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NASA NTRS1989

Euler procedure for three-dimensional transonic wall interference

Based on an optimization formulation, a procedure has been developed to evaluate Mach number and angle-of-attack corrections. The Euler equations are assumed to be the flow governing equations. To obtain efficient solutions for the optimization problem, the iterative solutions for the flow variables and the design parameters are simultaneously updated. In addition to the model lift and geometry, the procedure requires pressure measurements near the tunnel walls. The tunnel boundary conditions are based on the introduction of Reimann invariants for a one-dimensional flow normal to the boundary. Computations are performed to verify that the errors introduced by this approximate boundary-condition formulation are acceptably small. The correction scheme is applied to an aircraft configuration in an open jet. The results indicate that the optimization scheme is highly efficient with the rate of convergence of the flow solution nearly equal to the corresponding rate of a regular analysis problem.

Rizk, Magdi H.↗

NASA NTRS1990

Spectral methods for time dependent problems

Spectral approximations are reviewed for time dependent problems. Some basic ingredients from the spectral Fourier and Chebyshev approximations theory are discussed. A brief survey was made of hyperbolic and parabolic time dependent problems which are dealt with by both the energy method and the related Fourier analysis. The ideas presented above are combined in the study of accuracy stability and convergence of the spectral Fourier approximation to time dependent problems.

Tadmor, Eitan↗

NASA NTRS1991

Seals Research at Texas A/M University

The Turbomachinery Laboratory at Texas A&M has been providing experimental data and computational codes for the design seals for many years. The program began with the development of a Halon based seal test rig. This facility provided information about the effective stiffness and damping in whirling seals. The Halon effectively simulated cryogenic fluids. Another test facility was developed (using air as the working fluid) where the stiffness and damping matrices can be determined. This data was used to develop bulk flow models of the seal's effect upon rotating machinery; in conjunction with this research, a bulk flow model for calculation of performance and rotordynamic coefficients of annular pressure seals of arbitrary non-uniform clearance for barotropic fluids such as LH2, LOX, LN2, and CH4 was developed. This program is very efficient (fast) and converges for very large eccentricities. Currently, work is being performed on a bulk flow analysis of the effects of the impeller-shroud interaction upon the stability of pumps. The data was used along with data from other researchers to develop an empirical leakage prediction code for MSFC. Presently, the flow field inside labyrinth and annular seals are being studied in detail. An advanced 3-D Doppler anemometer system is being used to measure the mean velocity and entire Reynolds stress tensor distribution throughout the seals. Concentric and statically eccentric seals were studied; presently, whirling seals are being studied. The data obtained are providing valuable information about the flow phenomena occurring inside the seals, as well as a data base for comparison with numerical predictions and for turbulence model development. A finite difference computer code was developed for solving the Reynolds averaged Navier Stokes equation inside labyrinth seals. A multi-scale k-epsilon turbulence model is currently being evaluated. A new seal geometry was designed and patented using a computer code. A large scale, 2-D seal flow visualization facility is also being developed.

Morrison, Gerald L.↗

NASA NTRS1993

Pseudo-compressibility methods for the incompressible flow equations

Preconditioning methods to accelerate convergence to a steady state for the incompressible fluid dynamics equations are considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Thus the steady state of the preconditioned system is the same as the steady state of the original system. The method is compared to other types of pseudo-compressibility. For finite difference methods preconditioning can change and improve the steady state solutions. An application to viscous flow around a cascade with a non-periodic mesh is presented.

Turkel, Eli↗

NASA NTRS2004

Integrated Modeling Approach for the Terrestrial Planet Finder Mission

Because of the complexity of the Terrestrial Planet Finder (TPF) design concepts, the project will rely heavily on the use of engineering and science simulations to predict on-orbit performance. Furthermore, current understanding of these missions indicates that the 3m to 8m class optical systems need to be as stable as picometers in wavefront and sub-milli arcsec in pointing. These extremely small requirements impose on the models a level of predictive accuracy heretofore never achieved, especially in the area of microgravity effects, material property accuracy, thermal solution convergence, and all other second order modeling effects typically ignored. New modeling tools and analysis paradigms are developed which emphasize computational accuracy and fully integrated analytical simulations. The process is demonstrated on sample problems using the TPF Coronagraph design concept. The TPF project is also planning a suite of testbeds through which various aspects of the models and simulations will be verified.

terrestrial planet finder↗

NASA NTRS2019

MRAC with Time-Varying Reference Model from Convex Combination

An extension of model reference adaptive control is presented that accommodates use of a time-varying reference model. Specifically, the reference model is taken to be a time-varying convex combination of two linear, time-invariant models. The design is intended to act as a way to smoothly transition between two different reference models without resorting to a scheduled switch. It also provides the ability to use an interpolated reference model when the plant is operating between design points. The time variation of the combination must satisfy some requirements to ensure stability but is otherwise user choice. Subject to these requirements, bounded tracking error behavior is demonstrated via Lyapunov stability analysis for the single-input, single-output, output feedback case. Tracking error convergence is asymptotic when time variation ceases. The proposed design is demonstrated in simulation of a numerical model.

