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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 OSTI2019

Calculating the Symmetry Number of Flexible Sphere Clusters

We present a theoretical and computational framework to compute the symmetry number of a flexible sphere cluster in R 3 , using a definition of symmetry that arises naturally when calculating the equilibrium probability of a cluster of spheres in the sticky-sphere limit. We define the sticky symmetry group of the cluster as the set of permutations and inversions of the spheres which preserve adjacency and can be realized by continuous deformations of the cluster that do not change the set of contacts or cause particles to overlap. The symmetry number is the size of the sticky symmetry group. We introduce a numerical algorithm to compute the sticky symmetry group and symmetry number, and show it works well on several test cases. Furthermore, we show that once the sticky symmetry group has been calculated for indistinguishable spheres, the symmetry group for partially distinguishable spheres (those with nonidentical interactions) can be efficiently obtained without repeating the laborious parts of the computations. Finally, we use our algorithm to calculate the partition functions of every possible connected cluster of six identical sticky spheres, generating data that may be used to design interactions between spheres so they self-assemble into a desired structure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Multiscale geometric modeling of macromolecules I: Cartesian representation

This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the polarized curvature, for the prediction of protein binding sites.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1971

The application of generalized, cyclic, and modified numerical integration algorithms to problems of satellite orbit computation

Generalized, cyclic, and modified multistep numerical integration methods are developed and evaluated for application to problems of satellite orbit computation. Generalized methods are compared with the presently utilized Cowell methods; new cyclic methods are developed for special second-order differential equations; and several modified methods are developed and applied to orbit computation problems. Special computer programs were written to generate coefficients for these methods, and subroutines were written which allow use of these methods with NASA's GEOSTAR computer program.

Chesler, L.↗
NASA NTRS2004

Fourth Computational Aeroacoustics (CAA) Workshop on Benchmark Problems

This publication contains the proceedings of the Fourth Computational Aeroacoustics (CAA) Workshop on Benchmark Problems. In this workshop, as in previous workshops, the problems were devised to gauge the technological advancement of computational techniques to calculate all aspects of sound generation and propagation in air directly from the fundamental governing equations. A variety of benchmark problems have been previously solved ranging from simple geometries with idealized acoustic conditions to test the accuracy and effectiveness of computational algorithms and numerical boundary conditions; to sound radiation from a duct; to gust interaction with a cascade of airfoils; to the sound generated by a separating, turbulent viscous flow. By solving these and similar problems, workshop participants have shown the technical progress from the basic challenges to accurate CAA calculations to the solution of CAA problems of increasing complexity and difficulty. The fourth CAA workshop emphasized the application of CAA methods to the solution of realistic problems. The workshop was held at the Ohio Aerospace Institute in Cleveland, Ohio, on October 20 to 22, 2003. At that time, workshop participants presented their solutions to problems in one or more of five categories. Their solutions are presented in this proceedings along with the comparisons of their solutions to the benchmark solutions or experimental data. The five categories for the benchmark problems were as follows: Category 1:Basic Methods. The numerical computation of sound is affected by, among other issues, the choice of grid used and by the boundary conditions. Category 2:Complex Geometry. The ability to compute the sound in the presence of complex geometric surfaces is important in practical applications of CAA. Category 3:Sound Generation by Interacting With a Gust. The practical application of CAA for computing noise generated by turbomachinery involves the modeling of the noise source mechanism as a vortical gust interacting with an airfoil. Category 4:Sound Transmission and Radiation. Category 5:Sound Generation in Viscous Problems. Sound is generated under certain conditions by a viscous flow as the flow passes an object or a cavity.

