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

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

BEYOND MIXING-LENGTH THEORY: A STEP TOWARD 321D

We examine the physical basis for algorithms to replace mixing-length theory (MLT) in stellar evolutionary computations. Our 321D procedure is based on numerical solutions of the Navier–Stokes equations. These implicit large eddy simulations (ILES) are three-dimensional (3D), time-dependent, and turbulent, including the Kolmogorov cascade. We use the Reynolds-averaged Navier–Stokes (RANS) formulation to make concise the 3D simulation data, and use the 3D simulations to give closure for the RANS equations. We further analyze this data set with a simple analytical model, which is non-local and time-dependent, and which contains both MLT and the Lorenz convective roll as particular subsets of solutions. A characteristic length (the damping length) again emerges in the simulations; it is determined by an observed balance between (1) the large-scale driving, and (2) small-scale damping. The nature of mixing and convective boundaries is analyzed, including dynamic, thermal and compositional effects, and compared to a simple model. We find that (1) braking regions (boundary layers in which mixing occurs) automatically appear beyond the edges of convection as defined by the Schwarzschild criterion, (2) dynamic (non-local) terms imply a non-zero turbulent kinetic energy flux (unlike MLT), (3) the effects of composition gradients on flow can be comparable to thermal effects, and (4) convective boundaries in neutrino-cooled stages differ in nature from those in photon-cooled stages (different Péclet numbers). The algorithms are based upon ILES solutions to the Navier–Stokes equations, so that, unlike MLT, they do not require any calibration to astronomical systems in order to predict stellar properties. Implications for solar abundances, helioseismology, asteroseismology, nucleosynthesis yields, supernova progenitors and core collapse are indicated.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Numerical methods for high-dimensional probability density function equations

In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker–Planck and Dostupov–Pugachev equations), random wave theory (Malakhov–Saichev equations) and coarse-grained stochastic systems (Mori–Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Pseudo-differential representation of the metaplectic transform and its application to fast algorithms

The metaplectic transform (MT), also known as the linear canonical transform, is a unitary integral mapping that is widely used in signal processing and can be viewed as a generalization of the Fourier transform. For a given function $ψ$ on an $N$-dimensional continuous space q , the MT of $ψ$ is parameterized by a rotation (or more generally, a linear symplectic transformation) of the 2$N$-dimensional phase space ( q,p ), where p is the wavevector space dual to q . In this study, we derive a pseudo-differential form of the MT. For small-angle rotations, or near-identity transformations of the phase space, it readily yields asymptotic differential representations of the MT, which are easy to compute numerically. Rotations by larger angles are implemented as successive applications of $K \gg 1$ small-angle MTs. The algorithm complexity scales as $O(KN^3N_p)$ where $N_p$ is the number of grid points. Here, we present a numerical implementation of this algorithm and discuss how to mitigate the associated numerical instabilities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Xyce TM Parallel Electronic Simulator: Users’ Guide, Version 5.3

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been designed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: ■ Capability to solve extremely large circuit problems by supporting large-scale parallel computing platforms (up to thousands of processors). Note that this includes support for most popular parallel and serial computers. ■ Improved performance for all numerical kernels (e.g., time integrator, nonlinear and linear solvers) through state-of-the-art algorithms and novel techniques. ■ Device models which are specifically tailored to meet Sandia’s needs, including some radiation-aware devices (for Sandia users only). ■ Object-oriented code design and implementation using modern coding practices that ensure that the Xyce Parallel Electronic Simulator will be maintainable and extensible far into the future. Xyce is a parallel code in the most general sense of the phrase - a message passing parallel implementation - which allows it to run efficiently on the widest possible number of computing platforms. These include serial, shared-memory and distributed-memory parallel as well as heterogeneous platforms. Careful attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows. The development of Xyce provides a platform for computational research and development aimed specifically at the needs of the Laboratory. With Xyce, Sandia has an “in-house” capability with which both new electrical (e.g., device model development) and algorithmic (e.g., faster time-integration methods, parallel solver algorithms) research and development can be performed. As a result, Xyce is a unique electrical simulation capability, designed to meet the unique needs of the laboratory

