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NASA NTRSDate not supplied

High-Order Shock Fitting with Finite Element Methods

A moving-grid, shock-tracking, finite element method has been implemented that can achieve high-order accuracy for flow simulations with shocks. In this approach, element edges in the computational mesh are fitted to the shock front and moved with the shock throughout the simulation. The Euler equations are solved on the moving mesh in an arbitrary Lagrangian-Eulerian framework. Three different methods for specifying the shock motion have been tested,and the order of accuracy of the resulting solutions was verified. It was found that one of the methods is applicable only for problems with a constant upstream flow state, whereas the other two methods converge to the expected solution for general shock problems. When using a finite element method with polynomial degree p, the two general shock motion methods converged with the expected order of accuracy of (p+1). Finally, accurate solutions are obtained for supersonic nozzle and blunt body bow shock problems. Based on the results, it is concluded that the shock tracking method can preserve high-order solution accuracy in the vicinity of a shock wave.

Luke D'Aquila↗
NASA NTRS1997

The Reduction of Ducted Fan Engine Noise Via A Boundary Integral Equation Method

The development of a Boundary Integral Equation Method (BIEM) for the prediction of ducted fan engine noise is discussed. The method is motivated by the need for an efficient and versatile computational tool to assist in parametric noise reduction studies. In this research, the work in reference 1 was extended to include passive noise control treatment on the duct interior. The BEM considers the scattering of incident sound generated by spinning point thrust dipoles in a uniform flow field by a thin cylindrical duct. The acoustic field is written as a superposition of spinning modes. Modal coefficients of acoustic pressure are calculated term by term. The BEM theoretical framework is based on Helmholtz potential theory. A boundary value problem is converted to a boundary integral equation formulation with unknown single and double layer densities on the duct wall. After solving for the unknown densities, the acoustic field is easily calculated. The main feature of the BIEM is the ability to compute any portion of the sound field without the need to compute the entire field. Other noise prediction methods such as CFD and Finite Element methods lack this property. Additional BIEM attributes include versatility, ease of use, rapid noise predictions, coupling of propagation and radiation both forward and aft, implementable on midrange personal computers, and valid over a wide range of frequencies.

Tweed, J.↗
NASA NTRS2003

Toward Immersed Boundary Simulation of High Reynolds Number Flows

In the immersed boundary (IB) method, the surface of an object is reconstructed with forcing terms in the underlying flow field equations. The surface may split a computational cell removing the constraint of the near wall gridlines to be aligned with the surface. This feature greatly simplifies the grid generation process which is cumbersome and expensive in particular for structured grids and complex geometries. The IB method is ideally suited for Cartesian flow solvers. The flow equations written in Cartesian coordinates appear in a very simple form and several numerical algorithms can be used for an efficient solution of the equations. In addition, the accuracy of numerical algorithms is dependent on the underlying grid and it usually deteriorates when the grid deviates from a Cartesian mesh. The challenge for the IB method lies in the representation of the wall boundaries and in providing an adequate near wall flow field resolution. The issue of enforcing no-slip boundary conditions at the immersed surface has been addressed by several authors by imposing a local reconstruction of the solution. Initial work by Verzicco et al. was based on a simple linear, one-dimensional operator and this approach proved to be accurate for boundaries largely aligned with the grid lines. Majumdar et al. used various multidimensional and high order polynomial interpolations schemes. These high order schemes, however, are keen to introduce wiggles and spurious extrema. Iaccarino & Verzicco and Kalitzin & Iaccarino proposed a tri-linear reconstruction for the velocity components and the turbulent scalars. A modified implementation that has proven to be more robust is reported in this paper. The issue of adequate near wall resolution in a Cartesian framework can initially be addressed by using a non-uniform mesh which is stretched near the surface. In this paper, we investigate an unstructured approach for local grid refinement that utilizes Cartesian mesh features. The computation of high Reynolds number wall bounded flows is particularly challenging as it requires the consideration of thin turbulent boundary layers, i.e. near wall regions with large gradients of the flow field variables. For such flows, the representation of the wall boundary has a large impact on the accuracy of the computation. It is also critical for the robustness and convergence of the flow solver.

