A method for computation of meteoroid impact distribution over spacecraft
Computer program using numerical integration techniques for computation of meteoroid impact and angular distributions over complex geometric spacecraft configurations
Fu, T.↗
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Results for “numerical computation”
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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Analytic partial derivatives for estimating low-thrust parameters.
Analytic partial derivatives for estimating orbital low-thrust parameters via differential correction are developed and compared with two different numerical methods. The formulation is independent of the particular thrust model used and is applicable to all physically possible elliptic orbits. The starting point for the development is the set of variational equations of the elliptic orbital elements in the form due to Lagrange. The first time derivatives of the elements are transformed to derivatives with respect to the space variable, true anomaly, and integrated to first order in closed form in a straightforward general perturbations approach, with one exception: particular attention is given to the mean anomaly as influenced by thrust perturbations in the semimajor axis so that the complete first-order effect is included. The partials of the elements are then taken with respect to any given thrust parameter. Two comparisons are made with numerical methods for computing these thrust partials: numerical quotients and numerical integration of the variational equations for thrust.
Cunningham, G. W.↗
A view of Kanerva's sparse distributed memory
Pentti Kanerva is working on a new class of computers, which are called pattern computers. Pattern computers may close the gap between capabilities of biological organisms to recognize and act on patterns (visual, auditory, tactile, or olfactory) and capabilities of modern computers. Combinations of numeric, symbolic, and pattern computers may one day be capable of sustaining robots. The overview of the requirements for a pattern computer, a summary of Kanerva's Sparse Distributed Memory (SDM), and examples of tasks this computer can be expected to perform well are given.
Denning, P. J.↗
Parallel-vector computation for CSI-design code
Computational aspects of Control-Structure Interaction (CSI) DESIGN code is reviewed. Numerical intensive computation portions of CSI-DESIGN code were identified. Improvements in computational speed for the CSI-DESIGN code can be achieved by exploiting parallel and vector capabilities offered by modern computers, such as the Alliant, Convex, Cray-2, and Cray-YMP. Four options to generate the coefficient stiffness matrix and to solve the system of linear, simultaneous equations are currently available in the CSI-DESIGN code. A preprocessor to use RCM (Reverse Cuthill-Mackee) algorithm for bandwidth minimization was also developed for the CSI-DESIGN code. Preliminary results obtained by solving a small-scale, 97 node CSI finite element model (for eigensolution) have indicated that this new CSI-DESIGN code is 5 to 6 times faster (using 1 Alliant processor) than the old version of CSI-DESIGN code. This speed-up was achieved due to the RCM algorithm and the use of a new skyline solver. Efforts are underway to further improve the vector speed for CSI-DESIGN code, to evaluate its performance on a larger scale CSI model (such as phase zero CSI model) to make the code run efficiently on multiprocessor, parallel computer environment, and to make the code portable among different parallel computers available at NASA LaRC, such as Alliant, Convex, and Cray computers.
Nguyen, Duc T.↗
Numerical simulation of a hovering rotor using embedded grids
The flow field for a rotor blade in hover was computed by numerically solving the compressible thin-layer Navier-Stokes equations on embedded grids. In this work, three embedded grids were used to discretize the flow field - one for the rotor blade and two to convect the rotor wake. The computations were performed at two hovering test conditions, for a two-bladed rectangular rotor of aspect ratio six. The results compare fairly with experiment and illustrates the use of embedded grids in solving helicopter type flow fields.
