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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 973 records · Page 54

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NASA NTRS1979

An implicit factored scheme for the compressible Navier-Stokes equations. II - The numerical ODE connection

An attempt is made to establish a connection between linear multistep methods for applications to ordinary differential equations and their extension (by approximate factorization) to alternating direction implicit methods for partial differential equations. An earlier implicit factored scheme for the compressible Navier-Stokes equations is generalized by innovations that (1) increase the class of temporal difference schemes to include all linear multistep methods, (2) optimize the class of unconditionally stable factored schemes by a new choice of unknown variable, and (3) improve the computational efficiency by the introduction of quasi-one-leg methods.

Beam, R. M.↗

NASA NTRS1978

The velocity dispersion in Saturn's rings

The collisional dynamics of a differentially rotating disk of particles are considered. The investigation is to some extent an analytic counterpart of the numerical studies of Brahic (1977). Following Brahic, it is assumed that the particles are identical, indestructible, imperfectly elastic, smooth spheres. Gravitational interactions between the particles are neglected. The main result of the reported analysis is the derivation of the relation between the coefficient of restitution and the optical depth for a differentially rotating disk of identical, inelastic, smooth spheres. Questions concerning the applicability of the obtained results to Saturn's rings are studied. It is felt that the calculations should give accurate quantitative results if the rings' filling factor is small. If this assumption is not justified, the calculations should be at least qualitatively correct.

Goldreich, P.↗

NASA NTRS1977

TOMCAT - A code for numerical generation of boundary-fitted curvilinear coordinate systems on fields containing any number of arbitrary two-dimensional bodies

A method for automatic generation of boundary-fitted curvilinear coordinate systems, where the transformed coordinates are solutions of an elliptic differential system in the physical plane, and where the coordinate lines are coincident with all boundaries of a general multiply-connected, two-dimensional region containing any number of arbitrarily shaped bodies, and is described along with a suitable computer code for implementing the method. Any partial differential system can be solved on the boundary-fitted coordinate system by appropriate transformations. The transformed equations are approximated by finite differences and solved numerically in the transformed plane. All computations, whether for generating coordinate system or then solving the transformed equations, can be done on a rectangular field with square mesh with no interpolation required on the boundaries. The physical boundaries may even be time-dependent.

Thompson, J. F.↗

NASA NTRS1981

Stability analysis of numerical boundary conditions and implicit difference approximations for hyperbolic equations

Implicit, noniterative, finite difference schemes were recently developed by several authors for multidimensional systems of nonlinear hyperbolic partial differential equations. When applied to linear model equations with periodic boundary conditions those schemes are unconditionally stable (A-stable). As applied in practice the algorithms often face a severe time step restriction. A major source of the difficulty is the treatment of the numerical boundary conditions. One conjecture was that unconditional stability requires implicit numerical boundary conditions. An apparent counter example was the space time extrapolation considered by Gustafsson, Kreiss, and Sunstrom. Spatial (implicit) and space time (explicit) extrapolation using normal mode analysis for a finite and infinite number of spatial mesh intervals are examined. The results indicate that for unconditional stability with a finite number of spatial mesh intervals, the numerical boundary conditions must be implicit.

Beam, R. M.↗

DOE OSTI2023

An Efficient Three-Dimensional CFD-Based Numerical Wave Tank for a Wave Energy Converter in Extreme Irregular Waves: Preprint

