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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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33 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A second-order-in-time, explicit approach addressing the redundancy in the low-Mach, variable-density Navier-Stokes equations

A novel algorithm for explicit temporal discretization of the variable-density, low-Mach Navier-Stokes equations is presented here in this study. Recognizing there is a redundancy between the mass conservation equation, the equation of state, and the transport equation(s) for the scalar(s) which characterize the thermochemical state, and that it destabilizes explicit methods, we demonstrate how to analytically eliminate the redundancy and propose an iterative scheme to solve the resulting transformed scalar equations. The method obtains second-order accuracy in time regardless of the number of iterations, so one can terminate this subproblem once stability is achieved. Hence, flows with larger density ratios can be simulated while still retaining the efficiency, low cost, and parallelizability of an explicit scheme. The temporal discretization algorithm is used within a pseudospectral direct numerical simulation which extends the method of Kim, Moin, and Moser for incompressible flow to the variable-density, low-Mach setting, where we demonstrate stability for density ratios up to ~25.7.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

An explicit, energy-conserving particle-in-cell scheme

We present an explicit temporal discretization of particle-in-cell schemes for the non-relativistic Vlasov equation that results in exact energy conservation when combined with an appropriate spatial discretization. The scheme is inspired by a simple, second-order explicit scheme that conserves energy exactly in the Eulerian context. We show that direct translation to particle-in-cell does not result in strict conservation, but derive a simple correction based on an analytically solvable optimization problem that recovers conservation. While this optimization problem is not guaranteed to have a real solution for every particle, we provide a correction that makes imaginary values extremely rare and still admits $\mathcal{O}$(10 –12 ) fractional errors in energy for practical simulation parameters. We present the scheme in both electrostatic – where we use the Ampère formulation – and electromagnetic contexts. With an electromagnetic field solve, the field update is most naturally linearly implicit, but the more computationally intensive particle update remains fully explicit. Here, we also show how the scheme can be extended to use the fully explicit leapfrog and pseudospectral analytic time-domain (PSATD) field solvers. The scheme is tested on standard kinetic plasma problems, confirming its conservation properties.

Energy conservation↗
DOE OSTI2025

Scaling Field-Theoretic Simulation for Multicomponent Mixtures with Neural Operators

Multicomponent polymer mixtures are ubiquitous in biological self-organization but are notoriously difficult to study computationally. Plagued by both slow single molecule relaxation times and slow equilibration within dense mixtures, molecular dynamics simulations are typically infeasible at the spatial scales required to study the stability of mesophase structure. Polymer field theories offer an attractive alternative, but analytical calculations are only tractable for mean-field theories and nearby perturbations, constraints that become especially problematic for fluctuation-induced effects such as coacervation. Here, we show that a recently developed technique for obtaining numerical solutions to partial differential equations based on operator learning, neural operators, lends itself to a highly scalable training strategy by parallelizing per-species operator maps. We illustrate the efficacy of our approach on six-component mixtures with randomly selected compositions and that it significantly outperforms the state-of-the-art pseudospectral integrators for field-theoretic simulations, especially as polymer lengths become long.

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

DESC: A stellarator equilibrium solver

In this paper, the new code DESC is presented to solve for fixed-boundary ideal magnetohydrodynamic equilibria in stellarators. The approach directly solves the equilibrium force balance as a system of nonlinear equations in the form f(x) = 0. The independent variables x represent nested magnetic flux surfaces expressed in the inverse representation with toroidal flux coordinates, and the equations f(x) quantify equilibrium force balance errors at discrete points in real space. Discretizing with global Fourier–Zernike basis functions properly treats the magnetic axis and minimizes the number of coefficients needed to describe the flux surfaces. The pseudospectral method provides great flexibility in where the errors are evaluated, and the system of equations is efficiently solved with a Newton–Raphson iteration. Equilibria are computed and compared against VMEC for both axisymmetric and non-axisymmetric examples. The results show fast convergence rates and solutions with low errors throughout the plasma volume.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Accurate numerical simulations of open quantum systems using spectral tensor trains

Decoherence between qubits is a major bottleneck in quantum computations. Decoherence results from intrinsic quantum and thermal fluctuations as well as noise in the external fields that perform the measurement and preparation processes. With prescribed colored noise spectra for intrinsic and extrinsic noise, we present a numerical method, Quantum Accelerated Stochastic Propagator Evaluation (Q-ASPEN), to solve the time-dependent noise-averaged reduced density matrix in the presence of intrinsic and extrinsic noise. Q-ASPEN is arbitrarily accurate and can be applied to provide estimates for the resources needed to error-correct quantum computations. We employ spectral tensor trains, which combine the advantages of tensor networks and pseudospectral methods, as a variational ansatz to the quantum relaxation problem and optimize the ansatz using methods typically used to train neural networks. Here, the spectral tensor trains in Q-ASPEN make accurate calculations with tens of quantum levels feasible. We present benchmarks for Q-ASPEN on the spin-boson model in the presence of intrinsic noise and on a quantum chain of up to 32 sites in the presence of extrinsic noise. In our benchmark, the memory cost of Q-ASPEN scales as a low-order polynomial in the size of the system once the number of system states surpasses the number of basis functions used in the spectral expansion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Classifying photonic topology using the spectral localizer and numerical K -theory