Dahl, Milo D.↗
DOE OSTI2015

Numerical estimation of phase transformations in solid state during Yb:YAG laser heating of steel sheets

This work concerns the numerical modeling of heat transfer and phase transformations in solid state occurring during the Yb:YAG laser beam heating process. The temperature field is obtained by the numerical solution into transient heat transfer equation with convective term. The laser beam heat source model is developed using the Kriging interpolation method with experimental measurements of Yb:YAG laser beam profile taken into account. Phase transformations are calculated on the basis of Johnson - Mehl - Avrami (JMA) and Koistinen - Marburger (KM) kinetics models as well as continuous heating transformation (CHT) and continuous cooling transformation (CCT) diagrams for S355 steel. On the basis of developed numerical algorithms 3D computer simulations are performed in order to predict temperature history and phase transformations in Yb:YAG laser heating process.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Universal Tripartite Entanglement in One-Dimensional Many-Body Systems

Motivated by conjectures in holography relating the entanglement of purification and reflected entropy to the entanglement wedge cross section, we introduce two related non-negative measures of tripartite entanglement g and h. We prove structure theorems which show that states with nonzero g or h have nontrivial tripartite entanglement. We then establish that in one dimension these tripartite entanglement measures are universal quantities that depend only on the emergent low-energy theory. For a gapped system, we argue that either g≠0 and h=0 or g=h=0, depending on whether the ground state has long-range order. For a critical system, we develop a numerical algorithm for computing g and h from a lattice model. We compute g and h for various CFTs and show that h depends only on the central charge whereas g depends on the whole operator content.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

thornado+FLASH-X: A Hybrid Discontinuous Galerkin–Implicit-explicit and Finite-volume Framework for Neutrino-radiation Hydrodynamics in Core-collapse Supernovae

We present neutrino-transport algorithms implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado) and their coupling to self-gravitating hydrodynamics within the adaptive mesh refinement–based multiphysics simulation framework FLASH-X. thornado, developed primarily for simulations of core-collapse supernovae (CCSNe), employs a spectral, six-species two-moment formulation with algebraic closure and special-relativistic observer corrections accurate to $\mathcal{O}(v/c)$, and uses discontinuous Galerkin (DG) methods for phase-space discretization combined with implicit-explicit time stepping. A key development is a nonlinear neutrino–matter coupling algorithm based on nested fixed-point iteration with Anderson acceleration, enabling fully implicit treatment of collisional processes, including energy-coupling interactions such as neutrino–electron scattering and pair production. Coupling to finite-volume (FV) hydrodynamics is achieved through a hybrid DG-FV representation of the fluid variables and operator-split evolution within FLASH-X. The implementation is verified using basic transport tests with idealized opacities and relaxation and deleptonization problems with tabulated microphysics. Spherically symmetric CCSN simulations demonstrate accuracy and robustness of the coupled scheme, including close agreement with the CCSN simulation code Chimera. An axisymmetric CCSN simulation further demonstrates the viability of DG-based neutrino transport for multidimensional supernova modeling within FLASH-X. thornado’s neutrino-transport solver is GPU-enabled using OpenMP offloading or OpenACC, and all CCSN applications included in this work use the GPU implementation. Together, these results establish a foundation for future enhancements in physics fidelity, numerical algorithms, and computational performance, for increasingly realistic large-scale CCSN simulations.

Endeve, Eirik [Oak Ridge National Laboratory (ORNL↗
NASA NTRS1984

Design of an optimal output feedback control system with modal insensitivity

This paper deals with the design of an output feedback controller which results in selected modal insensitivity, and at the same time optimizes a quadratic performance index representative of desired system performance for nominal plant parameter values. The approach taken here is to characterize the class of attainable eigenvectors for a given set of eigenvalues (distinct or non-distinct) which lie in a subspace called the 'Modal Insensitivity Subspace'. A constraint is established on the feedback matrix which results in modal insensitivity. Necessary conditions for optimality subject to the constraint on the feedback matrix are given. This forms the basis for a numerical algorithm to compute the optimal feedback gain which analyzed for convergence. To illustrate the procedure, a design is carried out using the lateral dynamics of an L-1011 aircraft.

Raman, K. V.↗
NASA NTRS1984

Modal insensitivity with optimality

This paper deals with the design of a constant gain, feedback controller which results in selected modal insensitivity, and at the same time optimizes a quadratic performance index representative of desired system performance for nominal plant parameter values. Both full state and output feedback control are considered. A constraint is established for the feedback gain matrix that results in modal insensitivity, and necessary conditions for optimality subject to this constraint are given. This forms the basis for a numerical algorithm to compute the optimal feedback gain. To illustrate the procedure, a design is carried out using the lateral dynamics of an L-1011 aircraft.

