Results for “Implicit” — Page 78

NASA NTRS1999

An O(Nm(sup 2)) Plane Solver for the Compressible Navier-Stokes Equations

A hierarchical multigrid algorithm for efficient steady solutions to the two-dimensional compressible Navier-Stokes equations is developed and demonstrated. The algorithm applies multigrid in two ways: a Full Approximation Scheme (FAS) for a nonlinear residual equation and a Correction Scheme (CS) for a linearized defect correction implicit equation. Multigrid analyses which include the effect of boundary conditions in one direction are used to estimate the convergence rate of the algorithm for a model convection equation. Three alternating-line- implicit algorithms are compared in terms of efficiency. The analyses indicate that full multigrid efficiency is not attained in the general case; the number of cycles to attain convergence is dependent on the mesh density for high-frequency cross-stream variations. However, the dependence is reasonably small and fast convergence is eventually attained for any given frequency with either the FAS or the CS scheme alone. The paper summarizes numerical computations for which convergence has been attained to within truncation error in a few multigrid cycles for both inviscid and viscous ow simulations on highly stretched meshes.

Thomas, J. L.↗

NASA NTRS1997

Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids

An implicit code for computing inviscid and viscous incompressible flows on unstructured grids is described. The foundation of the code is a backward Euler time discretization for which the linear system is approximately solved at each time step with either a point implicit method or a preconditioned Generalized Minimal Residual (GMRES) technique. For the GMRES calculations, several techniques are investigated for forming the matrix-vector product. Convergence acceleration is achieved through a multigrid scheme that uses non-nested coarse grids that are generated using a technique described in the present paper. Convergence characteristics are investigated and results are compared with an exact solution for the inviscid flow over a four-element airfoil. Viscous results, which are compared with experimental data, include the turbulent flow over a NACA 4412 airfoil, a three-element airfoil for which Mach number effects are investigated, and three-dimensional flow over a wing with a partial-span flap.

Anderson, W. Kyle↗

NASA NTRS1993

Three Dimensional Aerodynamic Analysis of a High-Lift Transport Configuration

Two computational methods, a surface panel method and an Euler method employing unstructured grid methodology, were used to analyze a subsonic transport aircraft in cruise and high-lift conditions. The computational results were compared with two separate sets of flight data obtained for the cruise and high-lift configurations. For the cruise configuration, the surface pressures obtained by the panel method and the Euler method agreed fairly well with results from flight test. However, for the high-lift configuration considerable differences were observed when the computational surface pressures were compared with the results from high-lift flight test. On the lower surface of all the elements with the exception of the slat, both the panel and Euler methods predicted pressures which were in good agreement with flight data. On the upper surface of all the elements the panel method predicted slightly higher suction compared to the Euler method. On the upper surface of the slat, pressure coefficients obtained by both the Euler and panel methods did not agree with the results of the flight tests. A sensitivity study of the upward deflection of the slat from the 40 deg. flap setting suggested that the differences in the slat deflection between the computational model and the flight configuration could be one of the sources of this discrepancy. The computation time for the implicit version of the Euler code was about 1/3 the time taken by the explicit version though the implicit code required 3 times the memory taken by the explicit version.

Dodbele, Simha S.↗

NASA NTRS2004

Systematic Errors in Stereo PIV When Imaging through a Glass Window

This document assesses the magnitude of velocity measurement errors that may arise when performing stereo particle image velocimetry (PIV) with cameras viewing through thick, refractive window and where the calibration is performed in one plane only. The effect of the window is to introduce a refractive error that increases with window thickness and the camera angle of incidence. The calibration should be performed while viewing through the test section window, otherwise a potentially significant error may be introduced that affects each velocity component differently. However, even when the calibration is performed correctly, another error may arise during the stereo reconstruction if the perspective angle determined for each camera does not account for the displacement of the light rays as they refract through the thick window. Care should be exercised when applying in a single-plane calibration since certain implicit assumptions may in fact require conditions that are extremely difficult to meet in a practical laboratory environment. It is suggested that the effort expended to ensure this accuracy may be better expended in performing a more lengthy volumetric calibration procedure, which does not rely upon the assumptions implicit in the single plane method and avoids the need for the perspective angle to be calculated.

