Theoretical calculations of the bremsstrahlung cross section
Mathematical analysis and computer programming for theoretical calculations of bremsstrahlung cross section
NUMERICAL ANALYSIS↗
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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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A Computational and Experimental Investigation of Shear Coaxial Jet Atomization
The instability and subsequent atomization of a viscous liquid jet emanated into a high-pressure gaseous surrounding is studied both computationally and experimentally. Liquid water issued into nitrogen gas at elevated pressures is used to simulate the flow conditions in a coaxial shear injector element relevant to liquid propellant rocket engines. The theoretical analysis is based on a simplified mathematical formulation of the continuity and momentum equations in their conservative form. Numerical solutions of the governing equations subject to appropriate initial and boundary conditions are obtained via a robust finite difference scheme. The computations yield real-time evolution and subsequent breakup characteristics of the liquid jet. The experimental investigation utilizes a digital imaging technique to measure resultant drop sizes. Data were collected for liquid Reynolds number between 2,500 and 25,000, aerodynamic Weber number range of 50-500 and ambient gas pressures from 150 to 1200 psia. Comparison of the model predictions and experimental data for drop sizes at gas pressures of 150 and 300 psia reveal satisfactory agreement particularly for lower values of investigated Weber number. The present model is intended as a component of a practical tool to facilitate design and optimization of coaxial shear atomizers.
Ibrahim, Essam A.↗
The finite element method in low speed aerodynamics
The finite element procedure is shown to be of significant impact in design of the 'computational wind tunnel' for low speed aerodynamics. The uniformity of the mathematical differential equation description, for viscous and/or inviscid, multi-dimensional subsonic flows about practical aerodynamic system configurations, is utilized to establish the general form of the finite element algorithm. Numerical results for inviscid flow analysis, as well as viscous boundary layer, parabolic, and full Navier Stokes flow descriptions verify the capabilities and overall versatility of the fundamental algorithm for aerodynamics. The proven mathematical basis, coupled with the distinct user-orientation features of the computer program embodiment, indicate near-term evolution of a highly useful analytical design tool to support computational configuration studies in low speed aerodynamics.
Baker, A. J.↗
GASP Advancements With Symbolic Computations, Optimization, and Decoupled Numerical Methods
NASA is exploring advancements in hybrid-electric propulsion concepts for aircraft design. A new analysis capability has been deployed at NASA’s Ames Research Center using a new mathematical modeling framework in Python that leverages symbolic representation of mathematical expressions, optimization-based problem formulations, and standalone numerical methods. This capability, called Gascon, has been verified against NASA’s General Aviation Synthesis Program (GASP) results for several vehicles that exercise the analysis capability for a variety of aircraft classes and engine models, including both turbofans and turboprops. We believe this capability will set the stage for more rapid development of novel aircraft models with more flexible design assessments using optimization, and more traceable analysis for reproducibility. Additionally, a novel Pareto optimization-based design space exploration that shows the trade between range flown and fuel burn by manipulating the thrust split during cruise for a true parallel hybrid aircraft was developed by leveraging the unique features of Gascon.
aircraft design↗
Prediction of Fatigue Crack Growth Using Regularized Numerical Models
Though it is known in the engineering community that successful analyses rest upon the proper balance of (1) theoretical analysis of mathematical models, (2) physical experimentation and (3) computational simulation, this balance is currently handled in sometimes unwieldy and inefficient manner. It is proposed to investigate and develop rigorous and computationally efficient method to effectively combine all available information, from both experimental measurements and mathematical models, in the emulation of physical systems. This will be specifically applied to fatigue crack growth in metallic structures of interest to NASA.
Meade, Andrew J.↗
Fast and Accurate Intersections on a Sphere
We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and numerical robustness over the ones traditionally implemented in geoscience software. We then show how algorithms based on the concept of error-free transformations (EFT) can be applied to evaluate this formula within a relative error bound that is on the order of machine precision. Here, we demonstrate that, with a vectorized and parallelized implementation, this enhanced accuracy is achieved with no compute time overhead compared to a direct calculation in hardware floating point, making our algorithm suitable for performance-sensitive applications like regridding of high-resolution climate data. In contrast, evaluating our formula using high-precision data types like quadruple precision and arbitrary precision, or using the robust intersection computation routines from the Computational Geometry Algorithms Library, leads to significant computational overhead, especially since these alternatives inhibit vectorization. More generally, our work demonstrates how EFT techniques can be combined and extended to implement nontrivial geometric calculations with high accuracy and speed.
