Lunar profile from observations of the annular eclipse of May 20, 1966

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[标题]:Lunar profile from observations of the annular eclipse of May 20, 1966
[文摘]:( Geometric shape of lunar profile from annular phase of 20 May 1966 annular solar eclipse coronagraph plates, applying Fourier series and Pascal limacon approximation)

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[唯一标识符]:CDSTIC.AIAA 2009-1333
[标题]:Partition Design and Optimization for High Order Spectral Volume Schemes
[作者]:R. Harris, CFD Research Corporation, Huntsville, AL; Z. Wang, Iowa State University, Ames, IA
[文摘]:1Partition Design and Optimization for High-Order Spectral Volume Schemes Rob Harris1 CFD Research Corporation, Huntsville, AL 35805 Z. J. Wang2 Department of Aerospace Engineering, Iowa State University, Ames, IA 50011 An analysis of the accuracy and stability properties of the spectral volume (SV) method, with applicability to very high-order accurate simulations, is presented. In the SV method, each simplex grid cell is called a spectral volume (SV), and the SV is further partitioned into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In general, the partitioning of an SV into CVs is not uniquely defined, and thus it is of great importance to select a partition which yields favorable stability properties, and results in an interpolation polynomial of high quality. Here we present a new approach to efficiently locate stable partitions by means of constrained minimization. This is motivated by the fact that, at present, an exhaustive search approach to SV partition design would be prohibitively costly and thus not feasible. Once stable partitions are located, a high quality interpolation polynomial is then assured by subsequently minimizing the dissipation and dispersion errors of the stable partitions. Results are presented which demonstrate the potential of this method for producing stable and highly accurate partitions of arbitrary order. In particular, a new 4th-order partition is presented which has improved accuracy and stability properties over previously used partitions, and a new stable 5th-order partition is introduced. I. Introduction he spectral volume (SV) method is a recently developed finite volume method for hyperbolic conservation laws on unstructured grids.1-7 The SV method belongs to a general class of Godunov-type finite volume method8-9, which has been under development for several decades, and is considered to be the current state-of-the-art for the numerical solution of hyperbolic conservation laws. For a more detailed review of the literature on the Godunov-type method, refer to Wang1, and the references therein. Many of the most popular numerical methods, such as the k-exact finite volume10-11, the essentially non-oscillatory (ENO)12-13, and weighted ENO14 methods are also Godunov-type methods. A thorough review and comparison of these methods can be found in Wang.15 The SV method is also closely related to the discontinuous Galerkin (DG)16-20 method, a popular finite-element method for conservation laws. Both the SV and DG methods employ multiple degrees of freedom within a single element, but the SV method avoids the volume integral required in the DG method. Each simplex in the SV method utilizes a “structured” set of sub-cells, or control volumes (CVs), to support a polynomial reconstruction for the conserved variables, and a nodal set to support a polynomial reconstruction for the flux vector. For a more thorough comparison of the SV and DG methods, refer to Wang.1,15 The partitioning of an SV into CVs has been one of the greatest challenges in the implementation of the SV method since its inception. This partitioning defines the reconstruction stencil, and thus plays a vital role in determining the accuracy and stability properties of the scheme. Early on, several researchers focused on using the Lebesgue constant as a means to design accurate SV partitions. In particular, the work of Wang2, Liu5, and Chen21,22 is of relevance. While this criteria may be used to find partitions with lower error bounds, it does not guarantee that a particular scheme will be more or less accurate, and it offers no information about the stability of the scheme. A positive step towards addressing the issue of stability was given by Van den Abeele et al.23-25. In this work, some previously used SV partitions were found to be 1Project Engineer, Aeromechanics Dept., 215 Wynn Drive,, AIAA Member. 2Professor of Aerospace Engineering, 2271 Howe Hall,, Associate Fellow of AIAA. T
[会议名称]:47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition

[会议名称]:16th World Computer Congress (WCC 2000),BEIJING, PEOPLES R CHIN,August 21-25, 2000
[编辑者]:EG Ke;N Zhisheng
[主办单位]:China Inst Commun;Chinese Inst Electr;IEE, Electr Div;IEEE, Commun Soc;Natl Nat Sci Fdn;TC6, Int Federat Informat Process