A numerical wave tank approach for computational fluid dynamics (CFD) modelling of an extreme irregular seastate is presented. The technique couples a potential flow solution with a CFD solver for more efficient numerical predictions. This method has recently become attractive both for the research community and the industry working with offshore structures. The model is used to determine the response of a submerged pressure differential wave energy converter (WEC) in a fully nonlinear irregular wave condition using the high fidelity CFD code, STAR-CCM+. Potential flow based numerical models are commonly used to predict motions and performance of wave energy converters. Wave kinematics can deviate from potential flow predictions for extreme wave conditions; the excitation loads on an absorber can also be increasingly influenced by viscous effects, not captured in engineering level models. In these extreme conditions, a Reynolds-averaged Navier-Stokes CFD model can better predict motions and loads for a WEC. Long time series with varying random seed numbers can be used to identify singular extreme wave events from a stochastic irregular sea state. This approach simulates a more realistic wave series for a given sea state than a regular wave or a focused wave. However, it is computationally infeasible to run these long time series for three-dimensional (3D) CFD simulations. In this work, two-dimensional (2D) CFD simulations with a long domain allow the full development of an extreme nonlinear wave condition. The results are used to identify extreme events from a 50-year storm condition for the PacWave site off the coast of Oregon. A relatively short time window including this extreme event is then mapped to a 3D simulation using a user defined wave methodology. Convergence studies for domain length, wave forcing lengths, and time before the extreme event were conducted.

cfd↗

NASA NTRS2021

An evolutionary system of mineralogy, Part IV: Planetesimal differentiation and impact mineralization (4566 to 4560 Ma)

The fourth installment of the evolutionary system of mineralogy considers two stages of planetesimal mineralogy that occurred early in the history of the solar nebula, commencing by 4.566 Ga and lasting for at least 5 million years: (1) primary igneous minerals derived from planetesimal melting and differentiation into core, mantle, and basaltic components and (2) impact mineralization resulting in shock-induced deformation, brecciation, melting, and high-pressure phase transformations. We tabulate 90 igneous differentiated asteroidal minerals, including the earliest known occurrences of minerals with Ba, Cl, Cu, F, and V as essential elements, as well as the first appearances of numerous phosphates, quartz, zircon, and amphibole group minerals. We also record 40 minerals formed through high-pressure impact alteration, commencing with the period of asteroid accretion and differentiation. These stages of mineral evolution thus mark the first time that high pressures, both static and dynamic, played a significant role in mineral paragenesis.

Shaunna M. Morrison↗

DOE OSTI2022

Collision of localized shocks in AdS 5 as a series expansion in transverse gradients

We introduce a computational framework to more efficiently calculate the collision of localized shocks in five dimensional asymptotically Anti-de Sitter space. We expand the Einstein equations in transverse gradients and find that our numerical results agree well with exact solutions already at first order in the expansion. Moreover, the Einstein equations at first order in transverse gradients can be decoupled into two sets of differential equations. Here, the bulk fields of one of these sets has only a negligible contribution to boundary observables, such that the computation on each time slice can be simplified to the solution of several planar shockwave equations plus four further differential equations for each transverse plane ‘pixel’. At the cost of errors of ≲ 10% at the hydrodynamization time and for low to mid rapidities, useful numerical solutions can be sped up by roughly one order of magnitude.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Self-Consistent Relativistic Electron Scattering using the Sherlock Scattering Model for X-ray Diagnostics

We present on a new, self-consistent, arbitrary-temperature Romberg integration scheme for modeling electron scattering in materials in a LANL Lagrangian Shock Hydro (LSH) code. Electron beam-target interactions are fundamental to a wide range of scientific and technological applications. When high-energy electron beams hit their target, they may scatter, deposit energy, or ionize the source. These processes govern the behavior and outcomes in nanotechnology manufacturing, electron microscopy, and modern X-ray diagnostics. Simulating these interactions is essential for interpreting experimental results, predicting material responses, and designing efficient tools and experiments. At Los Alamos, this is done using a LSH code, which is a multi-dimension, multi-material, massively parallel, multi-physics code used to simulate applications from asteroid impacts to electron beam interactions. By effectively and efficiently modeling the way that electrons scatter from the beam we can bolster these simulations and more accurately predict experimental outcomes. The model currently implemented in the LSH of interest is based on work by Papp and does not self-consistently preserve momentum in the slightly relativistic regime; here we adopt a model proposed by Braams and Karney and implement a Romberg integration scheme to compute the diffusion tensor. In this paper we will provide background on the Braams-Karney diffusion tensor as well as the Romberg integration scheme we employed to numerically solve for it. We will show that our integration scheme is accurate in solving for the set of scalar potentials used to re-express the diffusion tensor in differential form, and in solving for the diffusion coefficients in the larger LSH code. By using this diffusion tensor rather than the existing Papp one, and numerically integrating it with a Romberg method, we produce much more accurate, self-consistent results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1992

