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NASA NTRS2013

Tethered Satellites as Enabling Platforms for an Operational Space Weather Monitoring System

Space weather nowcasting and forecasting models require assimilation of near‐real time (NRT) space environment data to improve the precision and accuracy of operational products. Typically, these models begin with a climatological model to provide "most probable distributions" of environmental parameters as a function of time and space. The process of NRT data assimilation gently pulls the climate model closer toward the observed state (e.g. via Kalman smoothing) for nowcasting, and forecasting is achieved through a set of iterative physics‐based forward‐prediction calculations. The issue of required space weather observatories to meet the spatial and temporal requirements of these models is a complex one, and we do not address that with this poster. Instead, we present some examples of how tethered satellites can be used to address the shortfalls in our ability to measure critical environmental parameters necessary to drive these space weather models. Examples include very long baseline electric field measurements, magnetized ionospheric conductivity measurements, and the ability to separate temporal from spatial irregularities in environmental parameters. Tethered satellite functional requirements will be presented for each space weather parameter considered in this study.

Krause, L. Habash↗

NASA NTRS2013

Tethered Satellites as an Enabling Platform for Operational Space Weather Monitoring Systems

Tethered satellites offer the potential to be an important enabling technology to support operational space weather monitoring systems. Space weather "nowcasting" and forecasting models rely on assimilation of near-real-time (NRT) space environment data to provide warnings for storm events and deleterious effects on the global societal infrastructure. Typically, these models are initialized by a climatological model to provide "most probable distributions" of environmental parameters as a function of time and space. The process of NRT data assimilation gently pulls the climate model closer toward the observed state (e.g., via Kalman smoothing) for nowcasting, and forecasting is achieved through a set of iterative semi-empirical physics-based forward-prediction calculations. Many challenges are associated with the development of an operational system, from the top-level architecture (e.g., the required space weather observatories to meet the spatial and temporal requirements of these models) down to the individual instruments capable of making the NRT measurements. This study focuses on the latter challenge: we present some examples of how tethered satellites (from 100s of m to 20 km) are uniquely suited to address certain shortfalls in our ability to measure critical environmental parameters necessary to drive these space weather models. Examples include long baseline electric field measurements, magnetized ionospheric conductivity measurements, and the ability to separate temporal from spatial irregularities in environmental parameters. Tethered satellite functional requirements are presented for two examples of space environment observables.

Gilchrist, Brian E.↗

NASA NTRS2011

Convergence of Defect-Correction and Multigrid Iterations for Inviscid Flows

Convergence of multigrid and defect-correction iterations is comprehensively studied within different incompressible and compressible inviscid regimes on high-density grids. Good smoothing properties of the defect-correction relaxation have been shown using both a modified Fourier analysis and a more general idealized-coarse-grid analysis. Single-grid defect correction alone has some slowly converging iterations on grids of medium density. The convergence is especially slow for near-sonic flows and for very low compressible Mach numbers. Additionally, the fast asymptotic convergence seen on medium density grids deteriorates on high-density grids. Certain downstream-boundary modes are very slowly damped on high-density grids. Multigrid scheme accelerates convergence of the slow defect-correction iterations to the extent determined by the coarse-grid correction. The two-level asymptotic convergence rates are stable and significantly below one in most of the regions but slow convergence is noted for near-sonic and very low-Mach compressible flows. Multigrid solver has been applied to the NACA 0012 airfoil and to different flow regimes, such as near-tangency and stagnation. Certain convergence difficulties have been encountered within stagnation regions. Nonetheless, for the airfoil flow, with a sharp trailing-edge, residuals were fast converging for a subcritical flow on a sequence of grids. For supercritical flow, residuals converged slower on some intermediate grids than on the finest grid or the two coarsest grids.

Diskin, Boris↗

NASA NTRS1992

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

Meade, Andrew J., Jr.↗

NASA NTRS1993

Semi-discrete Galerkin solution of the compressible boundary-layer equations with viscous-inviscid interaction

A semi-discrete Galerkin (SDG) method is under development to model attached, turbulent, and compressible boundary layers for transonic airfoil analysis problems. For the boundary-layer formulation the method models the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby providing high resolution near the wall and permitting the use of a uniform finite element grid which automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past RAE 2822 and NACA 0012 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack.

Day, Brad A.↗

NASA NTRS1989

Algorithm For Solution Of Navier-Stokes Equations

Advantages of two previous algorithms combined. Steady-state Navier-Stokes equations put in implicit finite-difference form solved by approximate Newton iteration. LU-SSOR scheme is new relaxation method combining advantages of LU factorization with Gauss-Seidel relaxation. Vectorizable LU-SSOR scheme, based on central differences, requires scalar diagonal inversions. Application of scheme to approximate Newton iteration of Navier-Stokes equations yields set of equations requiring no implicit smoothing on left side. Only adaptive, total-variation-diminishing, flux-limited dissipation terms added to right side. Algorithm used to predict laminar, turbulent, and hypersonic flows.