Kalitzin, Georgi↗
NASA NTRS2005

Creating Communications, Computing, and Networking Technology Development Road Maps for Future NASA Human and Robotic Missions

For human and robotic exploration missions in the Vision for Exploration, roadmaps are needed for capability development and investments based on advanced technology developments. A roadmap development process was undertaken for the needed communications, and networking capabilities and technologies for the future human and robotics missions. The underlying processes are derived from work carried out during development of the future space communications architecture, an d NASA's Space Architect Office (SAO) defined formats and structures for accumulating data. Interrelationships were established among emerging requirements, the capability analysis and technology status, and performance data. After developing an architectural communications and networking framework structured around the assumed needs for human and robotic exploration, in the vicinity of Earth, Moon, along the path to Mars, and in the vicinity of Mars, information was gathered from expert participants. This information was used to identify the capabilities expected from the new infrastructure and the technological gaps in the way of obtaining them. We define realistic, long-term space communication architectures based on emerging needs and translate the needs into interfaces, functions, and computer processing that will be required. In developing our roadmapping process, we defined requirements for achieving end-to-end activities that will be carried out by future NASA human and robotic missions. This paper describes: 10 the architectural framework developed for analysis; 2) our approach to gathering and analyzing data from NASA, industry, and academia; 3) an outline of the technology research to be done, including milestones for technology research and demonstrations with timelines; and 4) the technology roadmaps themselves.

Bhasin, Kul↗
NASA NTRS1973

Application of the generalized Galerkin method to the computation of fluid flows.

The purpose of this paper is to show that most existing methods for the calculation of fluid flows can be interpreted as special applications of a single mathematical formalism. This formalism, called the generalized Galerkin method, then provides a single conceptual framework for comparing various methods in terms of convergence and accuracy. The method is presented in sufficient mathematical detail to permit its interpretation as a projection in function space. In order to demonstrate the basic thesis, finite difference, finite element, strip integral, and classical integral methods of boundary layer theory are developed by application of the method.

Murphy, J. D.↗
NASA NTRS2018

Advanced Analytics and Big Earth Data

NASA's Earth Science Data Systems process, archive and distribute petabytes of Earth Observation data to a variety of end users. These end users will face dramatically increased data size in the near future, bringing about new challenges and opportunities in analyzing those data. One area of particular ferment currently is Machine Learning. Many Machine Learning methods are black boxes, limiting direct insight into the data's properties. However, they can be used for a variety of data enhancement purposes, such as parameter retrieval, data fusion and image classification and segmentation. The Earth Observing System Data and Information System is also evolving to host large data volumes in the cloud, enabling data proximal analysis. As part of this effort, an Analytics framework is being developed to support and enhance user analysis of the data. By using standards based services in the framework, diverse user communities can be served, while also allowing inter-system collaboration in the analysis process.

Cloud Computing↗
NASA NTRS2022

A Framework for Deep Learning Emulation of Numerical Models With a Case Study in Satellite Remote Sensing

Numerical models based on physics represent the state of the art in Earth system modeling and comprise our best tools for generating insights and predictions. Despite rapid growth in computational power, the perceived need for higher model resolutions overwhelms the latest generation computers, reducing the ability of modelers to generate simulations for understanding parameter sensitivities and characterizing variability and uncertainty. Thus, surrogate models are often developed to capture the essential attributes of the full-blown numerical models. Recent successes of machine learning methods, especially deep learning (DL), across many disciplines offer the possibility that complex nonlinear connectionist representations may be able to capture the underlying complex structures and nonlinear processes in Earth systems. A difficult test for DL-based emulation, which refers to function approximation of numerical models, is to understand whether they can be comparable to traditional forms of surrogate models in terms of computational efficiency while simultaneously reproducing model results in a credible manner. A DL emulation that passes this test may be expected to perform even better than simple models with respect to capturing complex processes and spatiotemporal dependencies. Here, we examine, with a case study in satellite-based remote sensing, the hypothesis that DL approaches can credibly represent the simulations from a surrogate model with comparable computational efficiency. Our results are encouraging in that the DL emulation reproduces the results with acceptable accuracy and often even faster performance. We discuss the broader implications of our results in light of the pace of improvements in high-performance implementations of DL and the growing desire for higher resolution simulations in the Earth sciences.

