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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Optimization-based, property-preserving finite element methods for scalar advection equations and their connection to Algebraic Flux Correction

In this paper, we continue our efforts to exploit optimization and control ideas as a common foundation for the development of property-preserving numerical methods. Here we focus on a class of scalar advection equations whose solutions have fixed mass in a given Eulerian region and constant bounds in any Lagrangian volume. Our approach separates discretization of the equations from the preservation of their solution properties by treating the latter as optimization constraints. This relieves the discretization process from having to comply with additional restrictions and makes stability and accuracy the sole considerations in its design. A property-preserving solution is then sought as a state that minimizes the distance to an optimally accurate but not property-preserving target solution computed by the scheme, subject to constraints enforcing discrete proxies of the desired properties. Furthermore, we consider two such formulations in which the optimization variables are given by the nodal solution values and suitably defined nodal fluxes, respectively. A key result of the paper reveals that a standard Algebraic Flux Correction (AFC) scheme is a modified version of the second formulation obtained by shrinking its feasible set to a hypercube. In conclusion, we present numerical studies illustrating the optimization-based formulations and comparing them with AFC

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Quantized State Integrator With Second Order Errors Over Monotonic Segments

We introduce a novel quantized state integration method that is analogous to the explicit, second order Runge-Kutta technique. A feature of this method is that, for a single differential equation over an interval where the solution is monotonic, it exhibits an error proportional to the square of the integration quantum. We offer a theoretical proof of this behavior and demonstrate it with a numerical example. At the same time, an extension of the method to a system with input causes the errors to become proportional to the integration quantum. The latter observation fits established theory; the former appears to be a new result that might offer new insights into the construction of quantized state integration methods.

Mahawattege, Rasika↗
DOE OSTI2025

Biased degenerate ground-state sampling of small Ising models with converged quantum approximate optimization algorithm

The quantum alternating operator ansatz, a generalization of the quantum approximate optimization algorithm (QAOA), is a quantum algorithm used for approximately solving combinatorial optimization problems. QAOA typically uses the transverse field mixer as the driving Hamiltonian. One of the interesting properties of the transverse field driving Hamiltonian is that it results in nonuniform sampling of degenerate ground states of optimization problems. In this study, we numerically examine the fair sampling properties of the transverse field mixer QAOA, and Grover mixer QAOA (GM-QAOA), which provides theoretical guarantees of fair sampling of degenerate optimal solutions, up to a large enough p such that the mean expectation value converges to an optimal approximation ratio of 1. This comparison is performed with high-quality heuristically computed, but not necessarily optimal, QAOA angles, which give strictly monotonically improving solution quality as p increases. These angles are computed using the Julia based numerical simulation software JuliQAOA. Fair sampling of degenerate ground states is quantified using the Shannon entropy of the ground-state amplitudes distribution. The fair sampling properties are reported on several quantum signature Hamiltonians from previous quantum annealing fair sampling studies. Small random fully connected spin glasses are shown, which exhibit exponential suppression of some degenerate ground states with transverse field mixer QAOA. The transverse field mixer QAOA simulations show that some problem instances clearly saturate the Shannon entropy of 0 with a maximally biased distribution that occurs when the learning converges to an approximation ratio of 1 while other problem instances never deviate from a maximum Shannon entropy (uniform distribution) at any p step. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Stability and convergence of nuclear detonations in white dwarf collisions

We investigate the numerical stability of thermonuclear detonations in 1D accelerated reactive shocks and 2D binary collisions of equal-mass magnetized and unmagnetized white dwarf stars. To achieve high resolution at initiation sites, we devised geometric gridding and mesh velocity strategies specially adapted to the unique requirements of head-on collisional geometries, scenarios in which one expects maximum production of iron-group products. We study the effects of grid resolution and the limiting of temperature, energy, and reactants for different stellar masses, separations, magnetic fields, inigenerationtial compositions, detonation mechanisms, and limiter parameters across a range of cell sizes from 1 to 100 km. Our results set bounds on the parameter space of limiter amplitudes for which both temperature- and energy-limiting procedures yield consistent and monotonically convergent solutions. Within these bounds, we find that grid resolutions of 5 km or better are necessary for uncertainties in total released energy and iron-group products to drop below 10%. Intermediate-mass products (e.g., calcium) exhibit similar convergence trends but with somewhat greater uncertainty. These conclusions apply equally to pure C/O white dwarfs, multispecies compositions (including helium shells), magnetized and unmagnetized cores, and either single or multiple detonation scenarios.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Super-time-stepping schemes for parabolic equations with boundary conditions