Hashemi, Kelley E.↗

DOE OSTI2022

Analysis of cell-based diffusion acceleration for the slice balance approach

In this work, we perform analysis on the use of cell-based diffusion acceleration methodologies to accelerate the convergence of transport solutions discretized with the slice balance approach (SBA) on unstructured polygonal grids.We investigated both linear diffusion synthetic acceleration (DSA) and non linear diffusion acceleration (NDA), including its partial-current variant (pNDA). DSA and NDA were both shown to diverge for intermediate ranges of mesh optical thicknesses. However, pNDA and Krylov methods like GMRES and Broyden stabilized the acceleration schemes, including problems with degenerate cells formed by mesh refinement. (author)

42 ENGINEERING↗

DOE OSTI2021

A hierarchical evaluation framework for assessing climate simulations relevant to the energy-water-land nexus (Final Report)

The overarching goal was to construct a hierarchy of new and well-tested metrics and analysis tools that support both fundamental and use-inspired research. Motivating this goal was a convergence of needs from climate scientists and stakeholders alike for a systematic, robust framework of model evaluation and diagnosis to provide scientific insights, inform model development, support best practices for the use of climate model outputs, and facilitate communication of climate information in the evolving landscapes of multi-model, multi-resolution, and large ensemble simulations that generate terabytes of data for any single climate run. Steps toward attaining these goals benefited from expertise and established capability of the project team, which included leadership of the North American Regional Climate Change Assessment Program (NARCCAP) and the Coordinated Regional Downscaling Experiment (CORDEX), development of hierarchical model evaluation approaches, and successful research in the analysis and diagnosis of climate model skill, as well as the understanding and modeling of regional climate processes in North America. As part of the overarching goal, the project worked to disseminate a suite of methodologies, algorithms, and software components that the wider community can employ to advance climate science and applications. With rigorous demonstration, the evaluation framework and the mix of standard and high risk / high reward approaches helped form the basis for future development of a computationally enabled user-friendly system for community use.

17 WIND ENERGY↗

NASA NTRS1994

Multigrid one shot methods for optimal control problems: Infinite dimensional control

The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

Arian, Eyal↗

NASA NTRS2003

Integrated Software for Analyzing Designs of Launch Vehicles

Launch Vehicle Analysis Tool (LVA) is a computer program for preliminary design structural analysis of launch vehicles. Before LVA was developed, in order to analyze the structure of a launch vehicle, it was necessary to estimate its weight, feed this estimate into a program to obtain pre-launch and flight loads, then feed these loads into structural and thermal analysis programs to obtain a second weight estimate. If the first and second weight estimates differed, it was necessary to reiterate these analyses until the solution converged. This process generally took six to twelve person-months of effort. LVA incorporates text to structural layout converter, configuration drawing, mass properties generation, pre-launch and flight loads analysis, loads output plotting, direct solution structural analysis, and thermal analysis subprograms. These subprograms are integrated in LVA so that solutions can be iterated automatically. LVA incorporates expert-system software that makes fundamental design decisions without intervention by the user. It also includes unique algorithms based on extensive research. The total integration of analysis modules drastically reduces the need for interaction with the user. A typical solution can be obtained in 30 to 60 minutes. Subsequent runs can be done in less than two minutes.

Philips, Alan D.↗

DOE OSTI2026

Multi-strain analysis of Pseudomonas putida reveals the metabolic and genetic diversity of the species