Green, Richard↗

NASA NTRS2006

Convergence Acceleration for Multistage Time-Stepping Schemes

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK scheme is reduced at least a factor of four.

Swanson, R. C.↗

NASA NTRS2006

Precision of Sensitivity in the Design Optimization of Indeterminate Structures

Design sensitivity is central to most optimization methods. The analytical sensitivity expression for an indeterminate structural design optimization problem can be factored into a simple determinate term and a complicated indeterminate component. Sensitivity can be approximated by retaining only the determinate term and setting the indeterminate factor to zero. The optimum solution is reached with the approximate sensitivity. The central processing unit (CPU) time to solution is substantially reduced. The benefit that accrues from using the approximate sensitivity is quantified by solving a set of problems in a controlled environment. Each problem is solved twice: first using the closed-form sensitivity expression, then using the approximation. The problem solutions use the CometBoards testbed as the optimization tool with the integrated force method as the analyzer. The modification that may be required, to use the stiffener method as the analysis tool in optimization, is discussed. The design optimization problem of an indeterminate structure contains many dependent constraints because of the implicit relationship between stresses, as well as the relationship between the stresses and displacements. The design optimization process can become problematic because the implicit relationship reduces the rank of the sensitivity matrix. The proposed approximation restores the full rank and enhances the robustness of the design optimization method.

Patnaik, Surya N.↗

NASA NTRS2006

Solver and Turbulence Model Upgrades to OVERFLOW 2 for Unsteady and High-Speed Applications

An implicit unfactored SSOR algorithm has been added to the overset Navier-Stokes CFD code OVERFLOW 2 for unsteady and moving body applications. The HLLEM and HLLC third-order spatial upwind convective flux models have been added for high-speed flow applications. A generalized upwind transport equation has been added for solution of the two-equation turbulence models and the species equations. The generalized transport equation is solved using an unfactored SSOR implicit algorithm. Three hybrid RANS/DES turbulence models have been added for unsteady flow applications. Wall function boundary conditions that include compressibility and heat transfer effects have been also been added to OVERFLOW 2.

Nichols, Robert H.↗

NASA NTRS2008

Mergers of Non-spinning Black-hole Binaries: Gravitational Radiation Characteristics

We present a detailed descriptive analysis of the gravitational radiation from black-hole binary mergers of non-spinning black holes, based on numerical simulations of systems varying from equal-mass to a 6:1 mass ratio. Our primary goal is to present relatively complete information about the waveforms, including all the leading multipolar components, to interested researchers. In our analysis, we pursue the simplest physical description of the dominant features in the radiation, providing an interpretation of the waveforms in terms of an implicit rotating source. This interpretation applies uniformly to the full wavetrain, from inspiral through ringdown. We emphasize strong relationships among the l = m modes that persist through the full wavetrain. Exploring the structure of the waveforms in more detail, we conduct detailed analytic fitting of the late-time frequency evolution, identifying a key quantitative feature shared by the l = m modes among all mass-ratios. We identify relationships, with a simple interpretation in terms of the implicit rotating source, among the evolution of frequency and amplitude, which hold for the late-time radiation. These detailed relationships provide sufficient information about the late-time radiation to yield a predictive model for the late-time waveforms, an alternative to the common practice of modeling by a sum of quasinormal mode overtones. We demonstrate an application of this in a new effective-one-body-based analytic waveform model.