42 ENGINEERING↗
DOE OSTI2022

Critical points of the random cluster model with Newman–Ziff sampling

Here, we present a method for computing transition points of the random cluster model using a generalization of the Newman–Ziff algorithm, a celebrated technique in numerical percolation, to the random cluster model. The new method is straightforward to implement and works for real cluster weight q > 0. Furthermore, results for an arbitrary number of values of q can be found at once within a single simulation. Because the algorithm used to sweep through bond configurations is identical to that of Newman and Ziff, which was conceived for percolation, the method loses accuracy for large lattices when q > 1. However, by sampling the critical polynomial, accurate estimates of critical points in two dimensions can be found using relatively small lattice sizes, which we demonstrate here by computing critical points for non-integer values of q on the square lattice, to compare with the exact solution, and on the unsolved non-planar square matching lattice. The latter results would be much more difficult to obtain using other techniques.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

General Multifidelity Surrogate Models: Framework and Active-Learning Strategies for Efficient Rare Event Simulation

Estimating the probability of failure for complex real-world systems using high-fidelity computational models is often prohibitively expensive, especially when the probability is small. Exploiting low-fidelity models can make this process more feasible, but merging information from multiple low-fidelity and high-fidelity models poses several challenges. Here, this paper presents a robust multi-fidelity surrogate modeling strategy in which the multi-fidelity surrogate is assembled using an active learning strategy using an on-the-fly model adequacy assessment set within a subset simulation framework for efficient reliability analysis. The multi-fidelity surrogate is assembled by first applying a Gaussian process correction to each low-fidelity model and assigning a model probability based on the model's local predictive accuracy and cost. Three strategies are proposed to fuse these individual surrogates into an overall surrogate model based on model averaging and deterministic/stochastic model selection. The strategies also dictate which model evaluations are necessary. No assumptions are made about the relationships between low-fidelity models, while the high-fidelity model is assumed to be the most accurate and most computationally expensive model. Through two analytical and two numerical case studies, including a case study evaluating the failure probability of Tristructural isotropic-coated (TRISO) nuclear fuels, the algorithm is shown to be highly accurate while drastically reducing the number of high-fidelity model calls (and hence computational cost).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Self-consistent mean-field quantum approximate optimization

We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions between them in a mean-field manner. These interactions are captured by a common environment, constructed self-consistently through a variational quantum circuit, and which modifies the subproblems to account for mutual influence while maintaining computational independence. Consequently, subproblems can be solved individually, avoiding the computational cost of the full problem. We explore the properties of the generated environment and assess the algorithm's performance through extensive numerical simulations on Sherrington-Kirkpatrick spin glasses. Furthermore, we apply it experimentally to a weighted maximum clique problem applied to molecular docking. This framework enables the solution of problems that would otherwise exceed the qubit and gate counts of current quantum hardware.

Dupont, Maxime [Rigetti Computing] (ORCID:00000001↗
DOE OSTI2026

Self-consistent mean-field quantum approximate optimization

We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions between them in a mean-field manner. These interactions are captured by a common environment, constructed self-consistently through a variational quantum circuit, and which modifies the subproblems to account for mutual influence while maintaining computational independence. Consequently, subproblems can be solved individually, avoiding the computational cost of the full problem. We explore the properties of the generated environment and assess the algorithm's performance through extensive numerical simulations on Sherrington-Kirkpatrick spin glasses. Furthermore, we apply it experimentally to a weighted maximum clique problem applied to molecular docking. This framework enables the solution of problems that would otherwise exceed the qubit and gate counts of current quantum hardware.

Dupont, Maxime [Rigetti Computing] (ORCID:00000001↗
DOE OSTI2026

Self-consistent mean-field quantum approximate optimization

We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions between them in a mean-field manner. These interactions are captured by a common environment, constructed self-consistently through a variational quantum circuit, and which modifies the subproblems to account for mutual influence while maintaining computational independence. Consequently, subproblems can be solved individually, avoiding the computational cost of the full problem. We explore the properties of the generated environment and assess the algorithm's performance through extensive numerical simulations on Sherrington-Kirkpatrick spin glasses. Furthermore, we apply it experimentally to a weighted maximum clique problem applied to molecular docking. This framework enables the solution of problems that would otherwise exceed the qubit and gate counts of current quantum hardware.