Recently, the spectral localizer framework has emerged as an efficient approach for classifying topology in photonic systems featuring local nonlinearities and radiative environments. In nonlinear systems, this framework provides rigorous definitions for concepts such as topological solitons and topological dynamics, where a system’s occupation induces a local change in its topology due to nonlinearity. For systems embedded in radiative environments that do not possess a shared bulk spectral gap, this framework enables the identification of local topology and shows that local topological protection is preserved despite the lack of a common gap. However, as the spectral localizer framework is rooted in the mathematics of C*-algebras, and not vector bundles, understanding and using this framework requires developing intuition for a somewhat different set of underlying concepts than those that appear in traditional approaches for classifying material topology. In this tutorial, we introduce the spectral localizer framework from a ground-up perspective and provide physically motivated arguments for understanding its local topological markers and associated local measure of topological protection. In doing so, we provide numerous examples of the framework’s application to a variety of topological classes, including crystalline and higher-order topology. We then show how Maxwell’s equations can be reformulated to be compatible with the spectral localizer framework, including the possibility of radiative boundary conditions. To aid in this introduction, we also provide a physics-oriented introduction to multi-operator pseudospectral methods and numerical K-theory, two mathematical concepts that form the foundation for the spectral localizer framework. Finally, we provide some mathematically oriented comments on the C*-algebraic origins of this framework, including a discussion of real C*-algebras and graded C*-algebras that are necessary for incorporating physical symmetries. Looking forward, we hope that this tutorial will serve as an approachable starting point for learning the foundations of the spectral localizer framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Construction of quasisymmetric stellarators using a direct coordinate approach

In this work, optimized stellarator configurations and their analytical properties are obtained using a near-axis expansion approach. Such configurations are associated with good confinement as the guiding center particle trajectories and neoclassical transport are isomorphic to those in a tokamak. This makes them appealing as fusion reactor candidates. Using a direct coordinate approach, where the magnetic field and flux surface functions are found explicitly in terms of the position vector at successive orders in the distance to the axis, the set of ordinary differential equations for first and second order quasisymmetry is derived. Examples of quasi-axisymmetric shapes are constructed using a pseudospectral numerical method. Finally, the direct coordinate approach is used to independently verify two hypotheses commonly associated with quasisymmetric magnetic fields, namely that the number of equations exceeds the number of parameters at third order in the expansion and that the near-axis expansion does not prohibit exact quasisymmetry from being achieved on a single flux surface.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Tidal disruption of solitons in self-interacting ultralight axion dark matter

We report ultralight axions (ULAs) are promising dark matter candidates that can have a distinct impact on the formation and evolution of structure on nonlinear scales relative to the cold, collisionless dark matter (CDM) paradigm. However, most studies of structure formation in ULA models do not include the effects of self-interactions, which are expected to arise generically. Here, we study how the tidal evolution of solitons is affected by ULA self-interaction strength and sign. Specifically, using the pseudospectral solver UltraDark.jl, we simulate the tidal disruption of self-interacting solitonic cores as they orbit a 10 11 M ⊙ Navarro-Frenk-White CDM host halo potential for a range of orbital parameters, assuming a fiducial ULA particle mass of 10 -22 eV . We find that repulsive (attractive) self-interactions significantly accelerate (decelerate) soliton tidal disruption. We also identify a degeneracy between the self-interaction strength and soliton mass that determines the efficiency of tidal disruption, such that disruption timescales are affected at the ~ 50 % level for variations in the dimensionless ULA self-coupling from λ = -10 -92 to λ = 10 -92 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Dynamical friction in self-interacting ultralight dark matter

Here, we explore how dynamical friction in an ultralight dark matter (ULDM) background is affected by dark matter self-interactions. We calculate the force of dynamical friction on a point mass moving through a uniform ULDM background with self-interactions, finding that the force of dynamical friction vanishes for sufficiently strong repulsive self-interactions. Using the pseudospectral solver ultraDark.jl, we show with simulations that reasonable values of the ULDM self-interaction strength and particle mass cause $\mathcal{O}$(1) differences in the acceleration of an object like a supermassive black hole (SMBH) traveling near the center of a soliton, relative to the case with no self-interactions. For example, repulsive self-interactions with λ=10 -90 yield a deceleration due to dynamical friction ≈ 70% smaller than a model with no self-interactions. We discuss the observational implications of our results for SMBHs near soliton centers and for massive satellite galaxies falling into ultralight axion halos and show that outcomes are dependent on whether a self-interaction is present or not.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Resolution requirements for numerical modeling of neutrino quantum kinetics