Yoon, Seokkwan↗

NASA NTRS2021

Patched Local Lunar Gravity Solutions using GRAIL Data

We present a method to determine local gravity fields for the Moon using Gravity Recovery and Interior Laboratory (GRAIL) data. We express gravity as gridded gravity anomalies on a sphere, and we estimate adjustments to a background global start model expressed in spherical harmonics. We processed GRAIL Ka-band range-rate data with a short-arc approach, using only data over the area of interest. We determine our gravity solutions using neighbor smoothing constraints. We divided the entire Moon into twelve regions and two polar caps, with a resolution of 0.15˚ x 0.15˚ (which is equivalent to degree and order 1199 in spherical harmonics), and determined the optimal smoothing parameter for each area by comparing localized correlations between gravity and topography for each solution set. Our selected areas share nodes with surrounding areas and they are overlapping. To mitigate boundary effects, we patch the solutions together by symmetrically omitting the boundary parts of overlapping solutions. Our new solution has been iterated, and it has improved correlations with topography when compared to a fully iterated global model. Our method requires fewer resources, and can easily handle regionally varying resolution or constraints. The smooth model describes small-scale features clearly, and can be used in local studies of the structure of the lunar crust.

Sander Goossens↗

NASA NTRS1984

Conjugate gradient coupled with multigrid for an indefinite problem

An iterative algorithm for the Helmholtz equation is presented. This scheme was based on the preconditioned conjugate gradient method for the normal equations. The preconditioning is one cycle of a multigrid method for the discrete Laplacian. The smoothing algorithm is red-black Gauss-Seidel and is constructed so it is a symmetric operator. The total number of iterations needed by the algorithm is independent of h. By varying the number of grids, the number of iterations depends only weakly on k when k(3)h(2) is constant. Comparisons with a SSOR preconditioner are presented.

Gozani, J.↗

NASA NTRS1987

Experience in grid optimization

Two optimization methods for solving a variational problem in grid generation are described and evaluated. The smoothness, cell volumes, and orthogonality of the variational integrals are examined. The Jacobi-Newton iterative method is compared to the Fletcher-Reeves conjugate gradient method. It is observed that a combination of the Jacobi-Newton iteration and the direct solution of the variational problem produces an algorithm which is easy to program and requires less storage and computer time/iteration than the conjugate gradient method.

Mastin, C. W.↗

NASA NTRS2007

NASA Tech Briefs, April 2007

Topics include: Wearable Environmental and Physiological Sensing Unit; Broadband Phase Retrieval for Image-Based Wavefront Sensing; Filter Function for Wavefront Sensing Over a Field of View; Iterative-Transform Phase Retrieval Using Adaptive Diversity; Wavefront Sensing With Switched Lenses for Defocus Diversity; Smooth Phase Interpolated Keying; Maintaining Stability During a Conducted-Ripple EMC Test; Photodiode Preamplifier for Laser Ranging With Weak Signals; Advanced High-Definition Video Cameras; Circuit for Full Charging of Series Lithium-Ion Cells; Analog Nonvolatile Computer Memory Circuits; JavaGenes Molecular Evolution; World Wind 3D Earth Viewing; Lithium Dinitramide as an Additive in Lithium Power Cells; Accounting for Uncertainties in Strengths of SiC MEMS Parts; Ion-Conducting Organic/Inorganic Polymers; MoO3 Cathodes for High-Temperature Lithium Thin-Film Cells; Counterrotating-Shoulder Mechanism for Friction Stir Welding; Strain Gauges Indicate Differential-CTE-Induced Failures; Antibodies Against Three Forms of Urokinase; Understanding and Counteracting Fatigue in Flight Crews; Active Correction of Aberrations of Low-Quality Telescope Optics; Dual-Beam Atom Laser Driven by Spinor Dynamics; Rugged, Tunable Extended-Cavity Diode Laser; Balloon for Long-Duration, High-Altitude Flight at Venus; and Wide-Temperature-Range Integrated Operational Amplifier.