Bayesian Deep Learning↗
NASA NTRS1995

Structural design using equilibrium programming formulations

Solutions to increasingly larger structural optimization problems are desired. However, computational resources are strained to meet this need. New methods will be required to solve increasingly larger problems. The present approaches to solving large-scale problems involve approximations for the constraints of structural optimization problems and/or decomposition of the problem into multiple subproblems that can be solved in parallel. An area of game theory, equilibrium programming (also known as noncooperative game theory), can be used to unify these existing approaches from a theoretical point of view (considering the existence and optimality of solutions), and be used as a framework for the development of new methods for solving large-scale optimization problems. Equilibrium programming theory is described, and existing design techniques such as fully stressed design and constraint approximations are shown to fit within its framework. Two new structural design formulations are also derived. The first new formulation is another approximation technique which is a general updating scheme for the sensitivity derivatives of design constraints. The second new formulation uses a substructure-based decomposition of the structure for analysis and sensitivity calculations. Significant computational benefits of the new formulations compared with a conventional method are demonstrated.

Scotti, Stephen J.↗
NASA NTRS1968

Computer program performs stiffness matrix structural analysis

Computer program generates the stiffness matrix for a particular type of structure from geometrical data, and performs static and normal mode analyses. It requires the structure to be modeled as a stable framework of uniform, weightless members, and joints at which loads are applied and weights are lumped.

Bamford, R.↗
NASA NTRS1993

On the design of fault-tolerant robotic manipulator systems

Robotic systems are finding increasing use in space applications. Many of these devices are going to be operational on board the Space Station Freedom. Fault tolerance has been deemed necessary because of the criticality of the tasks and the inaccessibility of the systems to maintenance and repair. Design for fault tolerance in manipulator systems is an area within robotics that is without precedence in the literature. In this paper, we will attempt to lay down the foundations for such a technology. Design for fault tolerance demands new and special approaches to design, often at considerable variance from established design practices. These design aspects, together with reliability evaluation and modeling tools, are presented. Mechanical architectures that employ protective redundancies at many levels and have a modular architecture are then studied in detail. Once a mechanical architecture for fault tolerance has been derived, the chronological stages of operational fault tolerance are investigated. Failure detection, isolation, and estimation methods are surveyed, and such methods for robot sensors and actuators are derived. Failure recovery methods are also presented for each of the protective layers of redundancy. Failure recovery tactics often span all of the layers of a control hierarchy. Thus, a unified framework for decision-making and control, which orchestrates both the nominal redundancy management tasks and the failure management tasks, has been derived. The well-developed field of fault-tolerant computers is studied next, and some design principles relevant to the design of fault-tolerant robot controllers are abstracted. Conclusions are drawn, and a road map for the design of fault-tolerant manipulator systems is laid out with recommendations for a 10 DOF arm with dual actuators at each joint.

Tesar, Delbert↗
NASA NTRS1999

Advanced Multigrid Solvers for Fluid Dynamics

The main objective of this project has been to support the development of multigrid techniques in computational fluid dynamics that can achieve "textbook multigrid efficiency" (TME), which is several orders of magnitude faster than current industrial CFD solvers. Toward that goal we have assembled a detailed table which lists every foreseen kind of computational difficulty for achieving it, together with the possible ways for resolving the difficulty, their current state of development, and references. We have developed several codes to test and demonstrate, in the framework of simple model problems, several approaches for overcoming the most important of the listed difficulties that had not been resolved before. In particular, TME has been demonstrated for incompressible flows on one hand, and for near-sonic flows on the other hand. General approaches were advanced for the relaxation of stagnation points and boundary conditions under various situations. Also, new algebraic multigrid techniques were formed for treating unstructured grid formulations. More details on all these are given below.