Pseudomonas putida is a gram-negative bacterial species increasingly utilized in biotechnology due to its robust growth, ability to degrade aromatic compounds, solvent tolerance, and genetic tractability. In this study, we report a comprehensive multi-strain analysis of 164 P. putida strains based on the reconstruction of a pan-putida metabolic network and the formulation of strain-specific genome-scale metabolic models (GEMs). We performed whole-genome sequencing and hybrid assembly for 40 strains, contributing a ~8% increase to the available genomic data for P. putida . Furthermore, high-throughput phenotypic profiling using the Biolog phenotype microarray system for 24 strains on 190 unique carbon sources, along with 15 aromatic compounds not present on Biolog plates, yielded 4,920 unique strain-phenotype measurements. These data were leveraged to curate GEMs for 24 representative strains, including a refined model for strain KT2440, which comprised 1,480 genes and 2,191 metabolites, achieving a prediction accuracy of 91.2% in carbon utilization. Systematic comparison of genomes and GEMs revealed both conserved core pathways and significant allelic and functional divergence across strains, highlighting strain-specific variation in aromatic degradation. While pathways for protocatechuate and phenylacetate degradation were widely conserved, metabolic capabilities for compounds such as ferulate, phenol, and cresols varied markedly, suggesting adaptation to distinct ecological niches. Alleleome analysis of enzymes, such as PcaI and PcaJ, revealed distinct, functionally similar clades, indicating possible convergent evolution or horizontal gene transfer. These results provide computable resources and informative models for selecting P. putida strains with desired traits for biomanufacturing and bioremediation and offer insights into the evolution and phylogeny of the P. putida species.

aromatics utilization↗

NASA NTRS2016

Climate Analytics as a Service

Exascale computing, big data, and cloud computing are driving the evolution of large-scale information systems toward a model of data-proximal analysis. In response, we are developing a concept of climate analytics as a service (CAaaS) that represents a convergence of data analytics and archive management. With this approach, high-performance compute-storage implemented as an analytic system is part of a dynamic archive comprising both static and computationally realized objects. It is a system whose capabilities are framed as behaviors over a static data collection, but where queries cause results to be created, not found and retrieved. Those results can be the product of a complex analysis, but, importantly, they also can be tailored responses to the simplest of requests. NASA's MERRA Analytic Service and associated Climate Data Services API provide a real-world example of climate analytics delivered as a service in this way. Our experiences reveal several advantages to this approach, not the least of which is orders-of-magnitude time reduction in the data assembly task common to many scientific workflows.

big data↗

NASA NTRS1997

Efficient Gradient-Based Shape Optimization Methodology Using Inviscid/Viscous CFD

The formerly developed preconditioned-biconjugate-gradient (PBCG) solvers for the analysis and the sensitivity equations had resulted in very large error reductions per iteration; quadratic convergence was achieved whenever the solution entered the domain of attraction to the root. Its memory requirement was also lower as compared to a direct inversion solver. However, this memory requirement was high enough to preclude the realistic, high grid-density design of a practical 3D geometry. This limitation served as the impetus to the first-year activity (March 9, 1995 to March 8, 1996). Therefore, the major activity for this period was the development of the low-memory methodology for the discrete-sensitivity-based shape optimization. This was accomplished by solving all the resulting sets of equations using an alternating-direction-implicit (ADI) approach. The results indicated that shape optimization problems which required large numbers of grid points could be resolved with a gradient-based approach. Therefore, to better utilize the computational resources, it was recommended that a number of coarse grid cases, using the PBCG method, should initially be conducted to better define the optimization problem and the design space, and obtain an improved initial shape. Subsequently, a fine grid shape optimization, which necessitates using the ADI method, should be conducted to accurately obtain the final optimized shape. The other activity during this period was the interaction with the members of the Aerodynamic and Aeroacoustic Methods Branch of Langley Research Center during one stage of their investigation to develop an adjoint-variable sensitivity method using the viscous flow equations. This method had algorithmic similarities to the variational sensitivity methods and the control-theory approach. However, unlike the prior studies, it was considered for the three-dimensional, viscous flow equations. The major accomplishment in the second period of this project (March 9, 1996 to March 8, 1997) was the extension of the shape optimization methodology for the Thin-Layer Navier-Stokes equations. Both the Euler-based and the TLNS-based analyses compared with the analyses obtained using the CFL3D code. The sensitivities, again from both levels of the flow equations, also compared very well with the finite-differenced sensitivities. A fairly large set of shape optimization cases were conducted to study a number of issues previously not well understood. The testbed for these cases was the shaping of an arrow wing in Mach 2.4 flow. All the final shapes, obtained either from a coarse-grid-based or a fine-grid-based optimization, using either a Euler-based or a TLNS-based analysis, were all re-analyzed using a fine-grid, TLNS solution for their function evaluations. This allowed for a more fair comparison of their relative merits. From the aerodynamic performance standpoint, the fine-grid TLNS-based optimization produced the best shape, and the fine-grid Euler-based optimization produced the lowest cruise efficiency.

Baysal, Oktay↗

DOE OSTI2024

Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations

Abstract In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then, we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis.