On an origin of numerical diffusion: Violation of invariance under space-time inversion

The invariant properties of the convection equation du/dt + adu/dx = 0 (where d is the partial differential operator) with respect to spatial reflection, time reversal, and space-time inversion are studied. Generally, a finite-difference analog of this equation may possess some or none of these properties. It is shown that, under certain conditions, the von Neumann amplification factor of an analog satisfies a special relation for each invariant property this analog possesses. Particularly, an analog is neutrally stable and thus free of numerical diffusion if it possesses the invariant property related to space-time inversion. It is also explained why generally (1) an upwind scheme possesses neither the invariant property related to spatial reflection nor that related to space-time inversion, and (2) an explicit scheme possesses neither the invariant property related to time reversal nor that related to space-time inversion. Extension to the viscous case and a remarkable connection between the current work and a new numerical framework for solving conservation laws are also discussed.

Chang, Sin-Chung↗

DOE OSTI2026

Narrow operator models of stellarator equilibria in Fourier Zernike basis

Numerical computation of the ideal magnetohydrodynamic (MHD) equilibrium magnetic field is at the base of stellarator optimisation and provides the starting point for solving more sophisticated partial differential equations like transport or turbulence models. Conventional approaches solve for a single stationary point of the ideal MHD equations, which is fully defined by three invariants and the numerical scheme employed by the solver. We present the first numerical approach that can solve for a continuous distribution of equilibria with fixed boundary and rotational transform, varying only the pressure invariant. This approach minimises the force residual by optimising parameters of multilayer perceptrons that map from a scalar pressure multiplier to the Fourier Zernike basis as implemented in the modern stellarator equilibrium solver DESC.

fusion plasma↗

DOE OSTI2020

Weak neutral current axial form factor using $ \left(\overline{\nu}\right)\nu $-nucleon scattering and lattice QCD inputs

We present a determination of the neutral current weak axial charge $G$ $^{Z}_{A}$(0) = –0.654(3) stat (5) sys using the strange quark axial charge $G$ $^{s}_{A}$(0) calculated with lattice QCD. We then perform a phenomenological analysis, where we combine the strange quark electromagnetic form factor from lattice QCD with (anti)neutrino-nucleon scattering differential cross section from MiniBooNE experiments in a momentum transfer region 0.24 ≲ Q 2 ≲ 0.71 GeV 2 to determine the neutral current weak axial form factor $G$ $^{Z}_{A}$(Q 2 ) in the range of 0 ≲ Q 2 ≤ 1 GeV 2 . This yields a phenomenological value of $G$ $^{Z}_{A}$(0) = –0.687(89)stat(40)sys. The value of $G$ $^{Z}_{A}$(0) constrained by the lattice QCD calculation of $G$ $^{s}_{A}$(0), when compared to its phenomenological determination, provides a significant improvement in precision and accuracy and can be used to provide a constraint on the fit to $G$ $^{Z}_{A}$(Q 2 ) for Q 2 > 0. This constrained fit leads to an unambiguous determination of (anti)neutrino-nucleon neutral current elastic scattering differential cross section near Q 2 = 0 and can play an important role in numerically isolating nuclear effects in this region. We show a consistent description of $G$ $^{Z}_{A}$(Q 2 ) obtained from the (anti)neutrino-nucleon scattering cross section data requires a nonzero contribution of the strange quark electromagnetic form factor. We demonstrate the robustness of our analysis by providing a post-diction of the BNL E734 experimental data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Refining the GENEVA method for Higgs boson production via gluon fusion