Duque, Earl-Peter N.↗
A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods
The development of shock-capturing finite difference methods for hyperbolic conservation laws has been a rapidly growing area for the last decade. Many of the fundamental concepts, state-of-the-art developments and applications to fluid dynamics problems can only be found in meeting proceedings, scientific journals and internal reports. This paper attempts to give a unified and generalized formulation of a class of high-resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock waves, perfect gases, equilibrium real gases and nonequilibrium flow computations. These numerical methods are formulated for the purpose of ease and efficient implementation into a practical computer code. The various constructions of high-resolution shock-capturing methods fall nicely into the present framework and a computer code can be implemented with the various methods as separate modules. Included is a systematic overview of the basic design principle of the various related numerical methods. Special emphasis will be on the construction of the basic nonlinear, spatially second and third-order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows will be discussed. Some perbolic conservation laws to problems containing stiff source terms and terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas-dynamics problems. The use of the Lax-Friedrichs numerical flux to obtain high-resolution shock-capturing schemes is generalized. This method can be extended to nonlinear systems of equations without the use of Riemann solvers or flux-vector splitting approaches and thus provides a large savings for multidimensional, equilibrium real gases and nonequilibrium flow computations.
Yee, H. C.↗
Modeling Astrophysical Explosions and Nucleosynthesis (Final Technical Report)
The goal of this project was to further our theoretical understanding of the extreme physics and heavy element nucleosynthesis occurring in stellar explosions, in particular supernovae and neutron star mergers. To study these systems, we further developed and applied numerical simulations (radiation hydrodynamical models and nuclear reaction networks) run on high performance computers. The numerical calculations and companion theoretical analysis helped to better define the sites of astrophysical nucleosynthesis, and make predictions of the associated observables (nucleosynthetic yields and electromagnetic signals) that can be used to anticipate and interpret experimental data. This project enhances the scientific value of the nuclear data obtained from current and future experimental facilities (e.g., rare isotope beams) by improving our understanding of the astrophysical context and specific physical conditions under which we expect such reactions to take place in Nature.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Discussion of DNS: Past, Present, and Future
This paper covers the review, status, and projected future of direct numerical simulation (DNS) methodology relative to the state-of-the-art in computer technology, numerical methods, and the trends in fundamental research programs.
Joslin, Ronald D.↗
Computer derivations of equations of motion in a general orthogonal curvilinear coordinate system using the Formac language
Non-numeric digital computer program using coordinate transformation in deriving equations of motion for particles in general orthogonal curvilinear system
DIGITAL COMPUTER↗
Some recent investigations in numerical averaging
The feasibility of using computer programs for numerical averaging in high drag orbit prediction calculations is considered.
Wexler, D.↗
Research in progress in applied mathematics, numerical analysis, fluid mechanics, and computer science
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1993 through March 31, 1994. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science.
Source record↗
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.↗
Numerical integration and other techniques for computer aided network design programming Final technical report, 1 Jan. 1970 - 1 Jan. 1971
Matrix method and stiffly stable algorithms in numerical integration for computer aided network design programming
Cooke, C. H.↗
A Mixed Integer Efficient Global Optimization Algorithm with Multiple Infill Strategy - Applied to a Wing Topology Optimization Problem
With the advancement in high performance computing and numerical optimization techniques,engineering design optimization problems are becoming more complex, larger scale,higher fidelity, and computationally more demanding, requiring longer run times than ever before. There exists methodologies and techniques that can address some of these challenges but very few can address all, and most are limited in the extent that these concerns can be addressed. With the goal of addressing such challenging engineering problems, we developed anew optimization framework, named AMIEGO, that combines concepts from surrogate-based optimization approaches, gradient-based numerical methods, Partial Least Squares, evolutionary algorithms, and Branch-and-Bound, providing newer capabilities that were not previouslyperceived. However, the original version of this framework, in the process of adaptive samplingto explore and exploit the design space, finds only a single sample point per iteration. The efforthere builds upon this previously developed optimization framework to include multiple infillsampling capability that combines the concept of generalized expected improvement function,unsupervised learning, and multi-objective evolutionary technique. To demonstrate, AMIEGOwith the multiple infill capability (called AMIEGO-MIMOS) solves a series of increasingly difficultengineering design optimization problems. The results reveal the performance of the newapproach is problem dependent. When applied to a ten-bar truss problem, the newly proposedmultiple infill strategy consistently leads to a better design solutions when compared to theexisting CPTV method (implemented with the context of the AMIEGO framework). On theother hand, when applied to a mixed-integer high fidelity wing topology optimization problem- MIMOS, despite showing a steeper convergence at the start, eventually leads to an inferiorsolution as compared to CPTV approach. These results also reveal that a small number ofstarting points, in general, are sufficient to lead to a good overall solution.
