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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 OSTI2025

Directional finite difference method for directly solving 3D gyrokinetic field equations with enhanced accuracy

The gyrokinetic (GK) field equation is a three-dimensional (3D) elliptic equation, but it is often simplified to a set of two-dimensional (2D) equations by assuming that the field does not vary along a specific direction. However, this simplification can introduce inevitable 0th-order numerical errors, as nonlinear mode coupling in toroidal geometry can produce undesirable harmonic modes that violate the assumption. In this work, we propose a novel directional finite difference method (FDM) with a local coordinate transformation to better resolve the target field of interest. The directional FDM can accurately solve 3D GK field equations without simplifications, which can overcome the limitations of conventional methods. The accuracy and efficiency of different FDMs are analyzed in great detail for a variety of geometries, from simple 2D Cartesian coordinates to realistic 3D curvilinear coordinates. The 0th-order numerical errors of simplified 2D GK equations were found to be more problematic for low-harmonic modes and low aspect ratio geometries such as spherical tokamaks. On the other hand, the directional 3D FDM can accurately resolve a much wider range of harmonic modes aligned to the direction of interest, including the low-harmonic modes. In conclusion, we demonstrate that the directional 3D FDM is a highly effective algorithm for solving the 3D GK field equations, achieving accuracy improvements of 10 to 100 times or more, particularly for low-harmonic modes in spherical tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A $C^1$-Conforming Arbitrary-Order Two-Dimensional Virtual Element Method for the Fourth-Order Phase-Field Equation

We present a two-dimensional conforming virtual element method for the fourth-order phase-field equation. Our proposed numerical approach to the solution of this high-order phase-field (HOPF) equation relies on the design of an arbitrary-order accurate, virtual element space with $C^1$ global regularity. Such regularity is guaranteed by taking the values of the virtual element functions and their full gradient at the mesh vertices as degrees of freedom. Attaining high-order accuracy requires also edge polynomial moments of the trace of the virtual element functions and their normal derivatives. In this work, we detail the scheme construction, and prove its convergence by deriving error estimates in different norms. A set of representative test cases allows us to assess the behavior of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Mean-field equation for phase-modulated optical parametric oscillator

The widely established techniques for the generation of ultrashort optical pulses rely on passive mode locking of lasers, with the output pulse duration and emission spectrum determined by the intrinsic lifetime of laser transition in the gain medium. Due to the instantaneous nature of nonlinear gain, optical parametric oscillators (OPOs) are capable of generating optical radiation in all timescales from continuous-wave (cw) to ultrashort femtosecond regime, if driven by laser pump sources in the corresponding time domain. In the ultrashort timescale, operation of OPOs conventionally relies on mode-locked pump lasers, with the concomitant disadvantages of large footprint and high cost. At the same time, the lack of gain storage mandates the use of synchronous pumping, resulting in increased complexity. In this paper, we present the concept of phase-modulated OPO driven by cw pump laser. The approach overcomes the traditional drawbacks of ultrafast OPOs, enabling femtosecond pulse generation without the need for synchronous pumping, resulting in a simplified, compact, and cost-effective architecture using cw input pump lasers. We derive a mean-field equation for a degenerate χ ( 2 ) OPO driven by a cw laser with intracavity electro-optic modulator (EOM), and also including dispersion compensation. The equation predicts the formation of stable femtosecond pulses ( < 200 fs ) , in both normal and anomalous dispersion regimes, with a controllable repetition rate determined by the frequency of the EOM. The remarkable functionality of the proposed scheme paves the way for the development of an alternative class of widely tunable coherent femtosecond light sources in both bulk and integrated format based on χ ( 2 ) OPOs using cw pump lasers. Published by the American Physical Society 2024

Sanchez, A. D. (ORCID:0000000327630339)↗
DOE OSTI2023

Projective embedding of dynamical systems: Uniform mean field equations

Herein we study embeddings of continuous dynamical systems in larger dimensions via projector operators. We call this technique PEDS, projective embedding of dynamical systems, as the stable fixed point of the original system dynamics are recovered via projection from the higher dimensional space. In this paper we provide a general definition and prove that for a particular type of rank-1 projector operator, the uniform mean field projector, the equations of motion become a mean field approximation of the dynamical system. While in general the embedding depends on a specified variable ordering, the same is not true for the uniform mean field projector. We prove a variety of results on the relationship between the spectrum of the Jacobian for fixed points in the original and in the embedded system. Direct applications of PEDS can be non-convex optimization and machine learning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Tusas: A fully implicit parallel approach for coupled phase-field equations