Dupont, Maxime [Rigetti Computing] (ORCID:00000001↗
DOE OSTI2024

Small arms suppression project (LLNL final report)

US Special Operations Command (USSOCOM) was seeking a technological leap in small firearms weapon suppressor technology, because anticipated enemy capabilities are requiring the operators to have smaller detection cross sections to ensure the safe execution of missions. Suppressors have been developed almost exclusively through trial-and-error methods since the time of the original design by Hiram Maxim over one hundred years ago. Consequently USSOCOM deemed it prudent to perform a physicsbased study of weapon suppression to understand performance limits and possibly identify breakthrough technologies. Lawrence Livermore National Laboratory’s (LLNL’s) high performance production level computational tool called ALE3D (Arbitrary Lagrangian-Eulerian 3D and 2D) has unique physics models and numerical algorithms for modeling suppressor dynamics. The flexible and extendable code framework supports fully integrated hydrodynamics, heat transfer, solid and fluid dynamics, and chemistry that can be applied to simulating propellant-driven motion of a bullet down a gun barrel, the transfer of heat from the burning propellant to the barrel and suppressor, the chemistry of muzzle flash, and the shock/acoustic/optical signatures in the near-field. LLNL’s originally anticipated role was to augment ALE3D for this task, by developing the software and analysis methodologies specific to the simulation of blast and muzzle flash phenomena. It was believed that insights provided by our ALE3D simulations in tandem with a coordinated experimental component by our other team members from Oak Ridge National Laboratory (ORNL) and the U. S. Army Armament, Research, Development and Engineering Center (ARDEC), would have excellent prospects of yielding useful suppressor design improvements that could be transitioned to industry and utilized by US Special Operations Command. The three year effort has come to fruition with the development of revolutionary suppressor designs that far outperform any previous or current design by anyone outside this multi-lab team.

42 ENGINEERING↗
DOE OSTI2018

Numerical Method for Fractional Advection-Diffusion Equation with Heredity

We propose a method of construction of difference schemes for fractional partial differential equations with delay in time. For the fractional equation with two-sided diffusion, fractional transfer in time, and a functional aftereffect, we construct an implicit difference scheme. We use the shifted Grünwald–Letnikov formulas for the approximation of fractional derivatives with respect to spatial variables and the L1-algorithm for the approximation of fractional derivatives in time. Also we use piecewise constant interpolation and extrapolation by extending the discrete prehistory of the model in time. The algorithm is a fractional analog of a purely implicit method; on each time step, it is reduced to the solution of linear algebraic systems. We prove the stability of the method and find its order of convergence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Cost-efficient finite-volume high-order schemes for compressible magnetohydrodynamics

We present an efficient dimension-by-dimension finite-volume method which solves the adiabatic magnetohydrodynamics equations at high discretization order, using the constrained-transport approach on Cartesian grids. Results are presented up to tenth order of accuracy. The algorithmic architecture of this method is very close to that of commonly employed second-order schemes: it requires only one reconstructed value per face for each computational cell, independently of the scheme's order. This property is highly beneficial for the numerical efficiency. It results from reusing the required values already available in neighboring grid cells, in contrast to standard algorithms that require a number of reconstructions and evaluations which increases with the scheme's order of accuracy. At a given resolution, these high-order schemes present significantly less numerical dissipation than commonly employed lower-order approaches. Thus, results of comparable accuracy are achievable at a substantially coarser resolution, yielding overall performance gains. We also present a way to include physical dissipative terms: viscosity, magnetic diffusivity and cooling functions, respecting the finite-volume and constrained-transport frameworks. Benefits of this method are shown through applications in turbulent flows.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

MHD flow of a micropolar fluid over a stretchable disk in a porous medium with heat and mass transfer

This article studies the simultaneous impacts of heat and mass transfer of an incompressible electrically conducting micropolar fluid generated by the stretchable disk in presence of porous medium. The thermal radiation effect is accounted via Rosseland’s approximation. The governing boundary layer equations are reduced into dimensionless form by employing the suitable similarity transformations. A finite difference base algorithm is utilized to obtain the solution expressions. The impacts of physical parameters on dimensionless axial velocity, radial velocity, micro-rotation, temperature and concentrations profiles are presented and examined carefully. Numerical computation is performed to compute shear stress, couple stress, heat and mass rate at the disk.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Synchronous and Concurrent Multidomain Computing Method for Cloud Computing Platforms

