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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 1,225 records · Page 68
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

COMPARING NUMERICAL METHODS FOR ISOTHERMAL MAGNETIZED SUPERSONIC TURBULENCE

Many astrophysical applications involve magnetized turbulent flows with shock waves. Ab initio star formation simulations require a robust representation of supersonic turbulence in molecular clouds on a wide range of scales imposing stringent demands on the quality of numerical algorithms. We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine popular astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. These applications employ a variety of numerical approaches, including both split and unsplit, finite difference and finite volume, divergence preserving and divergence cleaning, a variety of Riemann solvers, and a range of spatial reconstruction and time integration techniques. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss the convergence of various characteristics for the turbulence decay test and the impact of various components of numerical schemes on the accuracy of solutions. The nine codes gave qualitatively the same results, implying that they are all performing reasonably well and are useful for scientific applications. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the magnetic field using the constrained transport method and using little to no explicit artificial viscosity. Codes that fall short in one or more of these areas are still useful, but they must compensate for higher numerical dissipation with higher numerical resolution. This paper is the largest, most comprehensive MHD code comparison on an application-like test problem to date. We hope this work will help developers improve their numerical algorithms while helping users to make informed choices about choosing optimal applications for their specific astrophysical problems.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1983

Advanced algorithm for orbit computation

Computational and analytical techniques which simplify the solution of complex problems in orbit mechanics, Astrodynamics and Celestial Mechanics were developed. The major tool of the simplification is the substitution of transformations in place of numerical or analytical integrations. In this way the rather complicated equations of orbit mechanics might sometimes be reduced to linear equations representing harmonic oscillators with constant coefficients.

Szenbehely, V.↗
NASA NTRS1996

CI Controls for Energy and Environment

Computational intelligence (CI) is a rapidly evolving field that utilizes life imitating metaphors for guiding model building including, but not limited to neural networks, fuzzy logic, genetic algorithms, artificial life, and hybrid CI paradigms. Although the boundaries between artificial intelligence (AI) and CI are not distinct, their research communities are separate and distinct. CI researchers tend to focus on processing numerical data from sensors, while the AI community generally relies on symbolic computing to capture human knowledge. In both areas, there is a great deal of interest and activity in hybrid systems that can offset the limitations of individual methods, extend their capabilities, and create new capabilities. Examples of the benefits that can accrue from hybrid systems are contained.

Biondo, Samuel J.↗
NASA NTRS2000

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Shu, Chi-Wang↗
NASA NTRS1995

Parallel rendering

This article provides a broad introduction to the subject of parallel rendering, encompassing both hardware and software systems. The focus is on the underlying concepts and the issues which arise in the design of parallel rendering algorithms and systems. We examine the different types of parallelism and how they can be applied in rendering applications. Concepts from parallel computing, such as data decomposition, task granularity, scalability, and load balancing, are considered in relation to the rendering problem. We also explore concepts from computer graphics, such as coherence and projection, which have a significant impact on the structure of parallel rendering algorithms. Our survey covers a number of practical considerations as well, including the choice of architectural platform, communication and memory requirements, and the problem of image assembly and display. We illustrate the discussion with numerous examples from the parallel rendering literature, representing most of the principal rendering methods currently used in computer graphics.

Crockett, Thomas W.↗
DOE OSTI2011

Acceleration of Radiance for Lighting Simulation by Using Parallel Computing with OpenCL

We report on the acceleration of annual daylighting simulations for fenestration systems in the Radiance ray-tracing program. The algorithm was optimized to reduce both the redundant data input/output operations and the floating-point operations. To further accelerate the simulation speed, the calculation for matrix multiplications was implemented using parallel computing on a graphics processing unit. We used OpenCL, which is a cross-platform parallel programming language. Numerical experiments show that the combination of the above measures can speed up the annual daylighting simulations 101.7 times or 28.6 times when the sky vector has 146 or 2306 elements, respectively.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2016