In this study, we develop a fully-coupled, fully-implicit approach for phase-field modeling of solidification in metals and alloys. Predictive simulation of solidification in pure metals and metal alloys remains a significant challenge in the field of materials science, as microstructure formation during the solidification process plays a critical role in the properties and performance of the solid material. Our simulation approach consists of a finite element spatial discretization of the fully-coupled nonlinear system of partial differential equations at the microscale, which is treated implicitly in time with a preconditioned Jacobian-free Newton-Krylov method. The approach is algorithmically scalable as well as efficient due to an effective preconditioning strategy based on algebraic multigrid and block factorization. We implement this approach in the open-source Tusas framework, which is a general, flexible tool developed in C++ for solving coupled systems of nonlinear partial differential equations. The performance of our approach is analyzed in terms of algorithmic scalability and efficiency, while the computational performance of Tusas is presented in terms of parallel scalability and efficiency on emerging heterogeneous architectures. We demonstrate that modern algorithms, discretizations, and computational science, and heterogeneous hardware provide a robust route for predictive phase-field simulation of microstructure evolution during additive manufacturing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

General approach to the Lagrangian ambiguity in f(R, T) gravity

Abstract The f ( R , T ) gravity is a theory whose gravitational action depends arbitrarily on the Ricci scalar, R , and the trace of the stress–energy tensor, T ; its field equations also depend on matter Lagrangian, $$\mathscr {L}_{m}$$ L m . In the modified theories of gravity where field equations depend on Lagrangian, there is no uniqueness on the Lagrangian definition and the dynamics of the gravitational and matter fields can be different depending on the choice performed. In this work , we have eliminated the $$\mathscr {L}_{m}$$ L m dependence from f ( R , T ) gravity field equations by generalizing the approach of Moraes in Ref. [1]. We also propose a general approach where we argue that the trace of the energy–momentum tensor must be considered an “unknown” variable of the field equations. The trace can only depend on fundamental constants and few inputs from the standard model. Our proposal resolves two limitations: first the energy–momentum tensor of the f ( R , T ) gravity is not the perfect fluid one; second, the Lagrangian is not well-defined. As a test of our approach we applied it to the study of the matter era in cosmology, and the theory can successfully describe a transition between a decelerated Universe to an accelerated one without the need for dark energy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Code-verification techniques for the method-of-moments implementation of the magnetic-field integral equation

For computational physics simulations, code verification plays a major role in establishing the credibility of the results by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, surface integral equations, such as the method-of-moments implementation of the magnetic-field integral equation, are frequently used to solve Maxwell's equations on the surfaces of electromagnetic scatterers. These electromagnetic surface integral equations yield many code-verification challenges due to the various sources of numerical error and their possible interactions. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources. We demonstrate the effectiveness of these approaches for cases with and without coding errors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A consistent and conservative Phase-Field method for multiphase incompressible flows

In the present study, a consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the consistency of mass and momentum transport are implemented to address the issue of physically coupling the Phase-Field equation, which locates different phases, to the hydrodynamics. These two consistency conditions, as illustrated, provide the “optimal” coupling because (i) the new momentum equation resulting from them is Galilean invariant and implies the kinetic energy conservation, regardless of the details of the Phase-Field equation, and (ii) failures of satisfying the second law of thermodynamics or the consistency of reduction of the multiphase flow model only result from the same failures of the Phase-Field equation but are not due to the new momentum equation. Physical interpretation of the consistency conditions and their formulations are first provided, and general formulations that are obtained from the consistency conditions and independent of the interpretation of the velocity are summarized. Then, the present consistent and conservative multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several novel techniques are developed to inherit the physical properties of the multiphase flows after discretization, including the gradient-based phase selection procedure, the momentum conservative method for the surface force, and the general theorems to preserve the consistency conditions on the discrete level. Equipped with those novel techniques, a consistent and conservative scheme for the present multiphase flow model is developed and analyzed. The scheme satisfies the consistency conditions, conserves the mass and momentum, and assures the summation of the volume fractions to be unity, on the fully discrete level and for an arbitrary number of phases. All those properties are numerically validated. Finally, numerical applications demonstrate that the present model and scheme are robust and effective in studying complicated multiphase dynamics, especially for those with large-density ratios.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Code-verification techniques for the method-of-moments implementation of the combined-field integral equation