We present a numerical method for synchronous and concurrent solution of transient elastodynamics problem where the computational domain is divided into subdomains that may reside on separate computational platforms. Here, this work employs the variational multiscale discontinuous Galerkin (VMDG) method to develop interdomain transmission conditions for transient problems. The fine-scale modeling concept leads to variationally consistent coupling terms at the common interfaces. The method admits a large class of time discretization schemes, and decoupling of the solution for each subdomain is achieved by selecting any explicit algorithm. Numerical tests with a manufactured solution problem show optimal convergence rates. The energy history in a free vibration problem is in agreement with that of the solution from a monolithic computational domain.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Vibrations of Elastic Shells of Revolution Partially Filled with Ideal Liquid

We propose an algorithm for the numerical analyses of vibrations of elastic shells of revolution partially filled with ideal incompressible liquids. In the solution of this problem, the wave motions of liquid on its free surface are taken into account. The solution of the problem of hydroelasticity is based on the application of the method of decomposition of the domain of integration of equations of the theory of shells with the use of the variational statement of the problem and on the approximate construction of the operator inverse to the operator of the hydrodynamic part of the problem. We construct a generalized functional of displacements of the shell for which the role of conditions of matching for the solutions in different subdomains is played by the natural boundary conditions. The obtained numerical results are compared with the existing exact solutions of the analyzed problem for a shell in the form of a straight circular cylinder.

42 ENGINEERING↗
DOE OSTI2016

Modeling of diatomic molecule using the Morse potential and the Verlet algorithm

Performing molecular modeling usually uses special software for Molecular Dynamics (MD) such as: GROMACS, NAMD, JMOL etc. Molecular dynamics is a computational method to calculate the time dependent behavior of a molecular system. In this work, MATLAB was used as numerical method for a simple modeling of some diatomic molecules: HCl, H{sub 2} and O{sub 2}. MATLAB is a matrix based numerical software, in order to do numerical analysis, all the functions and equations describing properties of atoms and molecules must be developed manually in MATLAB. In this work, a Morse potential was generated to describe the bond interaction between the two atoms. In order to analyze the simultaneous motion of molecules, the Verlet Algorithm derived from Newton’s Equations of Motion (classical mechanics) was operated. Both the Morse potential and the Verlet algorithm were integrated using MATLAB to derive physical properties and the trajectory of the molecules. The data computed by MATLAB is always in the form of a matrix. To visualize it, Visualized Molecular Dynamics (VMD) was performed. Such method is useful for development and testing some types of interaction on a molecular scale. Besides, this can be very helpful for describing some basic principles of molecular interaction for educational purposes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Analytic reconstruction algorithms for triple-source CT with horizontal data truncation

Purpose: This paper explores a triple-source imaging method with horizontal data truncation to enlarge the field of view (FOV) for big objects. Methods: The study is conducted by using theoretical analysis, mathematical deduction, and numerical simulations. The proposed algorithms are implemented in c + + and MATLAB. While the basic platform is constructed in MATLAB, the computationally intensive segments are coded in c + +, which are linked via a MEX interface. Results: A triple-source circular scanning configuration with horizontal data truncation is developed, where three pairs of x-ray sources and detectors are unevenly distributed on the same circle to cover the whole imaging object. For this triple-source configuration, a fan-beam filtered backprojection-type algorithm is derived for truncated full-scan projections without data rebinning. The algorithm is also extended for horizontally truncated half-scan projections and cone-beam projections in a Feldkamp-type framework. Using their method, the FOV is enlarged twofold to threefold to scan bigger objects with high speed and quality. The numerical simulation results confirm the correctness and effectiveness of the developed algorithms. Conclusions: The triple-source scanning configuration with horizontal data truncation cannot only keep most of the advantages of a traditional multisource system but also cover a larger FOV for big imaging objects. In addition, because the filtering is shift-invariant, the proposed algorithms are very fast and easily parallelized on graphic processing units.

60 APPLIED LIFE SCIENCES↗