Baker, John G.↗

NASA NTRS2008

A Formal Framework for the Analysis of Algorithms That Recover From Loss of Separation

We present a mathematical framework for the specification and verification of state-based conflict resolution algorithms that recover from loss of separation. In particular, we propose rigorous definitions of horizontal and vertical maneuver correctness that yield horizontal and vertical separation, respectively, in a bounded amount of time. We also provide sufficient conditions for independent correctness, i.e., separation under the assumption that only one aircraft maneuvers, and for implicitly coordinated correctness, i.e., separation under the assumption that both aircraft maneuver. An important benefit of this approach is that different aircraft can execute different algorithms and implicit coordination will still be achieved, as long as they all meet the explicit criteria of the framework. Towards this end we have sought to make the criteria as general as possible. The framework presented in this paper has been formalized and mechanically verified in the Prototype Verification System (PVS).

Butler, RIcky W.↗

NASA NTRS2009

Formally Verified Practical Algorithms for Recovery from Loss of Separation

In this paper, we develop and formally verify practical algorithms for recovery from loss of separation. The formal verification is performed in the context of a criteria-based framework. This framework provides rigorous definitions of horizontal and vertical maneuver correctness that guarantee divergence and achieve horizontal and vertical separation. The algorithms are shown to be independently correct, that is, separation is achieved when only one aircraft maneuvers, and implicitly coordinated, that is, separation is also achieved when both aircraft maneuver. In this paper we improve the horizontal criteria over our previous work. An important benefit of the criteria approach is that different aircraft can execute different algorithms and implicit coordination will still be achieved, as long as they all meet the explicit criteria of the framework. Towards this end we have sought to make the criteria as general as possible. The framework presented in this paper has been formalized and mechanically verified in the Prototype Verification System (PVS).

Butler, Ricky W.↗

NASA NTRS2009

Multiscale Failure Analysis of Laminated Composite Panels Subjected to Blast Loading Using FEAMAC/Explicit

This preliminary report demonstrates the capabilities of the recently developed software implementation that links the Generalized Method of Cells to explicit finite element analysis by extending a previous development which tied the generalized method of cells to implicit finite elements. The multiscale framework, which uses explicit finite elements at the global-scale and the generalized method of cells at the microscale is detailed. This implementation is suitable for both dynamic mechanics problems and static problems exhibiting drastic and sudden changes in material properties, which often encounter convergence issues with commercial implicit solvers. Progressive failure analysis of stiffened and un-stiffened fiber-reinforced laminates subjected to normal blast pressure loads was performed and is used to demonstrate the capabilities of this framework. The focus of this report is to document the development of the software implementation; thus, no comparison between the results of the models and experimental data is drawn. However, the validity of the results are assessed qualitatively through the observation of failure paths, stress contours, and the distribution of system energies.

Pineda, Evan J.↗

NASA NTRS2010

Ablation, Thermal Response, and Chemistry Program for Analysis of Thermal Protection Systems

In previous work, the authors documented the Multicomponent Ablation Thermochemistry (MAT) and Fully Implicit Ablation and Thermal response (FIAT) programs. In this work, key features from MAT and FIAT were combined to create the new Fully Implicit Ablation, Thermal response, and Chemistry (FIATC) program. FIATC is fully compatible with FIAT (version 2.5) but has expanded capabilities to compute the multispecies surface chemistry and ablation rate as part of the surface energy balance. This new methodology eliminates B' tables, provides blown species fractions as a function of time, and enables calculations that would otherwise be impractical (e.g. 4+ dimensional tables) such as pyrolysis and ablation with kinetic rates or unequal diffusion coefficients. Equations and solution procedures are presented, then representative calculations of equilibrium and finite-rate ablation in flight and ground-test environments are discussed.