Code verification plays an important role in establishing the credibility of computational simulations by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, the numerical solution to integral equations incurs multiple interacting sources of numerical error, as well as other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the combined-field integral equation. Here, we demonstrate the effectiveness of these approaches for cases with and without coding errors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Solving gyrokinetic systems with higher-order time dependence

We discuss theoretical and numerical aspects of gyrokinetics as a Lagrangian field theory when the field perturbation is introduced into the symplectic part. A consequence is that the field equations and particle equations of motion in general depend on the time derivatives of the field. The most well-known example is when the parallel vector potential is introduced as a perturbation, where a time derivative of the field arises only in the equations of motion, so an explicit equation for the fields may still be written. We will consider the conceptually more problematic case where the time-dependent fields appear in both the field equations and equations of motion, but where the additional term in the field equations is formally small. The conceptual issues were described by Burby (J. Plasma Phys., vol. 82 (3), 2016, 905820304): these terms lead to apparent additional degrees of freedom to the problem, so that the electric field now requires an initial condition, which is not required in low-frequency (Darwin) Vlasov–Maxwell equations. Also, the small terms in the Euler–Lagrange equations are a singular perturbation, and these two issues are interlinked. For well-behaved problems the apparent additional degrees of freedom are spurious, and the physically relevant solution may be directly identified. Because we needed to assume that the system is well behaved for small perturbations when deriving gyrokinetic theory, we must continue to assume that when solving it, and the physical solutions are thus the regular ones. The spurious nature of the singular degrees of freedom may also be seen by changing coordinate systems so the varying field appears only in the Hamiltonian. We then describe how methods appropriate for singular perturbation theory may be used to solve these asymptotic equations numerically. We then describe a proof-of-principle implementation of these methods for an electrostatic strong-flow gyrokinetic system; two basic test cases are presented to illustrate code functionality.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Geometric integration of classical spin dynamics via a mean-field Schrödinger equation

The Landau-Lifshitz equation describes the time evolution of magnetic dipoles and can be derived by taking the classical limit of a quantum mechanical spin Hamiltonian. To take this limit, one constrains the many-body quantum state to a tensor product of coherent states, thereby neglecting entanglement between sites. Expectation values of the quantum spin operators produce the usual classical spin dipoles. One may also consider expectation values of polynomials of the spin operators, leading to quadrupole and higher-order spin moments, which satisfy a dynamical equation of motion that generalizes the Landau-Lifshitz dynamics [Zhang and Batista, Phys. Rev. B 104, 104409 (2021)]. Here we reformulate the dynamics of these N 2 –1 generalized spin components as a mean-field Schrödinger equation on the N-dimensional coherent state. Furthermore, this viewpoint suggests efficient integration methods that respect the local symplectic structure of the classical spin dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Characterization and integration of the singular test integrals in the method-of-moments implementation of the electric-field integral equation

In this paper, we characterize the logarithmic singularities arising in the method of moments from the Green’s function in integrals over the test domain, and we use two approaches for designing geometrically symmetric quadrature rules to integrate these singular integrands. These rules exhibit better convergence properties than quadrature rules for polynomials and, in general, lead to better accuracy with a lower number of quadrature points. In this work, we demonstrate their effectiveness for several examples encountered in both the scalar and vector potentials of the electric-field integral equation (singular, near-singular, and far interactions) as compared to the commonly employed polynomial scheme and the double Ma–Rokhlin–Wandzura (DMRW) rules, whose sample points are located asymmetrically within triangles.