Mathematics↗

NASA NTRS1981

Verification of an acoustic transmission matrix analysis of sound propagation in a variable area duct without flow

A predicted standing wave pressure and phase angle profile for a hard wall rectangular duct with a region of converging-diverging area variation is compared to published experimental measurements in a study of sound propagation without flow. The factor of 1/2 area variation used is sufficient magnitude to produce large reflections. The prediction is based on a transmission matrix approach developed for the analysis of sound propagation in a variable area duct with and without flow. The agreement between the measured and predicted results is shown to be excellent.

Miles, J. H.↗

DOE OSTI2021

Linear convergence of accelerated conditional gradient algorithms in spaces of measures

A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional Dirac-delta functions and optimizes the corresponding coefficients. Under general assumptions, a sub-linear [see formula in PDF] rate in the objective functional is obtained, which is sharp in most cases. To improve efficiency, one can fully resolve the finite-dimensional subproblems occurring in each iteration of the method. We provide an analysis for the resulting procedure: under a structural assumption on the optimal solution, a linear [see formula in PDF] convergence rate is obtained locally.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

High‐speed 4‐dimensional scanning transmission electron microscopy using compressive sensing techniques

Abstract Here we show that compressive sensing allows 4‐dimensional (4‐D) STEM data to be obtained and accurately reconstructed with both high‐speed and reduced electron fluence. The methodology needed to achieve these results compared to conventional 4‐D approaches requires only that a random subset of probe locations is acquired from the typical regular scanning grid, which immediately generates both higher speed and the lower fluence experimentally. We also consider downsampling of the detector, showing that oversampling is inherent within convergent beam electron diffraction (CBED) patterns and that detector downsampling does not reduce precision but allows faster experimental data acquisition. Analysis of an experimental atomic resolution yttrium silicide dataset shows that it is possible to recover over 25 dB peak signal‐to‐noise ratio in the recovered phase using 0.3% of the total data. Lay abstract : Four‐dimensional scanning transmission electron microscopy (4‐D STEM) is a powerful technique for characterizing complex nanoscale structures. In this method, a convergent beam electron diffraction pattern (CBED) is acquired at each probe location during the scan of the sample. This means that a 2‐dimensional signal is acquired at each 2‐D probe location, equating to a 4‐D dataset. Despite the recent development of fast direct electron detectors, some capable of 100kHz frame rates, the limiting factor for 4‐D STEM is acquisition times in the majority of cases, where cameras will typically operate on the order of 2kHz. This means that a raster scan containing 256^2 probe locations can take on the order of 30s, approximately 100‐1000 times longer than a conventional STEM imaging technique using monolithic radial detectors. As a result, 4‐D STEM acquisitions can be subject to adverse effects such as drift, beam damage, and sample contamination. Recent advances in computational imaging techniques for STEM have allowed for faster acquisition speeds by way of acquiring only a random subset of probe locations from the field of view. By doing this, the acquisition time is significantly reduced, in some cases by a factor of 10‐100 times. The acquired data is then processed to fill‐in or inpaint the missing data, taking advantage of the inherently low‐complex signals which can be linearly combined to recover the information. In this work, similar methods are demonstrated for the acquisition of 4‐D STEM data, where only a random subset of CBED patterns are acquired over the raster scan. We simulate the compressive sensing acquisition method for 4‐D STEM and present our findings for a variety of analysis techniques such as ptychography and differential phase contrast. Our results show that acquisition times can be significantly reduced on the order of 100‐300 times, therefore improving existing frame rates, as well as further reducing the electron fluence beyond just using a faster camera.

Robinson, Alex W.↗

NASA NTRS1994

Derivation and experimental verification of clock synchronization theory

The objective of this work is to validate mathematically derived clock synchronization theories and their associated algorithms through experiment. Two theories are considered, the Interactive Convergence Clock Synchronization Algorithm and the Mid-Point Algorithm. Special clock circuitry was designed and built so that several operating conditions and failure modes (including malicious failures) could be tested. Both theories are shown to predict conservative upper bounds (i.e., measured values of clock skew were always less than the theory prediction). Insight gained during experimentation led to alternative derivations of the theories. These new theories accurately predict the clock system's behavior. It is found that a 100% penalty is paid to tolerate worst case failures. It is also shown that under optimal conditions (with minimum error and no failures) the clock skew can be as much as 3 clock ticks. Clock skew grows to 6 clock ticks when failures are present. Finally, it is concluded that one cannot rely solely on test procedures or theoretical analysis to predict worst case conditions. conditions.

INTERACTIVE CONVERGENCE CLOCK↗