Source record↗

NASA NTRS1982

A mathematical model of post-instability in fluid mechanics

Postinstability of fluids is eliminated in numerical models by introducing multivalued velocity fields after discarding the principle of impenetrability. Smooth functions are shown to be incapable of keeping the derivatives from going towards infinity when iterating solutions for the governing equations such as those defined by Navier-Stokes. Enlarging the class of functions is shown to be necessary to eliminate the appearance of imaginary characteristic roots in the systems of arbitrary partial differential equations, a condition which leads to physically impossible motions. The enlarging is demonstrated to be achievable by allowing several individual particles with different velocities to appear at the same point of space, and the subsequent multivaluedness of the solutions is purely a mathematical concern, rather than one of actual physical existence. Applications are provided for an inviscid fluid and for turbulence.

Zak, M. A.↗

NASA NTRS1976

The multigrid method: Fast relaxation

A multi-level grid method was studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse (e.g. 4 x 2 mesh cells) to fine (e.g. 64 x 32); the coarser grids are used to diminish the magnitude of the smooth part of the residuals, hopefully with far less total work than would be required with optimal iterations on the finest grid. To date the method was applied quite successfully to the solution of the transonic small-disturbance equation for the velocity potential in conservation form. Nonlifting transonic flow past a parabolic arc airfoil is the example studied, with meshes of both constant and variable step size.

South, J. C., Jr.↗

NASA NTRS1980

Supersonic flow development in slotted wind tunnels

The development of test section slot shapes for achieving smooth supersonic Mach number distribution without overexpansion or waviness has, in the past, been largely an experimentally iterative or 'cutand try' procedure for each wind tunnel. To overcome the obvious disadvantages of time and expense involved in such an experimental approach, a simple analytical method has been developed to predict the supersonic flow development in a two-dimensional slotted tunnel given only the variation of open area ratio with downstream distance and the Mach number corresponding to the plenum static pressure. The well known method of characteristics is used with the constraint that it be compatible with the quadratic cross-flow pressure drop boundary condition at the slotted wall. The predicted results from this method agree remarkably well with the experimental calibration data available for some of the existing facilities. The flow mechanism responsible for causing overexpansion in the centerline Mach number distribution with some slot shapes has been brought to light.

Ramaswamy, M. A.↗

NASA NTRS1988

Collisional-radiative switching - A powerful technique for converging non-LTE calculations

A very simple technique has been developed to converge statistical equilibrium and model atmospheric calculations in extreme non-LTE conditions when the usual iterative methods fail to converge from an LTE starting model. The proposed technique is based on a smooth transition from a collision-dominated LTE situation to the desired non-LTE conditions in which radiation dominates, at least in the most important transitions. The proposed approach was used to successfully compute stellar models with He abundances of 0.20, 0.30, and 0.50; Teff = 30,000 K, and log g = 2.9.

Hummer, D. G.↗

NASA NTRS1989

A highly parallel multigrid-like method for the solution of the Euler equations

We consider a highly parallel multigrid-like method for the solution of the two dimensional steady Euler equations. The new method, introduced as filtering multigrid, is similar to a standard multigrid scheme in that convergence on the finest grid is accelerated by iterations on coarser grids. In the filtering method, however, additional fine grid subproblems are processed concurrently with coarse grid computations to further accelerate convergence. These additional problems are obtained by splitting the residual into a smooth and an oscillatory component. The smooth component is then used to form a coarse grid problem (similar to standard multigrid) while the oscillatory component is used for a fine grid subproblem. The primary advantage in the filtering approach is that fewer iterations are required and that most of the additional work per iteration can be performed in parallel with the standard coarse grid computations. We generalize the filtering algorithm to a version suitable for nonlinear problems. We emphasize that this generalization is conceptually straight-forward and relatively easy to implement. In particular, no explicit linearization (e.g., formation of Jacobians) needs to be performed (similar to the FAS multigrid approach). We illustrate the nonlinear version by applying it to the Euler equations, and presenting numerical results. Finally, a performance evaluation is made based on execution time models and convergence information obtained from numerical experiments.

Tuminaro, Ray S.↗

NASA NTRS1997

Registration of video sequences from multiple sensors

In this paper, we describe an approach for registration of video sequences from a suite of multiple sensors including television, infrared and radar. Video sequences generated by these sensors may contain abrupt changes in local contrast and inconsistent image features, which pose additional difficulties for registration. Our approach to registration addresses the difficulties caused by using multiple sensors. We use a representation for registration that is invariant to local contrast changes, followed by smoothing of the resulting error measure used for registration, for robust estimation of registration parameters. We use an iterative procedure to reduce the effect of inconsistent features. Finally, we describe a method that uses same-sensor registration to aide in performing registration of sequences of video frames across multiple sensors.

Sharma, Ravi K.↗

NASA NTRS1996

Guidance of Nonlinear Systems

The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordination, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.

Meyer, George↗

NASA NTRS1997

Guidance of Nonlinear Systems

The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.

Meyer, George↗