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Distribution of points on a sphere with application to star catalogs

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2000年第1期23卷 130-137页

作者： Bauer, R Bauer Engn Enterprises Langhorne PA 19047 USA

A new framework is introduced to analyze the spatial distribution of stars in a catalog, namely, the Voronoi diagram/Delaunay triangulation. The Voronoi diagram is a subdivision of the celestial sphere into polygonal cells, one for each star, so that the cell for star P consists of the region on the sphere closer to P than to any other star. The Delaunay triangulation is the topological dual with the important property that each spherical cap circumscribing a triangle contains no stars in its interior. Measures of the uniformity in star density and geometric arrangement based on the Voronoi diagram/Delaunay triangulation are presented and compared with existing measures, Methods to generate uniformly distributed points on the sphere, which serve as useful test cases for stellar attitude determination analysis, are formulated and compared. One such method, based on a spherical spiral, is easy to implement and yields a very uniform distribution of points. Finally, the Voronoi density reduction method is introduced to select stars for an onboard catalog from a larger candidate set. The candidate with the smallest Voronoi cell is removed, and the Voronoi diagram of the reduced set is constructed. This process is repeated until the desired number of stars remains.

关键词： Space Shuttle Attitude Determination algorithms Spacecraft Attitude Data Structures Satellites Earth Space Shuttle Missions numerical algorithms Geometry Functions Computer Memory

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Nonlinear time-step constraints based on the second law of thermodynamics

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 2000年第3期14卷 435-449页

作者： Camberos, JA USAF Res Lab Wright Patterson AFB OH 45433 USA

numerical calculations for a time-accurate solution of the equations of fluid dynamics often require a time-step constraint. One can reduce this constraint to an inequality relating the time step, the grid spacing, and some reference wave velocity. Historically, the literature in numerical analysis refers to this parametric cluster as the Courant number (nondimensional) and the condition for the linear case as the Courant-Friedrichs-Lewy (CFL) condition. Classically, numerical analysis relies on linearization and von Neumann's use of Fourier series to derive the CFL condition. In practice, computational fluid dynamics mostly relies on rules of thumb and heuristic arguments to justify the equation that determines time-step size and numerical stability for complicated and nonlinear calculations. The approach proposed in this paper uses the second law of thermodynamics as a way of imposing a restriction on the time step, applied to linear and nonlinear equations and systems of equations like the equations of gas dynamics. Basically, by transforming the truncation error for the numerical formula approximating a conservation equation into an equation representing the balance of entropy, one can obtain an inequality that restricts the time step to satisfy the second law. The second law as developed extends its role by analogy for the simple linear advection equation, then a nonlinear equation, and finally a system of equations representing the one-dimensional equations of gas dynamics. In each case results obtained agree with the classical approach for linear equations but differ in others, indicating that the second law has significant implications beyond its role in thermodynamics. This work develops the topic only for explicit numerical algorithms with truncation errors no greater than second order. By conjecture one expects that the most general conclusions will field for implicit and higher-order methods because of the universality of the second law and the concept o

关键词： Second Law of Thermodynamics Entropy Generation Rate Lax Friedrichs Method Courant Friedrichs Lewy Rankine Hugoniot Jump Conditions Thermophysics Conservation of Mass Thermodynamic Equilibrium Nonlinear Equation numerical algorithms

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Generalized characteristic boundary conditions for computational aeroacoustics

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AIAA JOURNAL 2000年第11期38卷 2040-2049页

作者： Kim, JW Lee, DJ Korea Adv Inst Sci & Technol Dept Aerosp Engn Yusong Gu Taejon 305701 South Korea

An extended conservative formalism of the characteristic boundary conditions is presented on the basis of the generalized coordinates for practical computational aeroacoustics. The formalism is derived for solving the entire conservative form of the compressible Euler or Navier-Stokes equations on the body-fitted grid mesh system by using the high-order and high-resolution numerical schemes. It includes the matrices of transformation between the conservative and the characteristic variables, which were already derived In the literature to analyze the eigenvalue-eigenvector modes in an arbitrary direction. The conservation-form governing equations with their full terms are solved at the boundaries, and no kind of extrapolation or simplification of the equations is included in this formalism. Additional correction terms are devised to preserve the conservative form of flux derivative terms in the generalized coordinates. Especially, the soft inflow conditions are presented to keep the nonreflecting features, as well as to maintain the mean value of inflow velocity at the inlet boundary. These boundary conditions are applied to the actual computation of two-dimensional viscous cylinder flows with Reynolds number of 400 on the grid meshes clustered on the cylinder surface and the downstream region. The Strouhal number due to von Karman vortex streets, root-mean-square lift coefficient, and mean drag coefficient are evaluated correctly in comparison,vith experimental data. The far-field sound pressure levels are measured directly in this computation, and the accuracy is validated by an analytic formula derived in the literature.