In this work, we present a super-time-stepping scheme for numerically solving parabolic partial differential equations with Dirichlet boundary conditions (BC). Using the general Forward Euler scheme, one can show that by taking varying step sizes there is the potential of propagating the solution forward in time by a greater amount than with uniform step sizes, while maintaining the same order of accuracy. As shown in previous works, if one further requires that the scheme have the Convex Monotone Property (CMP), then there exists a scheme which results in linear, monotone stability of the solution. This monotone stability is highly desirable in many physical situations, such as thermal diffusion, where the physical system will not oscillate, but will behave monotonically. However, the schemes devised in previous works do not include situations that have a boundary condition, and the inclusion of boundary conditions will henceforth be our focus. It is shown that a particular Runge-Kutta-Gegenbauer class of schemes [5] will maintain the CMP even in the presence of Dirichlet BC.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Gauge constrained algorithm of variational discrete action theory at N = 3 for the multiorbital Hubbard model

The recently developed variational discrete action theory (VDAT) provides a systematic variational approach to the ground state of the quantum many-body problem, where the quality of the solution is controlled by an integer N, and increasing N monotonically approaches the exact solution. VDAT can be exactly evaluated in the d = ∞ multiorbital Hubbard model using the self-consistent canonical discrete action theory (SCDA), which requires a self-consistency condition for the integer time Green's functions. Previous work demonstrates that N = 3 accurately captures multiorbital Mott/Hund physics at a cost similar to the Gutzwiller approximation. Here we employ a gauge constraint to automatically satisfy the self-consistency condition of the SCDA at N = 3, yielding an even more efficient algorithm with enhanced numerical stability. We derive closed form expressions of the gauge constrained algorithm for the multiorbital Hubbard model with general density-density interactions, allowing VDAT at N = 3 to be straightforwardly applied to the seven-orbital Hubbard model. We present results and a performance analysis using N = 2 and N = 3 for the SU⁡(2⁢N orb ) Hubbard model in d = ∞ with N orb = 2–8, and compare to numerically exact dynamical mean-field theory solutions where available. Finally, the developments in this work will greatly facilitate the application of VDAT at N = 3 to strongly correlated electron materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

A block-spectral adaptive H-/$p$-refinement strategy for shock-dominated problems

An adaptive H-/p-refinement strategy using a novel sensor is devised and tested in a block-spectral compressible Euler code equipped with adaptive-mesh refinement (AMR) and high-order flux-reconstruction numerics. At each Gauss quadrature point (or solution point) within each spectral block (or mesh element) the discrete velocity jump ΔU = ∂U/∂y 1 Δy 1 + ∂V/∂y 2 Δy 2 + ∂W/∂y 3 Δy 3 is calculated and normalized by the local speed of sound, a. Here, the grid spacing, Δx i , is calculated in each direction as the distance between auxiliary Gauss-Lobatto points, staggered relative to the solution points. The polynomial order is increased from p = 0 to p = p max in regions of weak compression, (ΔU/a) crit < ΔU/a < 0 and kept at p = p max in regions of flow expansion ΔU/a ≥ 0, while staying at the H = 0 base mesh level. Regions experiencing strong compressions, i.e. ΔU/a < (ΔU/a) crit , are H-refined up to H = H max where H max is applied at the location of maximum compression, ΔU/a = min(ΔU/a) in the domain, while keeping p = 0 to guarantee robustness and monotonicity of the solution in the H refined region. The critical value of (ΔU/a) crit = -0.06 is found to effectively separate smooth and non-smooth solution regions, supported by a 1D detonation initiation test case in ideal gas and a shock-to-detonation transition in high explosives. Using this value, the Sod shock tube, Shu-Osher problem, double Mach reflection and a 2D detonation in a high-explosive are simulated with the proposed adaptive H-/p-refinement. In the Sod shock tube case, p-refinement resolves the (weak) contact discontinuity while H-refinement enhances the grid resolution in the shock exploiting the monotonicity of the p = 0 reconstruction. For the Shu-Osher problem, p-refinement captures the small-scale oscillations trailing the shock that would be otherwise attenuated, while H-refinement triggered by the ΔU-sensor appropriately tracks the shock. In the double Mach reflection problem, H-refinement confines the numerical diffusion around the reflected shock while p-refinement recaptures many physical features trailing the shock. Finally, in the 2D high-explosive detonation case, H-refinement follows the leading shock and resolves the curvature of the detonation wave, while p-refinement adds resolution to the trailing reaction zone. Finally, the proposed methodology is tested in a detonation-wave propagation test case in high-explosives with numerical predictions comparing favorably against experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Feedback-based quantum algorithms for ground state preparation