42 ENGINEERING↗
DOE OSTI2025

Dust stars in the minimal exponential measure model

Here, we report the existence of horizonless compact object solutions supported by dust in the minimal exponential measure (MEMe) model, a theory which modifies the couplings between gravity and matter without introducing dynamical degrees of freedom. For a perfect fluid source, the field equations for the MEMe model can be rewritten as the Einstein field equations sourced by a perfect fluid with a transformed equation of state, which can endow a sufficiently dense cloud of dust with an effective pressure. The resulting dust-supported horizonless compact objects can have masses below ∼10 −11 ⁢𝑀 ⊙ , making them suitable as massive compact halo objects comprising a significant mass fraction for dark matter. A necessary condition for the existence of these compact object solutions is that the single free parameter in the MEMe model is positive valued. Additionally, we find that this positive sign for the parameter can provide a mechanism for suppressing the formation of (primordial) black holes from the gravitational collapse of matter below a certain mass scale.

alternative gravity theories↗
DOE OSTI2022

Bifurcation Analysis Reveals Solution Structures of Phase Field Models

The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, in this study, we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models. Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions. To elucidate the idea, we apply this analytical approach to three representative phase field equations: the Allen-Cahn equation, the Cahn-Hilliard equation, and the Allen-Cahn-Ohta-Kawasaki system. The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

From classical thermodynamics to phase-field method

Phase-field method is a density-based computational method at the mesoscale for modeling and predicting the temporal microstructure and property evolution during materials processes. The focus of this article is on connecting the most common phase-field equations to the very basic first and second laws of classical thermodynamics through rudimentary irreversible thermodynamics. It briefly discusses the relations of the continuum phase-field equations to their counter parts at the microscopic and atomic levels. It attempts to clarify the contributions of long-range elastic, electrostatic, and magnetic interactions to domain structure evolution during structural, ferroelectric, and ferromagnetic phase transformations by separating order parameter changes due to the presence of quasi-static fields and those arising from phase transformations. A few examples are presented to demonstrate the possibility of employing the phase-field method to provide guidance to designing materials for optimum properties or discovering novel mesoscale phenomena or new materials functionalities. Here, the article ends with a brief perspective on a number of potential future directions on the development and applications of phase-field method beyond its traditional applications to structural alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A two-phase three-field modeling framework for heat pipe application in nuclear reactors

Heat pipes and two-phase thermosyphons are highly efficient heat transfer devices utilizing continuous evaporation and condensation of working fluid for two-phase heat transport in closed systems. Because of the nearly isothermal and fully passive phase-change heat transfer mechanism, heat pipes and thermosyphons have found many applications in nuclear engineering, space technologies, and other energy systems. High-temperature heat pipes are used in nuclear microreactors to remove fission power from the primary system and are coupled with power conversion systems or process heat applications. Modeling of the two-phase flow phenomena inside a heat pipe is essential to its design and safety analysis. In this study, a comprehensive one-dimensional two-phase three-field flow model has been developed for the analysis of heat pipes in normal operation conditions and transients. The conservation or field equations of mass, momentum, and energy were developed for the liquid film, vapor, and droplet. In addition, constitutive models or correlations were reviewed thoroughly and provided for the closure of the three-field equations. Specific constitutive equations regarding interfacial mass and heat transfer at two interfaces, namely film-gas interface and gas-droplet interface, were reviewed for droplet entrainment and deposition rates as well as film and droplet evaporation rates. Furthermore, mechanistic correlations of annular flow film thickness were recommended for the modeling of the thermosyphons without a wick as a critical constitutive correlation. Furthermore, experimental data needs from new experiments using a prototype working fluid or surrogate fluids for the model validation of high-temperature heat pipes in microreactors were recommended for future research.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

A novel conditional formulation of the Vlasov–Ampère equations: a conservative, positivity, asymptotic and Gauss law preserving scheme

We propose a novel reformulation of the Vlasov–Ampère equations for plasmas that reveals discrete symmetries that enables simultaneous conservation of mass, momentum and energy; preservation of Gauss’s law; positivity of the distribution function; and consistency with quasi-neutral asymptotics. The approach employs variable and coordinate transformations to yield a coupled system comprising a modified Vlasov equation and associated moment–field equations. The modified Vlasov equation advances a conditional distribution function that excludes mass, momentum and energy densities, which are instead evolved through moment equations enforcing the relevant symmetries, conservation laws and involution constraints. This reformulation aligns naturally with a recent slow-manifold reduction technique, which separates fast electron time scales and simplifies the treatment of the quasi-neutral limit within the reduced moment–field subsystem. Using this framework, we develop a numerical method for the reduced 1D1V subsystem that, for the first time in the literature, satisfies all key physical constraints while maintaining a quasi-neutral asymptotic behaviour. The advantages of the method are demonstrated on canonical electrostatic test problems, including the multiscale ion acoustic shock wave.

1D1V↗