关键词： Computational Aeroacoustics Karman Vortex Street Freestream Mach Number Navier Stokes Equations Conservation Equations Convection numerical algorithms Static Pressure Courant Friedrichs Lewy Acoustic Phenomena

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Computational study of vibrationally relaxing gas past blunt body in hypersonic flows

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 2000年第1期14卷 18-26页

作者： Josyula, E USAF Res Lab Air Vehicles Directorate Wright Patterson AFB OH 45433 USA

numerical simulations are presented of a steady-state, hypersonic Row over a two-dimensional cylinder of 1 m radius under conditions where the relaxation of the vibrational modes is significant. A Mach 6.5 nitrogen flow was simulated at freestream pressures of 50, 250, and 500 Pa, with a freestream translational temperature of 300 K. Two different freestream vibrational temperatures, 300 K (causing vibrational heating) and 4000 K (causing vibrational cooling) were considered to study the effects on the flowfield. An upwind-difference numerical scheme was used to solve the inviscid Euler equations coupled to the vibrational kinetic models of diatomic nitrogen, assumed as an anharmonic oscillator of 40 quantum levels using two sets of reaction rates. Comparison with previously reported computations showed a maximum variation of 10% in translational and first-level vibrational temperature along the surface due to differences in numerical schemes and grid densities;variation caused hy the two different reaction rate sets was less than 2%. The vibrational cooling case showed a 10% higher shock-standoff distance than the vibrational heating case. The population distribution for the cooling Ease was non-Boltzmann due to nonresonant energy exchanges in the postshock region, greater in the shoulder region than in the stagnation region. An increase in freestream pressure for the cooling case increased the shock-standoff distance and non-Boltzmann behavior in the postshock region and near the surface. There was, however, a larger equilibrium region in between, in the stagnation region.

关键词： Freestream Conditions Stagnation Region Conservation Equations Hypersonic Flows numerical Simulation Stagnation Streamlines Shock Layers Vibrational Energy numerical algorithms Predictor Corrector Method

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Design of reliable control systems possessing actuator redundancies

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2000年第4期23卷 709-718页

作者： Jiang, J Zhao, Q Univ Western Ontario Dept Elect & Comp Engn London ON N6A 5B9 Canada Univ Manitoba Dept Elect & Comp Engn Winnipeg MB R3T 5V6 Canada

The explicit definitions of actuator redundancies are introduced. A design scheme is then presented to synthesize reliable control against actuator failures for dynamic systems possessing actuator redundancies. The properly designed controller is able to guarantee the stability and to maintain the steady-state tracking performance in the event of actuator failures. The design method is based on a robust regional eigenvalue assignment technique with the help of a precompensator. The effectiveness of the proposed method has been verified using an example of the aircraft bank angle control problem.

关键词： Actuators Multiple Input Single Output Bank Angle Ailerons Linear Time Invariant System numerical algorithms Real Time Fault Detection Mathematical Models Transport Aircraft Space Missions

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Reduction of chemical kinetics in air pollution modeling

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JOURNAL OF COMPUTATIONAL PHYSICS 2000年第2期164卷 354-376页

作者： Sportisse, B Djouad, R Ecole Natl Ponts & Chaussees CEREVE F-77455 Champs Sur Marne France

We investigate in this article the use of reduction techniques in air pollution modeling. The reduction of chemical kinetics is performed on the basis of a timescale analysis and of lumping. Lumping techniques are widely used in air pollution modeling and consist of replacing some pure chemical species by linear combinations of species. We focus here on the theoretical justification of such techniques. We propose an algorithm in order to build up lumped species in a systematic way. An application to three kinetic schemes coupled with diffusion is presented in a monodimensional case. This justifies the way we couple a reduced kinetic scheme with other processes. (C) 2000 Academic Press.

关键词： air pollution modeling tropospheric ozone lumping techniques reduction of chemical kinetics numerical algorithms

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An acceleration procedure for discrete velocity approximation of the Boltzmann collision operator

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2000年第5-6期39卷 151-163页

作者： Platkowski, T Walus, W Univ Warsaw Inst Appl Math & Mech Dept Math Informat & Mech PL-02097 Warsaw Poland

In this paper, we investigate a method of realization of the discrete velocity approximation of the Boltzmann collision operator studied by Palczewski, Schneider and Bobylev. For this realization, we propose an acceleration procedure, which reduces the computational complexity of the method. The efficiency of the acceleration procedure is demonstrated through a set of numerical tests, which include space homogeneous relaxation problems and space nonhomogeneous problem of shock wave formation. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： boltzmann equation numerical algorithms discrete velocity approximation

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A new class of extremal composites