We describe a number of improvements to the Geneva method for matching NNLO calculations to parton shower programs. In particular, we detail changes to the resummed calculation used in the matching procedure, including disentangling the cross section dependence on factorisation and beam scales, and an improved treatment of timelike logarithms. We also discuss modifications in the implementation of the splitting functions which serve to make the resummed calculation differential in the higher multiplicity phase space. These changes improve the stability of the numerical cancellation of the nonsingular term at small values of the resolution parameter. As a case study, we consider the gluon-initiated Higgs boson production process gg → H. We validate the NNLO accuracy of our predictions against independent calculations, and compare our showered and hadronised results with recent data taken at the ATLAS and CMS experiments in the diphoton decay channel, finding good agreement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Block triangular preconditioning for stochastic Galerkin method

Here, in this paper, we develop a new block triangular preconditioner for solving partial differential equations with random coefficients. We prove spectral bounds for the preconditioned system. Several numerical examples are provided to demonstrate the efficiency of this preconditioner, especially for stochastic problems with large variance.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Data-driven selection of stiff chemistry ODE solver in operator-splitting schemes

Most computational fluid dynamics simulations of practical combustion applications employ operator-splitting schemes, where chemistry and transport are separated and integrated with distinct numerical methods. The changes in composition due to chemistry are evaluated by solving ordinary differential equations (ODE) in each cell of the computational domain, which typically dominates the computational cost when detailed chemistry is considered. In this work, a data-driven approach for the selection of chemistry ODE solvers in operator-splitting schemes is presented. Neural networks are used to predict the ODE solvers CPU times and errors for a given thermochemical state. This allows the selection of an optimal ODE solver on a cell-by-cell, timestep-by-timestep basis. The models are trained using a wide set of thermochemical states generated through partially-stirred reactors and flames simulations. The methodology is validated by quantifying the prediction errors, the classification accuracy, and the computational speedup. The model predicts the optimal ODE solver for 70 to 95% of the validation cases and decreases the computional cost by a factor of 3 or more. The generalizability of the methodology to different chemical mechanisms and different fuels is assessed and it is shown that the model’s performance is only slightly degraded and its applicability is significantly enhanced if the inputs to the neural networks are restricted to a small set of thermochemical state variables present in most chemical mechanisms. In conclusion, the models are used in an homogeneous reactor case and a multi-dimensional CFD simulation of a diesel spray at high pressure where a speedup of more than 3 is achieved.

42 ENGINEERING↗

DOE OSTI2020

Mesoscopic structure of mixed type domain walls in multiaxial ferroelectrics

The structure of a 180° uncharged rotational domain wall in a multiaxial ferroelectric film is studied in the framework of an analytical Landau-Ginzburg-Devonshire (LGD) approach. Finite element modeling (FEM) is used to solve numerically the system of the coupled nonlinear Euler-Lagrange (EL) second-order differential equations for two components of polarization. We show that the structure of the domain wall and corresponding metastable or stable phase of the film are controlled by a single parameter—the dimensionless ferroelectric anisotropy factor μ. We fitted the static profile of a solitary domain wall, calculated by FEM, with kinklike functions for polarization components, and extracted the five μ-dependent parameters from the fitting to FEM curves. The surprisingly high accuracy of the fitting results for two polarization components in the entire μ range allows us to conclude that the analytical functions, which are trial functions in the direct variational method, can be treated as a high-accuracy variational solution of the static EL equations. We further derive exact two-component analytical solutions of the static EL equations for a polydomain 180° domain structure in a multiaxial ferroelectric film. Using these, we derive analytical expressions for the system free energy and analyze its dependence on the film thickness and boundary conditions at the film surfaces. The single-domain state is ground for zero polarization derivative at the surfaces, while the polydomain states minimize the system energy for zero polarization at the surfaces. Counterintuitively, the energy of the polydomain states split into two levels, “0” and “1,” for zero polarization at the surfaces, and each of the levels contains a large number of close-energy sublevels, whose structure is characterized by a different number and type of domain walls. The analytical solutions can become a useful tool for Bayesian analysis of high-resolution scanning transmission electron microscopy images in ferroelectric films.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Electromagnetic Transient Simulation Algorithms for Evaluation of Large-Scale Extreme Fast Charging Systems (Distribution Grid Models)

