluid-structure interaction and cardiac flow problems through multigrid-reduction-in-time

In this study, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic MGRIT algorithm is applied to a variety of linear and nonlinear single- and multiphysics problems that are periodic-in-time. It is demonstrated that the proposed parallel-in-time algorithm can obtain the same time-periodic steady-state solution as sequential time-stepping. It is shown that the required number of MGRIT iterations can be estimated a priori and that the new MGRIT variant can significantly and consistently reduce the time-to-solution compared to sequential time-stepping, irrespective of the number of dimensions, linear or nonlinear PDE models, single-physics or coupled problems and the employed computing resources. The numerical experiments demonstrate that the time-periodic MGRIT algorithm enables a greater level of parallelism yielding faster turnaround, and thus, facilitating more complex and more realistic problems to be solved.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition

In a previous paper Christlieb et al. (A particle-in-cell method for plasmas with a generalized momentum formulation, part I: Model formulation, 2024), we developed a new particle-in-cell (PIC) method for the relativistic Vlasov–Maxwell system in which the electromagnetic fields and the equations of motion for the particles were cast in terms of scalar and vector potentials through a Hamiltonian formulation. This new method evolved the potentials under the Lorenz gauge using integral equation methods. New methods to construct spatial derivatives of the potentials that converge at the same rates as the fields were also presented. The new particle method was compared against standard explicit discretizations, including the well-known FDTD-PIC method, for a range of applications involving sheaths and particle beams. Here, this paper extends this new class of methods by focusing on the enforcement the Lorenz gauge condition in both exact and approximate forms using co-located meshes. A time-consistency property of the proposed field solver for the vector potential form of Maxwell’s equations is established, which is shown to preserve the equivalence between the semi-discrete Lorenz gauge condition and the analogous semi-discrete continuity equation. Using this property, we present three methods to enforce a semi-discrete gauge condition. The first method introduces an update for the continuity equation that is consistent with the discretization of the Lorenz gauge condition. Both the finite difference and spectral implementations satisfy this discrete gauge condition to machine precision. The second approach we propose enforces a semi-discrete continuity equation using the boundary integral solution to the field equations. The potential benefit of this approach is that it eliminates spatial derivatives that appear on the particle data, namely the current density, which is often calculated by linear combinations of low-order spline basis functions. This method is ideally suited to boundary integral equation methods that invert multi-dimensional operators without dimensional splitting techniques and will be the subject of future work. The third approach introduces a gauge correcting method that makes direct use of the gauge condition to modify the scalar potential and uses local maps for both the charge and current densities. This results in a gauge error, as the maps do not enforce the continuity equation. The vector potential coming from the current density is taken to be exact, and using the Lorenz gauge, we compute a correction to the scalar potential that makes the two potentials satisfy the gauge condition. This method also enforces the gauge condition to machine precision. We demonstrate two of the proposed methods in the context of periodic domains. Problems defined on bounded domains, including those with complex geometric features remain an ongoing effort. However, this work shows that it is possible to design computationally efficient methods that can effectively enforce the Lorenz gauge condition in a non-staggered PIC formulation.

97 MATHEMATICS AND COMPUTING↗