Machine learning strategy for accelerated design of polymer dielectrics

The ability to efficiently design new and advanced dielectric polymers is hampered by the lack of sufficient, reliable data on wide polymer chemical spaces, and the difficulty of generating such data given time and computational/experimental constraints. Here, we address the issue of accelerating polymer dielectrics design by extracting learning models from data generated by accurate state-of-the-art first principles computations for polymers occupying an important part of the chemical subspace. The polymers are ‘fingerprinted’ as simple, easily attainable numerical representations, which are mapped to the properties of interest using a machine learning algorithm to develop an on-demand property prediction model. Further, a genetic algorithm is utilised to optimise polymer constituent blocks in an evolutionary manner, thus directly leading to the design of polymers with given target properties. Furthermore, while this philosophy of learning to make instant predictions and design is demonstrated here for the example of polymer dielectrics, it is equally applicable to other classes of materials as well.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Sylvester-preconditioned adaptive-rank implicit time integrators for advection-diffusion equations with variable coefficients

Here, we consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For d-dimensional problems (here, d = 2 or 3), the computational complexity and memory storage of the approach are found numerically to scale as and $\mathscr{O}(Nr^2) + \mathscr{O} (r^{d+1})$ and $\mathscr{O}(Nr) + \mathscr{O} (r^{d})$, respectively, with the one-dimensional resolution and the maximal rank during the Krylov iteration (which we find to be largely independent of on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Cone-grid scheme for solving hyperbolic systems of conservation laws and one application

In this work, we introduce a new numerical method, the so-called cone-grid scheme for solving hyperbolic systems of conservation laws. The formulation and the theoretical analysis for this scheme are slightly simpler than other algorithms. Simultaneously, our technique leads to a more efficacious numerical scheme. The Riemann solution is the basic ingredient for this scheme. We also give the main application of this technique, namely the global weak solutions for the one-dimensional model prescribes heat conduction in solids at low temperature, which called phonon–Bose model. This system consists of a conservation equation for the energy density and the heat flux. The scheme also satisfies positivity. The cone-grid scheme was compared with exact solution by three numerical examples, where explicit solutions are known. These numerical results verify the accuracy of the proposed scheme qualitatively and quantitatively.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

On the computation and updating of the modified Cholesky decomposition of a covariance matrix

Methods for obtaining and updating the modified Cholesky decomposition (MCD) for the particular case of a covariance matrix when one is given only the original data are described. These methods are the standard method of forming the covariance matrix K then solving for the MCD, L and D (where K=LDLT); a method based on Householder reflections; and lastly, a method employing the composite-t algorithm. For many cases in the analysis of remotely sensed data, the composite-t method is the superior method despite the fact that it is the slowest one, since (1) the relative amount of time computing MCD's is often quite small, (2) the stability properties of it are the best of the three, and (3) it affords an efficient and numerically stable procedure for updating the MCD. The properties of these methods are discussed and FORTRAN programs implementing these algorithms are listed.

Vanrooy, D. L.↗
NASA NTRS1993

The use of linked lists in the simulation of controller-structure interaction

An algorithm for the computer simulation of large space structures under active control is considered. Linked lists are used in a matrix data structure to implement the trapezoidal rule on the system differential equations. The use of the trapezoidal rule ensures that the numerical stability is equivalent to the system stability, which is essential for this type of simulation. The sparsity of the system matrices is exploited by the linked lists, and the algorithm efficiently steps through the lists in an orderly fashion. Results of simulations on a NASA large space structure experiment are reported.

Quan, Ralph↗
DOE OSTI2024

Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimension. In this paper, we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control. We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians. Additionally, we present an efficient, grid-free numerical solver based on our representation formulas, which is shown to scale linearly with the state dimension, and thus, to overcome the curse of dimensionality. Using existing optimization methods and the min-plus technique, we extend our numerical solvers to address more general classes of convex and nonconvex initial costs. We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit (CPU) and a field-programmable gate array (FPGA). In several cases, our FPGA implementation obtains over a 10 times speedup compared to the CPU, which demonstrates the promising performance boosts FPGAs can achieve. Furthermore, our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Manifold Sampling for Optimization of Nonconvex Functions That Are Piecewise Linear Compositions of Smooth Components

