Topic
Elliptic coordinate system
About: Elliptic coordinate system is a research topic. Over the lifetime, 670 publications have been published within this topic receiving 11135 citations. The topic is also known as: elliptical coordinate system & elliptic coordinates.
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TL;DR: In this article, an inverse inviscid target pressure theory for the design of turbomachinery stator blade sections lying on an arbitrary axisymmetric stream surface with varying stream-surface width is presented.
Abstract: The object of this paper is to present a concise inverse inviscid target pressure theory for the design of turbomachinery stator blade sections lying on an arbitrary axisymmetric stream-surface with varying stream-surface width. The flow is considered irrotational and compressible. Introducing the potential (φ) and the streamfunction (ψ) as independent natural coordinates, a curvilinear coordinate transformation is performed, which expresses the governing flow equations in the natural coordinates space using differential geometry arguments. The flow equations are then solved on the (φ,ψ) plane using as Dirichlet conditions the imposed target pressure. Geometry is determined by integrating the generalized Frenet equations along the natural coordinate lines. Particular attention is given to the numerical implementation of the method. An auxiliary coordinate transformation permits the definition of C-type computational grids on the (φ,ψ) plane resulting in a more accurate description of the leading edge regi...
2 citations
01 Jan 2007
TL;DR: In this article, the authors proposed a new class of approximate local DtN boundary conditions to be applied on prolate spheroid-shaped exterior boundaries when solving acoustic scattering problems by elongated obstacles.
Abstract: We propose a new class of approximate {\it local} DtN boundary conditions to be applied on prolate spheroid-shaped exterior boundaries when solving acoustic scattering problems by elongated obstacles. These conditions are : (a) exact for the first modes, (b) easy to implement and to parallelize, (c) compatible with the local structure of the computational finite element scheme, and (d) applicable to exterior elliptical-shaped boundaries that are more suitable in terms of cost-effectiveness for surrounding elongated scatterers. Moreover, these conditions coincide with the classical local DtN condition designed for spherical-shaped boundaries. We investigate analytically and numerically the effect of the frequency regime and the slenderness of the boundary on the accuracy of these conditions when applied for solving radiators and scattering problems. We also compare their performance to the second order absorbing boundary condition (BGT2) designed by Bayliss, Gunzburger and Turkel when expressed in prolate spheroidal coordinates. The analysis reveals that, in the low frequency regime, the new second order DtN condition (DtN2) retains a good level of accuracy regardless of the slenderness of the boundary. In addition, the DtN2 boundary condition outperforms the BGT2 condition. Such superiority is clearly noticeable for large eccentricity values.
2 citations
TL;DR: In this paper, the vibration-rotational kinetic energy operators of four-particle system in various coordinates were derived using a new and simple angular momentum method, respectively suitable for studying the systems described by scattering coordinate, valence coordinate, Radau coordinate, radau/Jacobi and Jacobi/valence hybrid coordinates and so on.
Abstract: The vibration-rotational kinetic energy operators of four-particle system in various coordinates are derived using a new and simple angular momentum method. The operators are respectively suitable for studying the systems described by scattering coordinate, valence coordinate, Radau coordinate, Radau/Jacobi and Jacobi/valence hybrid coordinates and so on. Certain properties of these operators and their possible applications are discussed.
2 citations
30 Apr 2016
2 citations
12 May 2003
TL;DR: In this article, the authors considered the trajectory of a charged particle in an arbitrary external magnetic field and derived partial differential equations for the magnetic fields fix conditions among its local multipole components, which can be viewed as a generalization of the usual multipole expansion of the magnetic elements.
Abstract: We consider the trajectory of a charged particle in an arbitrary external magnetic field A local orthogonal coordinate system is given by the tangential, curvature, and torsion vectors We write down Maxwell's equations in this coordinate system The resulting partial differential equations for the magnetic fields fix conditions among its local multipole components, which can be viewed as a generalization of the usual multipole expansion of the fields of magnetic elements
2 citations