The ground state properties of quantum many-body systems are a subject of interest across chemistry, materials science, and physics. Thus, algorithms for finding ground states can have broad impacts. Variational quantum algorithms are one class of ground state algorithms that has received significant attention in recent years. These algorithms utilize a hybrid quantum-classical computing framework to prepare ground states on quantum computers. However, this requires solving a classical optimization problem that can become prohibitively expensive in high dimensions. Here, we develop formulations of feedback-based quantum algorithms for ground state preparation that can be used to address this challenge for two broad classes of Hamiltonians: Fermi-Hubbard Hamiltonians, and molecular Hamiltonians represented in second quantization. Feedback-based quantum algorithms are optimization-free; in place of classical optimization, quantum circuit parameters are set according to a deterministic feedback law derived from quantum Lyapunov control principles. This feedback law guarantees a monotonic improvement in solution quality with respect to the depth of the quantum circuit. A variety of numerical illustrations are provided that analyze the convergence and robustness of feedback-based quantum algorithms for these problem classes. Published by the American Physical Society 2024

Larsen, James B. (ORCID:000000020777440X)↗
DOE OSTI2020

Computational modeling and neutron imaging to understand interface shape and solute segregation during the vertical gradient freeze growth of BaBrCl:Eu

In this work we apply continuum models to analyze phase change, heat transfer, fluid flow, solute transport, and segregation in order to understand prior neutron imaging observations of the vertical gradient freeze growth of Eu-doped BaBrCl. The models provide a rigorous framework in which to understand the mechanisms that are responsible for the complicated evolution of interface shape and dopant distribution in the growth experiment. We explain how a transition in the solid/liquid interface shape from concave to convex is driven by changes in radial heat transfer caused by furnace design. We also provide a mechanistic explanation of how dynamic growth conditions and changes of the flow structure in the melt result in complicated segregation patterns in this system. A growth pause caused by controller lock-up is shown to result in a band of solute depletion in accordance with classical theory. However, changing flow patterns during growth result in a non-monotonic axial distribution of solute that cannot be explained by simple application of classical segregation models. We assert that the approach presented here, namely the use of rigorous models in conjunction advanced diagnostics, such as neutron imaging, provides an exciting path forward for process optimization and control, accelerating the incremental advances that have, in the past, typically relied on empiricism, experience, and intuition.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A remapping scheme for history-dependent material state variables

Here, we present an interpolation scheme for use with material models involving history-dependent state variables. The interpolation scheme is based on the solution of a constrained optimization problem, to identify the smoothest monotone curve which produces an admissible solution. Unlike classical schemes used for transport equations, the proposed methodology accounts for the interdependence of the history variables and produces admissible interpolations of the material's state variables. After introducing a general solution scheme for the problem, a simplified and more computationally efficient method is derived. Finally, as a validation problem for the proposed methods, we consider the advection of internal state variables belonging to material models with highly nonlinear yield surfaces.