Neutrino quantum kinetics is a rapidly evolving field in computational astrophysics, with a primary focus on collective neutrino oscillations in core-collapse supernovae and postmerger phases of binary neutron star mergers. In recent years, there has been considerable debate concerning resolution dependence in numerical simulations. In this paper, we conduct a comprehensive resolution study in both angular- and spatial directions by using two independent schemes of quantum kinetic neutrino transport: finite volume and pseudospectral methods. We complement our discussion by linear stability analysis including inhomogeneous modes. Our result suggests that decreasing spatial resolutions underestimates the growth of flavor instability, and then leads to wrong asymptotic states of flavor conversions, which potentially has a critical impact on astrophysical consequences. We further delve into numerical results of low resolution simulations, that reveals the underlying mechanism responsible for numerical artifacts caused by insufficient resolutions. Finally, this study settles the debate on requirements of resolutions and serves as a guideline for numerical modeling of quantum kinetic neutrino transport.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Towards Automated Reasoning Chains for Verification of LLM-Generated Scientific Code

With the rise of Large Language Model (LLM) generated code, including in domains like scientific computing, ensuring not only syntactical, but also mathematical correctness, has become a critical task. Traditional formal methods approaches often struggle with the ambiguity of floating-point code, and full symbolic execution is extremely costly and limited. We propose a chain-of-reasoning approach that iteratively lifts basic semantics from code into the SPIRAL system and then establishes numerical equivalency to the desired mathematical operation. Here, we leverage the ample mathematical knowledge already formalized in SPIRAL to enable the system to recognize not just different implementations of the same algorithm but fully separate approaches to solving the given problem. The chain establishes tight error bounds on the output of given code with respect to the true continuous solution it approximates, quantifying all sources of error. We demonstrate this approach by establishing the correctness of a pseudospectral solver for a simple 1-dimensional Poisson problem.

Oschatz, Quentin [Carnegie Mellon University,Pitts↗
DOE OSTI2020

Pyomo Optimization Example Problems v.1.0

This code is comprised of example problems to show implementation details of our SCITECH 2021 paper :Open-Source, Object-Oriented, Multi-Phase Pseudospectral Optimization Using Pyomo." Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. SAND2020-13973

Schlossman, Rachel↗
DOE OSTI2026

ShenCFD

ShenCFD is a fast pseudospectral solver for fluid dynamics written to be maximally Pythonic and maximally useful for machine-learning-based turbulence model discovery.

Saenz, Juan↗
DOE OSTI2022

Final Technical Report for "Cloud-based Low-Scaling Quantum Chemistry Simulations for Materials"

The objective of phase I was to develop the basic infrastructure for performing efficient hybrid DFT calculations on solid materials with a turnaround time amenable to the use in large-scale data-driven approaches. To fulfill the goal we have developed a novel algorithm that significantly reduces the cost of exchange matrix formation. The algorithm does so by making use of three ingredients (a) interpolative decomposition of the electron integrals (b) robust pseudospectral method and (c) occ-RI approach. Our published work demonstrates that the algorithm is orders of magnitude faster than any other hybrid-DFT method and is on the order of only 3-4 times slower than pure DFT. All steps of the algorithm developed during phase I can be accelerated to the point that, for large enough systems, the diagonalization of the Fock matrix will become the most expensive step. To treat such large systems we have created an interface to the ASCR-funded PEXSI library. The PEXSI method is used to compute the density matrix directly from the Fock matrix in a manner that preserves the sparsity of the local representation.

Shiozaki, Toru↗
DOE OSTI2025

A Model Predictive Control to Improve Grid Resilience

The following article details a model predictive control (MPC) to improve grid resilience when faced with variable generation resources. This topic is of significant interest to utility power systems where distributed intermittent energy sources will increase significantly and be relied on for electric grid ancillary services. Previous work on MPCs has focused on narrowly targeted control applications such as improving electric vehicle (EV) charging infrastructure or reducing the cost of integrating Energy Storage Systems (ESSs) into the grid. In contrast, this article develops a comprehensive treatment of the construction of an MPC tailored to electric grids and then applies it integration of intermittent energy resources. To accomplish this, the following article includes a description of a reduced order model (ROM) of an electric power grid based on a circuit model, an optimization formulation that describes the MPC, a collocation method for solving linear time-dependent differential algebraic equations (DAEs) that result from the ROM, and an overall strategy for iteratively refining the behavior of the MPC. Next, the algorithm is validated using two separate numerical experiments. First, the algorithm is compared to an existing MPC code and the results are verified by a numerically precise simulation. It is shown that this algorithm produces a control comparable to existing algorithms and the behavior of the control carefully respects the bounds specified. Second, the MPC is applied to a small nine bus system that contains a mix of turbine-spinning-machine-based and intermittent generation in order to demonstrate the algorithm’s utility for resource planning and control of intermittent resources. This study demonstrates how the MPC can be tuned to change the behavior of the control, which can then assist with the integration of intermittent resources into the grid. The emphasis throughout the paper is to provide systematic treatment of the topic and produce a novel nonlinear control compatible design framework applicable to electric grids and the control of variable resources. This differs from the more targeted application-based focus in most presentations.

microgrid↗