Environmental sciences↗
Trends in computerized structural analysis and synthesis; Proceedings of the Symposium, Washington, D.C., October 30-November 1, 1978
The subjects considered are related to future directions of structural applications and potential of new computing systems, advances and trends in data management and engineering software development, advances in applied mathematics and symbolic computing, computer-aided instruction and interactive computer graphics, nonlinear analysis, dynamic analysis and transient response, structural synthesis, structural analysis and design systems, advanced structural applications, supercomputers, numerical analysis, and trends in software systems. Attention is given to the reliability and optimality of the finite element method, computerized symbolic manipulation in structural mechanics, a standard computer graphics subroutine package, and a drag method as a finite element mesh generation scheme.
Noor, A. K.↗
ComPort: Rigorous Testing Methods to Safeguard Software Porting (Final UW Report)
This report summarizes the University of Washington’s contributions to the ComPort project, Rigorous Testing Methods to Safeguard Software Porting, funded under the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR), award number DE-SC0022081. UW’s work addressed numerics-driven correctness challenges arising in heterogeneous and rapidly evolving computing environments. Our efforts focused on developing interactive analysis tools, correctness-preserving rewriting systems, semantic-aware code-transformation infrastructure, and multi-language support for reproducible numerical experiments.
97 MATHEMATICS AND COMPUTING↗
Analysis of geologic terrain models for determination of optimum SAR sensor configuration and optimum information extraction for exploration of global non-renewable resources. Pilot study: Arkansas Remote Sensing Laboratory, part 1, part 2, and part 3
Computer-generated radar simulations and mathematical geologic terrain models were used to establish the optimum radar sensor operating parameters for geologic research. An initial set of mathematical geologic terrain models was created for three basic landforms and families of simulated radar images were prepared from these models for numerous interacting sensor, platform, and terrain variables. The tradeoffs between the various sensor parameters and the quantity and quality of the extractable geologic data were investigated as well as the development of automated techniques of digital SAR image analysis. Initial work on a texture analysis of SEASAT SAR imagery is reported. Computer-generated radar simulations are shown for combinations of two geologic models and three SAR angles of incidence.
Kaupp, V. H.↗
Development of analytical orbit propagation technique with drag
Two orbit computation methods were used: (1) numerical method- The solution to the satellite differential equations were solved in a step-by-step manner, using a mathematical algorithm taken from numerical analysis; and (2) analytical method - The solution was expressed by explicit functions of the independent variable. Analytical drag modules, tesseral terms initialization module, second order and long period terms module, and verification testing of the ASOP program were also considered.
Source record↗
Error Correction for Tandem Data-Transmission Paths
Mathematical analysis for digital data transmission calculates optimum number of binary error-correcting repeaters to install in given number of wideband channel links. Asymptotic results compared to computed numerical results.
Posner, E. C.↗
Use of non-spherical gravity harmonics for relative motion GN/C (category 2)
Detailed analysis of the Automatic Rendezvous and Capture problem indicate a need for three different regions of mathematical description for the GN&C algorithms: (1) multi-vehicle orbital mechanics to the rendezvous interface point, i.e., within 100 nm; (2) relative motion solutions (such as Clohessy-Wiltshire type) from the far-field to the near-field interface, i.e., within 1 nm and; (3) close proximity motion - the near-field motion where the relative differences in the gravitational and orbit inertial accelerations can be neglected from the equations of motion. Limit boundaries to these regions can be precisely defined by further analysis and will be functions of the tracking measurement accuracies and the computer resources available for the solution of the algorithms. This paper analyzes the relative motion in Regions 2 and 3 above and present the derivation and discussion of the general case of non-spherical gravitational perturbed relative motion. Mathematical deviations from the numerically integrated spherical gravity case and solutions from the Clohessy-Wiltshire equations are presented in the analysis. Based upon this preliminary analysis, it is recommended that further efforts be used to assess the relative position and velocity differences in Region 2 due to non-spherical gravity harmonics and that viable GN&C algorithms be developed to include these gravity perturbations (especially the effects of the first gravity harmonic, J2).
Henderson, David M.↗
A theory of supercritical wing sections, with computer programs and examples.