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2000年第2期48卷 397-428页

作者： Sigmund, O Tech Univ Denmark Dept Solid Mech DK-2800 Lyngby Denmark

The paper presents a new class of two-phase isotropic composites with extremal bulk modulus. The new class consists of micro geometrics for which exact solutions can be proven and their bulk moduli are shown to coincide with the Hashin-Shtrikman bounds. The results hold for two and three dimensions and for both well- and non-well-ordered isotropic constituent phases. The new class of composites constitutes an alternative to the three previously known extremal composite classes: finite rank laminates, composite sphere assemblages and Vigdergauz microstructures. An isotropic honeycomb-like hexagonal microstructure belonging to the new class of composites has maximum bulk modulus and lower shear modulus than any previously known composite. Inspiration for the new composite class comes from a numerical topology design procedure which solves the inverse homogenization problem of distributing two isotropic material phases in a periodic isotropic material structure such that the effective properties are extremized. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： homogenization microstructures constitutive behaviour optimization numerical algorithms

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Fuzzy-logic-based closed-loop optimal law for homing missiles guidance

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2000年第3期23卷 573-574页

作者： Rahbar, N Menhaj, MB Amir Kabir Univ Technol Dept Mech Engn Tehran 158754413 Iran Amir Kabir Univ Technol Dept Elect Engn Tehran 158754413 Iran

THE usefulness of optimal control is sharply divided between two distinct classes of dynamic systems, namely, linear systems and nonlinear systems. For linear systems, the theory is complete in the sense that given a quadratic cost and closed-loop or feedback, a guidance law may be determined. For nonlinear systems, generally the best one can do is to determine an open-loop guidance law. Research efforts have produced many numerical algorithms for an open-loop solution for such problems using digital computers. The main disadvantage of these algorithms is that they generally converge slowly and are not suitable for real-time applications. In an open-loop solution, the control at any lime instant is not explicitly determined by the states of the system at that time instant. It is well known that a system with an open-loop controller can be sensitive to noise and external disturbances. In contrast, closed-loop control, in which the control is a function of the instantaneous stales of the system, is generally robust with respect to such disturbances. Unfortunately, only rarely is it feasible to determine the feedback law for nonlinear systems of any practical *** the past four decades, a considerable number of homing missile guidance laws have been proposed. One of the most widely used methods is the proportional navigation guidance (PNG) law. The simplicity of the PNG law has been widely recognised. Furthermore, Ho et al. have shown that the conventional PNG law is optimal inthe sense that it drives the miss distance to zero while minimizing the integral of the square of missile acceleration. Most existing missiles are guided by PNG law; however, the linear-quadratic guidance rule contains PNG as a particular case for linear state equations, and most envisioned missile engagements exceed these limits because of high tangential and normal accelerations.

关键词： Open Loop Controller Fuzzy Logic Missile Guidance Optimal Control Guidance Laws Nonlinear Systems Proportional Navigation Homing Missile MATLAB numerical algorithms

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Multiphase composites with extremal bulk modulus

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2000年第3期48卷 461-498页

作者： Gibiansky, LV Sigmund, O Tech Univ Denmark Dept Solid Mech DK-2800 Lyngby Denmark

This paper is devoted to the analytical and numerical study of isotropic elastic composites made of three or more isotropic phases. The ranges of their effective bulk and shear moduli are restricted by the Hashin-Shtrikman-Walpole (HSW) bounds. For two-phase composites, these bounds are attainable, that is, there exist composites with extreme bulk and shear moduli. For multiphase composites, they may or may not be attainable depending on phase moduli and volume fractions. Sufficient conditions of attainability of the bounds and various previously known and new types of optimal composites are described. Most of our new results are related to the two-dimensional problem. A numerical topology optimization procedure that solves the inverse homogenization problem is adopted and used to look for two-dimensional three-phase composites with a maximal effective bulk modulus. For the combination of parameters where the HSW bound is known to be attainable, new microstructures are found numerically that possess bulk moduli close to the bound. Moreover, new types of microstructures with bulk moduli close to the bound are found numerically for the situations where the aforementioned attainability conditions are not met. Based on the numerical results, several new types of structures that possess extremal bulk modulus are suggested and studied analytically. The bulk moduli of the new structures are either equal to the HSW bound or higher than the bulk modulus of any other known composite with the same phase moduli and volume fractions. It is proved that the HSW bound is attainable in a much wider range than it was previously believed. Results are readily applied to two-dimensional three-phase isotropic conducting composites with extremal conductivity. They can also be used to study transversely isotropic three-dimensional three-phase composites with cylindrical inclusions of arbitrary cross-sections (plane strain problem) or transversely isotropic thin plates (plane stress or bend

关键词： homogenization microstructures constitutive behaviour optimization numerical algorithms

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