Mixed-integer optimization↗
Numerical solution of a class of integral equations arising in two-dimensional aerodynamics
We consider the numerical solution of a class of integral equations arising in the determination of the compressible flow about a thin airfoil in a ventilated wind tunnel. The integral equations are of the first kind with kernels having a Cauchy singularity. Using appropriately chosen Hilbert spaces, it is shown that the kernel gives rise to a mapping which is the sum of a unitary operator and a compact operator. This allows the problem to be studied in terms of an equivalent integral equation of the second kind. A convergent numerical algorithm for its solution is derived by using Galerkin's method. It is shown that this algorithm is numerically equivalent to Bland's collocation method, which is then used as the method of computation. Extensive numerical calculations are presented establishing the validity of the theory.
Fromme, J.↗
Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers
In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures. Throughout this work, we have adhered to specific guiding principles that minimized the impact to current users while providing maximum flexibility for later evolution of solvers and data structures. The redesign was done through the addition of new linear and nonlinear solvers classes, enhancements to the vector class, and the creation of modern Fortran interfaces. The vast majority of this work has been performed “behind-the-scenes,” with minimal changes to the user interface and no reduction in solver capabilities or performance. These changes allow SUNDIALS users to more easily utilize external solver libraries and create highly customized solvers, enabling greater flexibility on extreme-scale, heterogeneous computational architectures.
97 MATHEMATICS AND COMPUTING↗
Multi-resolution analysis for ENO schemes
Given a function u(x) which is represented by its cell-averages in cells which are formed by some unstructured grid, we show how to decompose the function into various scales of variation. This is done by considering a set of nested grids in which the given grid is the finest, and identifying in each locality the coarsest grid in the set from which u(x) can be recovered to a prescribed accuracy. We apply this multi-resolution analysis to Essentially Non-oscillatory Schemes (ENO) schemes in order to reduce the number of numerical flux computations which is needed in order to advance the solution by one time-step. This is accomplished by decomposing the numerical solution at the beginning of each time-step into levels of resolution, and performing the computation in each locality at the appropriate coarser grid. We present an efficient algorithm for implementing this program in the one-dimensional case; this algorithm can be extended to the multi-dimensional case with cartesian grids.
Harten, Ami↗
Machine Learning Analysis of Hydrologic Exchange Flows and Transit Time Distributions in a Large Regulated River
Hydrologic exchange between river channels and adjacent subsurface environments is a key process that influences water quality and ecosystem function in river corridors. High-resolution numerical models were often used to resolve the spatial and temporal variations of exchange flows, which are computationally expensive. In this study, we adopt Random Forest (RF) and Extreme Gradient Boosting (XGB) approaches for deriving reduced order models of hydrologic exchange flows and associated transit time distributions, with integrated field observations (e.g., bathymetry) and hydrodynamic simulation data (e.g., river velocity, depth). The setup allows an improved understanding of the influences of various physical, spatial, and temporal factors on the hydrologic exchange flows and transit times. The predictors also contain those derived using hybrid clustering, leveraging our previous work on river corridor system hydromorphic classification. The machine learning-based predictive models are developed and validated along the Columbia River Corridor, and the results show that the top parameters are the thickness of the top geological formation layer, the flow regime, river velocity, and river depth; the RF and XGB models can achieve 70% to 80% accuracy and therefore are effective alternatives to the computational demanding numerical models of exchange flows and transit time distributions. Each machine learning model with its favorable configuration and setup have been evaluated. The transferability of the models to other river reaches and larger scales, which mostly depends on data availability, is also discussed.
97 MATHEMATICS AND COMPUTING↗