42 ENGINEERING↗
DOE OSTI2021

Variational Discrete Action Theory

In this work, we propose the variational discrete action theory (VDAT) to study the ground state properties of quantum many-body Hamiltonians. VDAT is a variational theory based on the sequential product density matrix (SPD) ansatz, characterized by an integer $\mathscr{N}$, which monotonically approaches the exact solution with increasing $\mathscr{N}$. To evaluate the SPD, we introduce a discrete action and a corresponding integer time Green’s function. We use VDAT to exactly evaluate the SPD in two canonical models of interacting electrons: the Anderson impurity model and the d = ∞ Hubbard model. For the latter, we evaluate $\mathscr{N}$ = 2 – 4, where $\mathscr{N}$ = 2 recovers the Gutzwiller approximation (GA), and we show that $\mathscr{N}$ = 3, which exactly evaluates the Gutzwiller-Baeriswyl wave function, provides a truly minimal yet precise description of Mott physics with a cost similar to that of the GA. VDAT is a flexible theory for studying quantum Hamiltonians, competing both with state-of-the-art methods and simple, efficient approaches all within a single framework.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Effect of Production Bias on Radiation-Induced Segregation in Ni-Cr Alloys

We present an in-depth investigation into the Radiation-Induced Segregation (RIS) phenomenon in Ni-Cr alloys. All the pivotal factors affecting RIS such as surface’s absorption efficiency, grain size, production bias, dose rate, temperature, and sink density were systematically studied. Through comprehensive simulations, the individual and collective impacts of these factors were analyzed, enabling a refined understanding of RIS. A notable finding was the significant influence of production bias on point defects’ interactions with grain boundaries/surfaces, thereby playing a crucial role in RIS processes. Production bias alters the neutrality of these interactions, leading to a preferential absorption of one type of point defect by the boundary and consequent establishment of distinct surface-mediated patterns of point defects. These spatial patterns further result in non-monotonic spatial profiles of solute atoms near surfaces/grain boundaries, corroborated by experimental observations. In particular, a positive production bias, signifying a higher production rate of vacancies over interstitials, drives more Cr depletion at the grain boundary. Moreover, a temperature-dependent production bias must be considered to recover the experimentally reported dependence of RIS on temperature. The severity of radiation damage and RIS becomes more pronounced with increased production bias, dose rate, and grain size, while high temperatures or sink density suppress the RIS severity. Model predictions were validated against experimental data, showcasing robust qualitative and quantitative agreements. The findings pave the way for further exploration of these spatial dependencies in subsequent studies, aiming to augment the comprehension and predictability of RIS processes in alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Linear and nonlinear viscoelasticity of concentrated thermoresponsive microgel suspensions

We present an integrated experimental and theoretical study of the dynamics and rheology of self-crosslinked, slightly charged, temperature responsive soft poly(N-isopropylacrylamide) (pNIPAM) microgels over a wide range of concentration and temperature spanning the sharp change in particle size and intermolecular interactions across the lower critical solution temperature (LCST). Dramatic, non-monotonic changes in viscoelasticity are observed as a function of temperature, with distinct concentration dependence in the dense fluid, glassy, and soft-jammed regimes. Motivated by our experimental observations, we formulate a minimalistic model for the size dependence of a single microgel particle and the change of the interparticle interaction from purely repulsive to attractive upon heating. Using microscopic equilibrium and time-dependent statistical mechanical theories, theoretical predictions are quantitatively compared with experimental measurements of the shear modulus. Good agreement is found for the nonmonotonic temperature behavior that originates as a consequence of the competition between reduced microgel packing fraction and increasing interparticle attractions. Furthermore, testable predictions are made for nonlinear rheological properties such as the yield stress and strain. To our knowledge, this is the first attempt to quantitatively understand in a unified manner the viscoelasticity of dense, temperature-responsive microgel suspensions spanning a wide range of temperatures and concentrations.

