Solutions of the Navier-Stokes equations in various flow regimes on fields containing any number of arbitrary bodies using boundary-fitted coordinate systems
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The essential part of numerical solutions of partial differential equations is the representation of gradients and integrals by, respectively, differences between points and summations over points. In order for such numerical representations to be accurate, it is necessary that these points be more closely spaced in regions of large gradients. The need for accurate representation is particularly acute near body surfaces, since the boundary conditions are generally the most influential part of a partial differential equation solution. This is especially true of viscous solutions at high Reynolds number, where very large gradients occur in the boundary layer.
A method for constructing a direct functional relation between the computational and physical domains such that boundaries in the computational domain map into boundaries in the physical domain is presented. This method which is called the 'two-boundary technique' is based on generating functions that represent two disconnected boundaries in the physical domain and an independent function which connects one boundary with another to generate grids. The suggested connecting functions are simple linear and cubic parametric polynomials with parameters based on position and derivatives at the disconnected boundaries. The boundaries can be defined by analytical, approximate, and tension spline functions; the grid density in specified regions is controlled by embedding contraction functions in either the boundary representation or the connecting function.
(Previously announced in STAR as N81-12525)
This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.
This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.
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The Aerial Regional-Scale Environmental Survey (ARES) is a Mars exploration mission concept with the goal of taking scientific measurements of the atmosphere, surface, and subsurface of Mars by using an airplane as the payload platform. ARES team first conducted a Phase-A study for a 2007 launch opportunity, which was completed in May 2003. Following this study, significant efforts were undertaken to reduce the risk of the atmospheric flight system, under the NASA Langley Planetary Airplane Risk Reduction Project. The concept was then proposed to the Mars Scout program in 2006 for a 2011 launch opportunity. This paper summarizes the design and development of the ARES airplane propulsion subsystem beginning with the inception of the ARES project in 2002 through the submittal of the Mars Scout proposal in July 2006.
The presentation will introduce topics of note regarding CCS status for the Earth Science Constellation (ESC) Mission Operations Working Group (MOWG).
Means of determining the Hipparcos satellite instrumental system rotation and for tying Hipparcos system coordinates to a fundamental coordinate system are discussed. Observational characteristics requirements for radio sources and stars, for a Hipparcos-Space Telescope reference tie are given. Rotation of the Hipparcos system with respect to the extragalactic system can be derived from observations of the relative radial positions and motions of selected Hipparcos stars and quasi-stellar objects.
In this report, the orbital separation between a STAR-48V upperstage motor and the COMET FreeFlyer is investigated. The time from nominal STAR-48 engine burnout is to be determined such that the STAR-48 will not collide with the FreeFlyer once the separation process has been initiated. To analyze this separation, the forces acting upon both the FreeFlyer and the STAR-48 are described in a body fixed coordinate system. These coordinates are then transformed into an Euler coordinate system and then further transformed into a relative inertial coordinate system. From this analysis and some basic assumptions about the Star-48/FreeFlyer vehicle, it can be concluded that the STAR-48 will not collide with the Free Flyer if the separation occurs at 120 seconds after nominal burnout of the STAR-48. In fact, the separation delay could be a shorter period of time, but it is recommended that this separation delay be as long as possible for risk mitigation. This delay is currently designed to be 120 seconds and the analysis presented in this report shows that this time is acceptable.
Coordinated cyber attacks tamper with measurement data to disrupt the situational awareness of active distribution systems. Various sensors report measurements asynchronously at different rates, which introduces challenges during state estimation. In addition, this forces cyber intruders to exert greater effort to compromise multiple communication channels and launch coordinated attacks. Therefore, multi-channel and asynchronous measurements could be harnessed to develop more secure cyber defense strategies. In this paper, a prediction-correction-based multi-rate observer is designed to exploit the value of asynchronous measurements for the detection of coordinated false data injection (FDI) attacks. First, a time-function-dependent prediction-correction strategy is proposed to adjust the sampling interval for each sensor’s measurement. Then, an observer is designed based on the trade-off between estimation error and the optimal period of the most recent sampling instant, with the convergence of estimation error with the maximum permitted sampling interval. Moreover, the conditions for exponential stability are developed using the Lyapunov–Krasovskii functional technique. Next, a coordinated FDI attack detection strategy is developed based on the dual nonlinear minimization problem. The proposed attack detection and secure state estimation strategies are tested on the IEEE 13-node system. Simulation results show that these schemes are effective in enhancing attack detection based on asynchronous measurements or compromised data.
Coordinating the behavior of a large number of agents to achieve a system level goal poses unique design challenges. In particular, problems of scaling (number of agents in the thousands to tens of thousands), observability (agents have limited sensing capabilities), and robustness (the agents are unreliable) make it impossible to simply apply methods developed for small multi-agent systems composed of reliable agents. To address these problems, we present an approach based on deriving agent goals that are aligned with the overall system goal, and can be computed using information readily available to the agents. Then, each agent uses a simple reinforcement learning algorithm to pursue its own goals. Because of the way in which those goals are derived, there is no need to use difficult to scale external mechanisms to force collaboration or coordination among the agents, or to ensure that agents actively attempt to appropriate the tasks of agents that suffered failures. To present these results in a concrete setting, we focus on the problem of finding the sub-set of a set of imperfect devices that results in the best aggregate device. This is a large distributed agent coordination problem where each agent (e.g., device) needs to determine whether to be part of the aggregate device. Our results show that the approach proposed in this work provides improvements of over an order of magnitude over both traditional search methods and traditional multi-agent methods. Furthermore, the results show that even in extreme cases of agent failures (i.e., half the agents failed midway through the simulation) the system's performance degrades gracefully and still outperforms a failure-free and centralized search algorithm. The results also show that the gains increase as the size of the system (e.g., number of agents) increases. This latter result is particularly encouraging and suggests that this method is ideally suited for domains where the number of agents is currently in the thousands and will reach tens or hundreds of thousands in the near future.
Earth satellite orbit computations - Diliberto general perturbation method application in improved coordinate system
Geodesy and cartography provide the geometric framework on which most investigations of planets are ultimately based. Specifically, the products of these disciplines provide information on the following: (1) the dimensions of the planet, (2) a mathematical figure of reference for the planet, (3) the orientation of the body in the celestial coordinate system, (4) the rotational constants, (5) a defined system of coordinates, (6) the location of surface points in the defined coordinate system, (7) the gravity potential expressed in spherical harmonics, (8) topographic and thematic maps, and (9) surface albedo in various wavelengths. The relevance of geodesy and cartography to planetology is discussed, and the requirements of data acquisition and mission design are considered.
A procedure for the finite-difference numerical solution of the lifting potential flow about any number of arbitrarily shaped bodies is given. The solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having coordinate lines coincident with the contours of all bodies in the field, regardless of their shapes and number. The effects of all numerical parameters involved are analyzed and appropriate values are recommended. Comparisons with analytic solutions for single Karman-Trefftz airfoils and a circular cylinder pair show excellent agreement. The technique of application of the boundary-fitted coordinate systems to the numerical solution of partial differential equations is illustrated.