Mathematical methods for the design of supercritical wings, which depend on the numerical solution of the partial differential equations of two-dimensional gas dynamics, are developed. The main contribution is a computer program for the design of shockless transonic airfoils using the hodograph transformation and analytic continuation into the complex domain. The mathematical theory is described, and a manual for users of the programs is provided. Numerical examples are given and computational results are discussed, and the computer programs themselves are listed. The analysis routine can be used to ascertain whether the profiles behave well at off-design conditions, or to smooth coordinates and obtain a desirable shape more quickly when perfectly shockless flow is not essential.
Bauer, F.↗
Analysis of boundary conditions for SSME subsonic internal viscous flow analysis
A study was completed of mathematically proper boundary conditions for unique numerical solution of internal, viscous, subsonic flows in the space shuttle main engine. The study has concentrated on well posed considerations, with emphasis on computational efficiency and numerically stable boundary condition statements. The method of implementing the established boundary conditions is applicable to a wide variety of finite difference and finite element codes, as demonstrated.
Baker, A. J.↗
Program Computes Flows Of Fluids And Heat
SINDA'85/FLUINT incorporates lumped-parameter-network and one-dimensional-flow mathematical models. System enables analysis of mutual influences of thermal and flow phenomena. Offers two finite-difference numerical solution techniques: forward-difference explicit approximation and Crank-Nicholson approximation. Enables simulation of nonuniform heating and facilitates mathematical modeling of thin-walled heat exchangers. Ability to model nonequilibrium behavior within two-phase volumes included. Recent changes in program improve modeling of real evaporator pumps and other capillary-assist evaporators. Written in FORTRAN 77.
Cullimore, Brent↗
Three-Dimensional Analysis and Modeling of a Wankel Engine
A new computer code, AGNI-3D, has been developed for the modeling of combustion, spray, and flow properties in a stratified-charge rotary engine (SCRE). The mathematical and numerical details of the new code are described by the first author in a separate NASA publication. The solution procedure is based on an Eulerian-Lagrangian approach where the unsteady, three-dimensional Navier-Stokes equations for a perfect gas-mixture with variable properties are solved in generalized, Eulerian coordinates on a moving grid by making use of an implicit finite-volume, Steger-Warming flux vector splitting scheme. The liquid-phase equations are solved in Lagrangian coordinates. The engine configuration studied was similar to existing rotary engine flow-visualization and hot-firing test rigs. The results of limited test cases indicate a good degree of qualitative agreement between the predicted and measured pressures. It is conjectured that the impulsive nature of the torque generated by the observed pressure nonuniformity may be one of the mechanisms responsible for the excessive wear of the timing gears observed during the early stages of the rotary combustion engine (RCE) development. It was identified that the turbulence intensities near top-dead-center were dominated by the compression process and only slightly influenced by the intake and exhaust processes. Slow mixing resulting from small turbulence intensities within the rotor pocket and also from a lack of formation of any significant recirculation regions within the rotor pocket were identified as the major factors leading to incomplete combustion. Detailed flowfield results during exhaust and intake, fuel injection, fuel vaporization, combustion, mixing and expansion processes are also presented. The numerical procedure is very efficient as it takes 7 to 10 CPU hours on a CRAY Y-MP for one entire engine cycle when the computations are performed over a 31 x16 x 20 grid.
Raju, M. S.↗
Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators
The control of high-dimensional distributed parameter systems (DPS) remains a challenge when explicit coarse-grained equations are unavailable. Classical equation-free (EF) approaches rely on fine-scale simulators treated as black-box timesteppers. However, repeated simulations for steady-state computation, linearization, and control design are often computationally prohibitive, or the microscopic timestepper may not even be available, leaving us with data as the only resource. We propose a data-driven alternative that uses local neural operators, trained on spatiotemporal microscopic/mesoscopic data, to obtain efficient short-time solution operators. These surrogates are employed within Krylov subspace methods to compute coarse steady and unsteady-states, while also providing Jacobian information in a matrix-free manner. Krylov-Arnoldi iterations then approximate the dominant eigenspectrum, yielding reduced models that capture the open-loop slow dynamics without explicit Jacobian assembly. Both discrete-time Linear Quadratic Regulator (dLQR) and pole-placement (PP) controllers are based on this reduced system and lifted back to the full nonlinear dynamics, thereby closing the feedback loop.
93B52, 93C20, 47N70, 65J15, 65M32, 68T07, 68T20, 6↗
Launch window analysis of satellites in high eccentricity or large circular orbits
Numerical methods and computer programs for studying the stability and evolution of orbits of large eccentricity are presented. Methods for determining launch windows and target dates are developed. Mathematical models are prepared to analyze the characteristics of specific missions.
Renard, M. L.↗