Here, we develop a manifold sampling algorithm for the minimization of a nonsmooth composite function $f \triangleq \psi + h \circ F$ when $\psi$ is smooth with known derivatives, $h$ is a known, nonsmooth, piecewise linear function, and $F$ is smooth but expensive to evaluate. The trust-region algorithm classifies points in the domain of $h$ as belonging to different manifolds and uses this knowledge when computing search directions. Since $h$ is known, classifying objective manifolds using only the values of $F$ is simple. We prove that all cluster points of the sequence of the manifold sampling algorithm iterates are Clarke stationary; this holds although points evaluated by the algorithm are not assumed to be differentiable and when only approximate derivatives of $F$ are available. Numerical results show that manifold sampling using zeroth-order information about $F$ is competitive with algorithms that employ exact subgradient values from $\partial f$.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A structure preserving Lanczos algorithm for computing the optical absorption spectrum

We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving full Bethe-Salpeter equation without Tamm-Dancoff approximation. The new algorithm is based on a structure preserving Lanczos procedure, which exploits the special block structure of Bethe-Salpeter Hamiltonian matrices. A recently developed technique of generalized averaged Gauss quadrature is incorporated to accelerate the convergence. We also establish the connection between our structure preserving Lanczos procedure with several existing Lanczos procedures developed in different contexts. Numerical examples are presented to demonstrate the effectiveness of our Lanczos algorithm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

An implicit, transonic, full-potential code for cascade flow on H-grid topology

A transonic, full-potential code is developed for computing the flow through two-dimensional cascades using an H-type grid topology that employs an implicit approximate-factorization scheme. The body-conforming H-grid is generated numerically by solving Poisson's equation. The flow-solution algorithm at the coordinate mapping singularity associated with this grid is investigated using two different types of finite-difference schemes. The grid-geometry effect on these schemes is also studied by noting free-stream capturing properties. It is found that by implementing a consistent spatial differencing scheme, the mapping singularities can be resolved numerically, and the grid-geometry-induced error minimized. The code is verified by computing model cascade flow problems.

Kwak, D.↗
NASA NTRS2002

Computational Study of Near-limit Propagation of Detonation in Hydrogen-air Mixtures

A computational investigation of the near-limit propagation of detonation in lean and rich hydrogen-air mixtures is presented. The calculations were carried out over an equivalence ratio range of 0.4 to 5.0, pressures ranging from 0.2 bar to 1.0 bar and ambient initial temperature. The computations involved solution of the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing (TVD) scheme, and a point implicit, first-order-accurate, time marching algorithm. The hydrogen-air combustion was modeled with a 9-species, 19-step reaction mechanism. A multi-level, dynamically adaptive grid was utilized in order to resolve the structure of the detonation. The results of the computations indicate that when hydrogen concentrations are reduced below certain levels, the detonation wave switches from a high-frequency, low amplitude oscillation mode to a low frequency mode exhibiting large fluctuations in the detonation wave speed; that is, a 'galloping' propagation mode is established.

Yungster, S.↗
NASA NTRS1990

Counterrotating prop-fan simulations which feature a relative-motion multiblock grid decomposition enabling arbitrary time-steps

Improvements are presented of a computer algorithm developed for the time-accurate flow analysis of rotating machines. The flow model is a finite volume method utilizing a high-resolution approximate Riemann solver for interface flux definitions. The numerical scheme is a block LU implicit iterative-refinement method which possesses apparent unconditional stability. Multiblock composite gridding is used to orderly partition the field into a specified arrangement of blocks exhibiting varying degrees of similarity. Block-block relative motion is achieved using local grid distortion to reduce grid skewness and accommodate arbitrary time step selection. A general high-order numerical scheme is applied to satisfy the geometric conservation law. An even-blade-count counterrotating unducted fan configuration is chosen for a computational study comparing solutions resulting from altering parameters such as time step size and iteration count. The solutions are compared with measured data.

Janus, J. Mark↗