Milos, Frank S.↗

NASA NTRS2012

Smart Composite Overwrapped Pressure Vessel - Integrated Structural Health Monitoring System to Meet Space Exploration and International Space Station Mission Assurance Needs

Currently there are no integrated NDE methods for baselining and monitoring defect levels in fleet for Composite Overwrapped Pressure Vessels (COPVs) or related fracture critical composites, or for performing life-cycle maintenance inspections either in a traditional remove-and-inspect mode or in a more modern in situ inspection structural health monitoring (SHM) mode. Implicit in SHM and autonomous inspection is the existence of quantitative accept-reject criteria. To be effective, these criteria must correlate with levels of damage known to cause composite failure. Furthermore, implicit in SHM is the existence of effective remote sensing hardware and automated techniques and algorithms for interpretation of SHM data. SHM of facture critical composite structures, especially high pressure COPVs, is critical to the success of nearly every future NASA space exploration program as well as life extension of the International Space Station. It has been clearly stated that future NASA missions may not be successful without SHM [1]. Otherwise, crews will be busy addressing subsystem health issues and not focusing on the real NASA mission

Saulsberry, Regor↗

NASA NTRS2013

The Chorus Conflict and Loss of Separation Resolution Algorithms

The Chorus software is designed to investigate near-term, tactical conflict and loss of separation detection and resolution concepts for air traffic management. This software is currently being used in two different problem domains: en-route self- separation and sense and avoid for unmanned aircraft systems. This paper describes the core resolution algorithms that are part of Chorus. The combination of several features of the Chorus program distinguish this software from other approaches to conflict and loss of separation resolution. First, the program stores a history of state information over time which enables it to handle communication dropouts and take advantage of previous input data. Second, the underlying conflict algorithms find resolutions that solve the most urgent conflict, but also seek to prevent secondary conflicts with the other aircraft. Third, if the program is run on multiple aircraft, and the two aircraft maneuver at the same time, the result will be implicitly co-ordinated. This implicit coordination property is established by ensuring that a resolution produced by Chorus will comply with a mathematically-defined criteria whose correctness has been formally verified. Fourth, the program produces both instantaneous solutions and kinematic solutions, which are based on simple accel- eration models. Finally, the program provides resolutions for recovery from loss of separation. Different versions of this software are implemented as Java and C++ software programs, respectively.

Butler, Ricky W.↗

NASA NTRS2014

Human-Robot Interaction Directed Research Project

Human-robot interaction (HRI) is a discipline investigating the factors affecting the interactions between humans and robots. It is important to evaluate how the design of interfaces and command modalities affect the human's ability to perform tasks accurately, efficiently, and effectively when working with a robot. By understanding the effects of interface design on human performance, workload, and situation awareness, interfaces can be developed to appropriately support the human in performing tasks with minimal errors and with appropriate interaction time and effort. Thus, the results of research on human-robot interfaces have direct implications for the design of robotic systems. This DRP concentrates on three areas associated with interfaces and command modalities in HRI which are applicable to NASA robot systems: 1) Video Overlays, 2) Camera Views, and 3) Command Modalities. The first study focused on video overlays that investigated how Augmented Reality (AR) symbology can be added to the human-robot interface to improve teleoperation performance. Three types of AR symbology were explored in this study, command guidance (CG), situation guidance (SG), and both (SCG). CG symbology gives operators explicit instructions on what commands to input, whereas SG symbology gives operators implicit cues so that operators can infer the input commands. The combination of CG and SG provided operators with explicit and implicit cues allowing the operator to choose which symbology to utilize. The objective of the study was to understand how AR symbology affects the human operator's ability to align a robot arm to a target using a flight stick and the ability to allocate attention between the symbology and external views of the world. The study evaluated the effects type of symbology (CG and SG) has on operator tasks performance and attention allocation during teleoperation of a robot arm. The second study expanded on the first study by evaluating the effects of the type of navigational guidance (CG and SG) on operator task performance and attention allocation during teleoperation of a robot arm through uplinked commands. Although this study complements the first study on navigational guidance with hand controllers, it is a separate investigation due to the distinction in intended operators (i.e., crewmembers versus ground-operators). A third study looked at superimposed and integrated overlays for teleoperation of a mobile robot using a hand controller. When AR is superimposed on the external world, it appears to be fixed onto the display and internal to the operators' workstation. Unlike superimposed overlays, integrated overlays often appear as three-dimensional objects and move as if part of the external world. Studies conducted in the aviation domain show that integrated overlays can improve situation awareness and reduce the amount of deviation from the optimal path. The purpose of the study was to investigate whether these results apply to HRI tasks, such as navigation with a mobile robot. HRP GAPS This HRI research contributes to closure of HRP gaps by providing information on how display and control characteristics - those related to guidance, feedback, and command modalities - affect operator performance. The overarching goals are to improve interface usability, reduce operator error, and develop candidate guidelines to design effective human-robot interfaces.