Brandt, Achi↗
NASA NTRS1998

Initial Results of an MDO Method Evaluation Study

The NASA Langley MDO method evaluation study seeks to arrive at a set of guidelines for using promising MDO methods by accumulating and analyzing computational data for such methods. The data are collected by conducting a series of re- producible experiments. In the first phase of the study, three MDO methods were implemented in the SIGHT: framework and used to solve a set of ten relatively simple problems. In this paper, we comment on the general considerations for conducting method evaluation studies and report some initial results obtained to date. In particular, although the results are not conclusive because of the small initial test set, other formulations, optimality conditions, and sensitivity of solutions to various perturbations. Optimization algorithms are used to solve a particular MDO formulation. It is then appropriate to speak of local convergence rates and of global convergence properties of an optimization algorithm applied to a specific formulation. An analogous distinction exists in the field of partial differential equations. On the one hand, equations are analyzed in terms of regularity, well-posedness, and the existence and unique- ness of solutions. On the other, one considers numerous algorithms for solving differential equations. The area of MDO methods studies MDO formulations combined with optimization algorithms, although at times the distinction is blurred. It is important to

Alexandrov, Natalia M.↗
NASA NTRS2008

A Multi-Scale Modeling System with Unified Physics

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 km, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. In recent years, exponentially increasing computer power has extended cloud-resolving-mode1 integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-km scales are resolved in horizontal domains as large as 10,000 km in two-dimensions, and 1,000 x 1,000 km2 in three-dimensions. Cloud resolving models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique.

Tao, Wei-Kuo↗
NASA NTRS2009

A Framework for Parallel Unstructured Grid Generation for Complex Aerodynamic Simulations

A framework for parallel unstructured grid generation targeting both shared memory multi-processors and distributed memory architectures is presented. The two fundamental building-blocks of the framework consist of: (1) the Advancing-Partition (AP) method used for domain decomposition and (2) the Advancing Front (AF) method used for mesh generation. Starting from the surface mesh of the computational domain, the AP method is applied recursively to generate a set of sub-domains. Next, the sub-domains are meshed in parallel using the AF method. The recursive nature of domain decomposition naturally maps to a divide-and-conquer algorithm which exhibits inherent parallelism. For the parallel implementation, the Master/Worker pattern is employed to dynamically balance the varying workloads of each task on the set of available CPUs. Performance results by this approach are presented and discussed in detail as well as future work and improvements.

Zagaris, George↗
NASA NTRS2013

Space Data Systems Applications in the iPAS Pathfinder Laboratory

The iPAS is an integrated hardware/software test and evaluation environment, in support of current and future spacecraft development The iPAS has two main elements. A common avionics, hardware, and software architecture that can be applied over various missions. A common testbed framework that supports integrated hardware/software testing for a variety of applications. The iPAS includes the following (non-flight qualified) components: Core Flight Software (from GSFC). Commercially available Proton and S950 Flight Computer boards. Power and propulsion systems based on representative flight hardware. A realistic flight deck based on the Multi-Purpose Crew Vehicle (MPCV), including realistic flight controls and displays. A Space Data System based on CCSDS protocols.