The distribution and transmission grids are observing an increased penetration of power electronics in loads and generations. For example, there is increasing interest in integrating in extreme fast charging (XFC) systems for fast charging of electrical vehicles. As these systems are integrated, developing high-fidelity electromagnetic transient model of XFC systems in distribution grids and evaluating their interactions with the power grid would be of significant interest. This model will be utilized for design of XFC systems, to identify upgrades in distribution and/or transmission grids, for planning purposes by transmission planners or operators or owners, among others. It can also be utilized in operations for improved reliable performance of the grid and/or XFC station. The challenge with simulating these models is the high computational complexity introduced by the large number of states present in the system and the time-step needed to simulate the system. In this paper, advanced simulations algorithms are applied to reduce the computational complexity of simulating large-scale XFC systems. The algorithms include numerical stiffness-based segregation, time constant-based segregation, clustering and aggregation on differential algebraic equations (DAEs), and multi-order integration approaches. While the first three algorithms split the matrix that needs to be inverted from a large matrix to much smaller matrices, the final algorithm reduces the computational burden of applying higher-order integration approaches in the complete system. The comparison made in the previous sentence is with respect to use of homogeneous integration approaches used in conventional electromagnetic transient simulators like power systems computer aided design (PSCAD). The approaches mentioned here have resulted in speed-up of 36x in the simulation of a single distribution system with 15 XFCs.

Debnath, Suman↗

DOE OSTI2022

Electromagnetic Transient (EMT) Simulation Algorithms for Evaluation of Large-Scale Extreme Fast Charging Systems (T&D Models)

Simulation of high-fidelity models of extreme fast charging (XFC) systems and large-area power grids with many XFCs can be time consuming in traditional simulators. Traditional simulators use a single method of discretization for all the components that results in imposing a large computational burden of inverting a large matrix as well as increased computations related to single method of discretization (that is typically a trapezoidal method). To overcome the problem of simulating large-area power grids with many XFCs, in this paper, advanced numerical simulation algorithms are applied for the first time together to reduce the dimension of matrix inversion. Here, the algorithms include numerical stiffness-based segregation, time constant-based segregation, clustering and aggregation on differential algebraic equations (DAEs), and multi-order integration approaches. These algorithms apply multiple discretization algorithms rather than a single discretization algorithm that further reduces the computational burden. The approaches mentioned here have resulted in speed-up of up to 18x in the simulation of a single distribution system with 15 XFCs and of up to 271x in the simulation of a transmission-distribution system with 300 XFCs in multiple distribution feeders with respect to conventional simulators (like power systems computer aided design [PSCAD]).

42 ENGINEERING↗

DOE OSTI2024

Leveraging Multitime Hamilton–Jacobi PDEs for Certain Scientific Machine Learning Problems

Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional quantity, HJ PDEs can be extended to the multi-time case. In this paper, we establish a novel theoretical connection between specific optimization problems arising in machine learning and the multi-time Hopf formula, which corresponds to a representation of the solution to certain multi-time HJ PDEs. Through this connection, we increase the interpretability of the training process of certain machine learning applications by showing that when we solve these learning problems, we also solve a multi-time HJ PDE and, by extension, its corresponding optimal control problem. As a first exploration of this connection, we develop the relation between the regularized linear regression problem and the Linear Quadratic Regulator (LQR). We then leverage our theoretical connection to adapt standard LQR solvers (namely, those based on the Riccati ordinary differential equations) to design new training approaches for machine learning. Lastly, we provide some numerical examples that demonstrate the versatility and possible computational advantages of our Riccati-based approach in the context of continual learning, post-training calibration, transfer learning, and sparse dynamics identification.

97 MATHEMATICS AND COMPUTING↗