Sandor, Aniko↗

NASA NTRS2014

Human-Robot Interaction Directed Research Project

Human-robot interaction (HRI) is a discipline investigating the factors affecting the interactions between humans and robots. It is important to evaluate how the design of interfaces and command modalities affect the human's ability to perform tasks accurately, efficiently, and effectively when working with a robot. By understanding the effects of interface design on human performance, workload, and situation awareness, interfaces can be developed to appropriately support the human in performing tasks with minimal errors and with appropriate interaction time and effort. Thus, the results of research on human-robot interfaces have direct implications for the design of robotic systems. This DRP concentrates on three areas associated with interfaces and command modalities in HRI which are applicable to NASA robot systems: 1) Video Overlays, 2) Camera Views, and 3) Command Modalities. The first study focused on video overlays that investigated how Augmented Reality (AR) symbology can be added to the human-robot interface to improve teleoperation performance. Three types of AR symbology were explored in this study, command guidance (CG), situation guidance (SG), and both (SCG). CG symbology gives operators explicit instructions on what commands to input, whereas SG symbology gives operators implicit cues so that operators can infer the input commands. The combination of CG and SG provided operators with explicit and implicit cues allowing the operator to choose which symbology to utilize. The objective of the study was to understand how AR symbology affects the human operator's ability to align a robot arm to a target using a flight stick and the ability to allocate attention between the symbology and external views of the world. The study evaluated the effects type of symbology (CG and SG) has on operator tasks performance and attention allocation during teleoperation of a robot arm. The second study expanded on the first study by evaluating the effects of the type of navigational guidance (CG and SG) on operator task performance and attention allocation during teleoperation of a robot arm through uplinked commands. Although this study complements the first study on navigational guidance with hand controllers, it is a separate investigation due to the distinction in intended operators (i.e., crewmembers versus ground-operators). A third study looked at superimposed and integrated overlays for teleoperation of a mobile robot using a hand controller. When AR is superimposed on the external world, it appears to be fixed onto the display and internal to the operators' workstation. Unlike superimposed overlays, integrated overlays often appear as three-dimensional objects and move as if part of the external world. Studies conducted in the aviation domain show that integrated overlays can improve situation awareness and reduce the amount of deviation from the optimal path. The purpose of the study was to investigate whether these results apply to HRI tasks, such as navigation with a mobile robot.

Sandor, Aniko↗

NASA NTRS2013

Design of a Variational Multiscale Method for Turbulent Compressible Flows

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

Design↗

NASA NTRS2014

Physics Based Model for Cryogenic Chilldown and Loading. Part I: Algorithm

We report the progress in the development of the physics based model for cryogenic chilldown and loading. The chilldown and loading is model as fully separated non-equilibrium two-phase flow of cryogenic fluid thermally coupled to the pipe walls. The solution follow closely nearly-implicit and semi-implicit algorithms developed for autonomous control of thermal-hydraulic systems developed by Idaho National Laboratory. A special attention is paid to the treatment of instabilities. The model is applied to the analysis of chilldown in rapid loading system developed at NASA-Kennedy Space Center. The nontrivial characteristic feature of the analyzed chilldown regime is its active control by dump valves. The numerical predictions are in reasonable agreement with the experimental time traces. The obtained results pave the way to the development of autonomous loading operation on the ground and space.

heat transfer↗