Calise, A. J.↗
NASA NTRS1985

Low-velocity impact response of laminated beams subjected to initial stresses

Finite element procedures are used in conjunction with a numerical algorithm to compute the impact response of a graphite-epoxy laminated beam subjected to tensile initial stresses. The effect of initial stresses on the contact duration, impact force, coefficient of restitution, and bending and shear stresses are discussed. The analytically computed contact force history and strain response are compared with some experimental results.

Sankar, B. V.↗
NASA NTRS1991

Turbulence modeling in aerodynamic shear flows - Status and problems

This paper briefly summarizes the status and problems of turbulence modeling for aerodynamical applications. For complex flows the 'approach of choice' is (increasingly) full second-order (Reynolds stress equation) closure. These closures have not yet developed to anywhere near their full potential, significant further research is required especially regarding length-scale equations, representation of pressure-strain correlations, and wall region treatments. Recent developments in computer capability, algorithms, numerical simulations, theory and quantitative flow visualization should assist in and hasten this research. Several problem areas such as shock interaction and discrete dynamic instabilities of turbulent flows may require mega-to-large eddy simulation or theoretical adjuncts.

Bushnell, D. M.↗
NASA NTRS1992

Development of new flux splitting schemes

Maximizing both accuracy and efficiency has been the primary objective in designing a numerical algorithm for computational fluid dynamics (CFD). This is especially important for solutions of complex three dimensional systems of Navier-Stokes equations which often include turbulence modeling and chemistry effects. Recently, upwind schemes have been well received for their capability in resolving discontinuities. With this in mind, presented are two new flux splitting techniques for upwind differencing. The first method is based on High-Order Polynomial Expansions (HOPE) of the mass flux vector. The second new flux splitting is based on the Advection Upwind Splitting Method (AUSM). The calculation of the hypersonic conical flow demonstrates the accuracy of the splitting in resolving the flow in the presence of strong gradients. A second series of tests involving the two dimensional inviscid flow over a NACA 0012 airfoil demonstrates the ability of the AUSM to resolve the shock discontinuity at transonic speed. A third case calculates a series of supersonic flows over a circular cylinder. Finally, the fourth case deals with tests of a two dimensional shock wave/boundary layer interaction.

Liou, Meng-Sing↗
DOE OSTI2013

Higher order treatment on temporal derivative of angular flux for time-dependent MOC

A new kinetic analysis method, whose angular dependence of temporal derivative for angular flux is accurately treated within practical memory requirement, is proposed. The method of characteristics (MOC) is being widely used for reactor analysis thanks to the advances of numerical algorithms and computer hardware. However, the computational resources, i.e., the memory capacity, can be still a crucial problem for rigorous kinetic calculations using MOC. In the straightforward approach for kinetic calculation using MOC, the segment-averaged angular fluxes should be stored on the memory in order to explicitly calculate the temporal derivative of the angular flux, which would require huge memory. Thus, in the conventional kinetic calculation code using MOC, the temporal derivative of the angular flux has been approximated as angularly isotropic in order to reduce the memory requirement (isotropic assumption). However, the approximation error caused by the conventional isotropic assumption has not been thoroughly and quantitatively investigated so far and an accurate kinetic calculation method, which can quantitatively estimate the above approximation error within practical memory storage, has not been developed. The present study tries to address this issue with a newly developed approach. Effect of the approximate treatment for the temporal derivative of angular flux is evaluated through benchmark calculations. (authors)

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Advances and trends in computational structures technology

The major goals of computational structures technology (CST) are outlined, and recent advances in CST are examined. These include computational material modeling, stochastic-based modeling, computational methods for articulated structural dynamics, strategies and numerical algorithms for new computing systems, multidisciplinary analysis and optimization. The role of CST in the future development of structures technology and the multidisciplinary design of future flight vehicles is addressed, and the future directions of CST research in the prediction of failures of structural components, the solution of large-scale structural problems, and quality assessment and control of numerical simulations are discussed.