Rich, Tom↗
NASA NTRS2016

Real-Time Safety Monitoring and Prediction for the National Airspace System

As new operational paradigms and additional aircraft are being introduced into the National Airspace System (NAS), maintaining safety in such a rapidly growing environment becomes more challenging. It is therefore desirable to have both an overview of the current safety of the airspace at different levels of granularity, as well an understanding of how the state of the safety will evolve into the future given the anticipated flight plans, weather forecasts, predicted health of assets in the airspace, and so on. To this end, we have developed a Real-Time Safety Monitoring (RTSM) that first, estimates the state of the NAS using the dynamic models. Then, given the state estimate and a probability distribution of future inputs to the NAS, the framework predicts the evolution of the NAS, i.e., the future state, and analyzes these future states to predict the occurrence of unsafe events. The entire probability distribution of airspace safety metrics is computed, not just point estimates, without significant assumptions regarding the distribution type and or parameters. We demonstrate our overall approach by predicting the occurrence of some unsafe events and show how these predictions evolve in time as flight operations progress.

National Airspace System↗
NASA NTRS2016

Investigating Global Ion and Neutral Atom Populations with IBEX and Voyager

The main objective of this project was to investigate pickup ion (PUI) production in the solar wind and heliosheath (the region between the termination shock and the heliopause) and compute the distributed energetic neutral atom fluxes throughout the helioshpere. The simulations were constrained by comparing the model output against observations from Ulysses, New Horizons, Voyager 1 and 2, and IBEX space probes. As evidenced by the number of peer reviewed journal publications resulting from the project (13 plus three submitted) and their citation rate (156 citations over three years), the project has made a lasting contribution to the field. The outcome is a significant improvement of our understanding of the pickup ion production and distribution in the distant heliosphere. The team has accomplished the entire set of tasks A-H set forth in the proposal. Namely, the transport modeling framework has been augmented with two populations of pickup ions (PUIs), the boundary conditions for the plasma and interstellar neutral hydrogen were verified against Ulysses and New Horizons PUI and an optimal set of velocity diffusion parameters established. The multi-component fluxes of PUIs were computed and isotropic velocity distributions generated for each cell in the computer simulation that covered the heliosphere from 1.5 AU to the heliopause. The distributions were carefully compared with in situ measurements at 3 AU (Ulysses), 12 AU (New Horizons), and 80-90 AU (Voyager 1 and 2) as well as those inferred from ENA fluxes measured by Cassini and IBEX (Wu et al., 2016). Some examples of modeldata comparison are shown in Figure 1. We have used coupled MHD-plasma and kinetic-neutral code to investigate the likely range of plasma and magnetic field parameters in the local interstellar medium (LISM), based on the assumption that the shape of the IBEX ribbon could be used to determine the orientation of the interstellar magnetic field. While the magnetic field is believed to be oriented toward the center of the ribbon, constraining its strength requires comparing the model-predicted angular diameter and circularity of the ribbon with the observations. The study, published in Heerikhuisen et al. (2014), found that the most likely range for the LISM magnetic field strength is between 0.2 and 0.3 nT, which is less than previously thought. Figure 2 shows the IBEX data (left) and compares it to the simulation with a 0.2 nT interstellar magnetic field (center) and a 0.4 nT (right).

Florinski, Vladimir↗
NASA NTRS1999

Feasibility of Decentralized Linear-Quadratic-Gaussian Control of Autonomous Distributed Spacecraft

A distributed satellite formation, modeled as an arbitrary number of fully connected nodes in a network, could be controlled using a decentralized controller framework that distributes operations in parallel over the network. For such problems, a solution that minimizes data transmission requirements, in the context of linear-quadratic-Gaussian (LQG) control theory, was given by Speyer. This approach is advantageous because it is non-hierarchical, detected failures gracefully degrade system performance, fewer local computations are required than for a centralized controller, and it is optimal with respect to the standard LQG cost function. Disadvantages of the approach are the need for a fully connected communications network, the total operations performed over all the nodes are greater than for a centralized controller, and the approach is formulated for linear time-invariant systems. To investigate the feasibility of the decentralized approach to satellite formation flying, a simple centralized LQG design for a spacecraft orbit control problem is adapted to the decentralized framework. The simple design uses a fixed reference trajectory (an equatorial, Keplerian, circular orbit), and by appropriate choice of coordinates and measurements is formulated as a linear time-invariant system.

Carpenter, J. Russell↗