42 ENGINEERING↗
DOE OSTI2022

Numerical Solution of the Steady-State Network Flow Equations for a Non-Ideal Gas

Herein we formulate a steady-state network flow problem for non-ideal gas that relates injection rates and nodal pressures in the network to flows in pipes. For this problem, we present and prove a theorem on uniqueness of generalized solution for a broad class of non-ideal pressure-density relations that satisfy a monotonicity property. Further, we develop a Newton-Raphson algorithm for numerical solution of the steady-state problem, which is made possible by a systematic non-dimensionalization of the equations. The developed algorithm has been extensively tested on benchmark instances and shown to converge robustly to a generalized solution. Previous results [1]-[4], indicate that the steady-state network flow equations for an ideal gas are difficult to solve by the Newton-Raphson method because of its extreme sensitivity to the initial guess. In contrast, we find that non-dimensionalization of the steady-state problem is key to robust convergence of the Newton-Raphson method. We identify criteria based on the uniqueness of solutions under which the existence of a non-physical generalized solution found by a non-linear solver implies non-existence of a physical solution, i.e., infeasibility of the problem. Finally, we compare pressure and flow solutions based on ideal and non-ideal equations of state to demonstrate the need to apply the latter in practice. The solver developed in this article is open-source and is made available for both the academic and research communities as well as the industry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Accelerated kinetic Monte Carlo: A case study; vacancy and dumbbell interstitial diffusion traps in concentrated solid solution alloys

Vacancy and self-interstitial atomic diffusion coefficients in concentrated solid solution alloys can have a non-monotonic concentration dependence. Here, the kinetics of monovacancies and $\langle$100$\rangle$ dumbbell interstitials in Ni–Fe alloys are assessed using lattice kinetic Monte Carlo (kMC). The non-monotonicity is associated with superbasins, which impels using accelerated kMC methods. Detailed implementation prescriptions for first passage time analysis kMC (FPTA-kMC), mean rate method kMC (MRM-kMC), and accelerated superbasin kMC (AS-kMC) are given. The accelerated methods are benchmarked in the context of diffusion coefficient calculations. The benchmarks indicate that MRM-kMC underestimates diffusion coefficients, while AS-kMC overestimates them. In this application, MRM-kMC and AS-kMC are computationally more efficient than the more accurate FPTA-kMC. Our calculations indicate that composition dependence of migration energies is at the origin of the vacancy’s non-monotonic behavior. In contrast, the difference between formation energies of Ni–Ni, Ni–Fe, and Fe–Fe dumbbell interstitials is at the origin of their non-monotonic diffusion behavior. Additionally, the migration barrier crossover composition—based on the situation where Ni or Fe atom jumps have lower energy barrier than the other one—is introduced. KMC simulations indicate that the interplay between composition dependent crossover of migration energy and geometrical site percolation explains the non-monotonic concentration-dependence of atomic diffusion coefficients.

36 MATERIALS SCIENCE↗
DOE OSTI2019

A finite scale model for shock structure

In this paper we explore the use of a finite scale model of fluid dynamics to predict the finite structure of a shock wave in a perfect gas. We begin by documenting the history and issues that have arisen when Navier–Stokes theory is applied to the shock structure problem, and continue by motivating the improvement that finite scale theory might provide from its representation of inviscid (anomalous) dissipation. Furthermore, our primary results include the formulation of a traveling wave equation from finite scale theory, an analysis of the solutions of that equation as regards shock width and monotonicity properties, and an estimation of the critical parameter of the theory from experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

DT-HYDRO

The software solves the time dependent, one dimensional (1D) coupled mass and momentum balance equations governing the elastic flow of water through the penstock, turbine and draft tube in a hydroelectric facility using a high order finite volume based method. The numerical method is based on the Kurganov-Tadmor central method paired with the Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL). This solution method accurately resolves the fast transient behavior of the flow, including water hammer. Additionally, the software estimates the full 3D flow field within the turbine chamber in real time, a feat that is made possible by leveraging pre-computed CFD results by utilizing a reduced order modeling method based on an efficient randomized singular value decomposition (SVD) driven proper orthogonal decomposition (POD) with POD-mode weight regression. The reduced order model of the 3D flow is directly coupled to the 1D elastic flow model so the entire flow field through the penstock and turbine system is resolved quickly and with high fidelity.

Gurecky, William [Oak Ridge National Laboratory (O↗
DOE OSTI2020

The Kalai-Smorodinsky solution for many-objective Bayesian optimization

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the R package GPGame available on CRAN at https://cran.r-project.org/package=GPGame.

Game theory↗