Noor, A. K.↗
NASA NTRS1990

An efficient numerical integral in three-dimensional electromagnetic field computations

An improved algorithm for efficiently computing a sinusoid and an exponential integral commonly encountered in method-of-moments solutions is presented. The new algorithm has been tested for accuracy and computer execution time against both numerical integration and other existing numerical algorithms, and has outperformed them. Typical execution time comparisons on several computers are given.

Whetten, Frank L.↗
DOE OSTI2023

Dyson maps and unitary evolution for Maxwell equations in tensor dielectric media

The propagation and scattering of electromagnetic waves in dielectric media is of theoretical and experimental interest in a wide variety of fields. An understanding of observational results generally requires a numerical solution of Maxwell equations—usually implemented on conventional computers using sophisticated numerical algorithms. In recent years, advances in quantum information science and in the development of quantum computers have piqued curiosity about taking advantage of these resources for an alternate numerical approach to Maxwell equations. This requires a reformulation of the classical Maxwell equations into a form suitable for quantum computers which, unlike conventional computers, are limited to unitary operations. In this paper, a unitary framework is developed for the propagation of electromagnetic waves in a spatially inhomogeneous, passive, nondispersive, and anisotropic dielectric medium. For such a medium, generally, the evolution operator in the combined Faraday-Ampere equations is not unitary. There are two steps needed to convert this equation into a unitary evolution equation. In the first step, a weighted Hilbert space is formulated in which the generator of dynamics is a pseudo-Hermitian operator. In the second step, a Dyson map is constructed which maps the weighted-physical-Hilbert space to the original Hilbert space. Furthermore, the resulting evolution equation for the electromagnetic wave fields is unitary. Utilizing the framework developed in these steps, a unitary evolution equation is derived for electromagnetic wave propagation in a uniaxial dielectric medium. The resulting form is suitable for quantum computing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

ZFP: A compressed array representation for numerical computations

HPC trends favor algorithms and implementations that reduce data motion relative to FLOPS. We investigate the use of lossy compressed data arrays in place of traditional IEEE floating point arrays to store the primary data of calculations. Simulation is fundamentally an exercise in controlled approximation, and error introduced by finite-precision arithmetic (or lossy compression) is just one of several sources of error that need to be managed to ensure sufficient accuracy in a computed result. We describe ZFP, a compressed numerical format designed for in-memory storage of multidimensional arrays, and summarize theoretical results that demonstrate that the error of repeated lossy compression can be bounded and controlled. Furthermore, we establish a relationship between grid resolution and compression-induced errors and show that, contrary to conventional floating point, ZFP reduces finite-difference errors with finer grids. We present example calculations that demonstrate data reduction by 4x or more with negligible impact on solution accuracy. Our results further demonstrate several orders-of-magnitude increase in accuracy using ZFP over IEEE floating point and Posits for the same storage budget.

Lindstrom, Peter↗
NASA NTRS2000

Experience with a Genetic Algorithm Implemented on a Multiprocessor Computer

Numerical experiments were conducted to find out the extent to which a Genetic Algorithm (GA) may benefit from a multiprocessor implementation, considering, on one hand, that analyses of individual designs in a population are independent of each other so that they may be executed concurrently on separate processors, and, on the other hand, that there are some operations in a GA that cannot be so distributed. The algorithm experimented with was based on a gaussian distribution rather than bit exchange in the GA reproductive mechanism, and the test case was a hub frame structure of up to 1080 design variables. The experimentation engaging up to 128 processors confirmed expectations of radical elapsed time reductions comparing to a conventional single processor implementation. It also demonstrated that the time spent in the non-distributable parts of the algorithm and the attendant cross-processor communication may have a very detrimental effect on the efficient utilization of the multiprocessor machine and on the number of processors that can be used effectively in a concurrent manner. Three techniques were devised and tested to mitigate that effect, resulting in efficiency increasing to exceed 99 percent.

Plassman, Gerald E.↗