Last edited by Yozshutilar

Tuesday, July 28, 2020 | History

3 edition of **A spectral mulit-domain technique application to generalized curvilinear coordinates** found in the catalog.

A spectral mulit-domain technique application to generalized curvilinear coordinates

- 75 Want to read
- 5 Currently reading

Published
**1986**
by National Aeronautics and Space Administration, Langley Research Center in Hampton, Va
.

Written in English

- Spectral theory (Mathematics),
- Fluid mechanics.,
- Domains.,
- Fluid mechanics.,
- Spectral methods.,
- Spherical coordinates.

**Edition Notes**

Microfiche. [Washington, D.C. : National Aeronautics and Space Administration], 1986. 1 microfiche.

Statement | Michele G. Macaraeg and Craig L. Streett. |

Series | NASA technical memorandum -- 87701. |

Contributions | Streett, Craig L., Langley Research Center. |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL16152758M |

coordinate system for fluid flow problems are nonorthogonal curvilinear coordinates. A special case of these are orthogonal curvilinear coordinates. Here we shall derive the appropriate relations for the latter using vector technique. It should be recognized that the derivation can also be accomplished using tensor analysis Size: KB. For the Love of Physics - Walter Lewin - - Duration: Lectures by Walter Lewin. They will make you ♥ Physics. Recommended for you.

Request this item to view in the Library's reading rooms using your library card. A spectral mulit-domain technique application to generalized curvilinear coordinates [microform] / Miche Explore. Find in other libraries; Preview at Google Books;. The construction principle is similar to well--known techniques which are used to transform a non--orthogonal grid into an orthogonal grid. From an initial grid, new coordinate lines in one parameter direction are determined by solving a set of ODEs.

Wall functions for the k — . turbulence model in generalized nonorthogonal curvilinear coordinates by Douglas L. Sondak A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Major: Mechanical Engineering Approved: In Charge of Major Work For the Major Department. Curvilinear coordinates utilize a coordinate system where the coordinate lines, or axes, can be curved. This is useful because some problems do not fit ideally into Cartesian (x, y, z) find the curvilinear coordinate for three functions of f (f 1 (x, y, z), f 2 (x, y, z), and f 3 (x, y, z)), set each function to a constant (u 1, u 2, and u 3), which defines each function as a.

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A multidomain spectral technique is adapted to the analysis of viscous flows of complex geometries by splitting a monodomain problem into a finite number of subdomain problems.

Get this from a library. A spectral multi-domain technique application to generalized curvilinear coordinates. [Michele G Macaraeg; Craig L Streett; Langley Research Center.].

A Spectral Multi-Domain Technique With Application to Generalized Coordinates Michele G. Macaraeg and Craig L. Streett NASA Langley Research Center INTRODUCTION Spectral collocation methods have proven to be efficient discretization schemes for many aerodynamic (see e.g., refs.

) and fluid mechanic (e.g., refs. One drawback to these techniques was the requirement that a complicated physical domain must map into a simple computational domain for discretization. This mapping must be smooth if the high order accuracy and expontential convergence rates associated with spectral methods are to be : M.

Macaraeg and C. Streett. Computational Techniques for Fluid Dynamics. Computational Techniques Srinivas K., Fletcher C.A.J. () Generalised Curvilinear Coordinates. In: Computational Techniques for Fluid Dynamics. Print ISBN ; Online ISBN ; eBook Packages Springer Book Archive; Buy this book on publisher's site; Reprints and Author: Karkenahalli Srinivas, Clive A.

Fletcher. Generalized Curvilinear Coordinates in Hybrid and Electromagnetic Codes Daniel W. Swift Geophysical Institute, University of Alaska, Fairbanks, Alaska,USA This paper describes the elements for writing hybrid and electromagnetic plasma simulation codes in generalized curvilinear coordinates.

coordinate system. Of course in Cartesian coordinates, the distance between two points whose coordinates diﬁer by dx;dy;dz is ds, where ds2 = dx2 +dy2 +dz2: (18) Your book calls ds the arc length. Now if you imagine squaring an equation like (17), you’ll get terms like dq2 1, but also terms like dq1dq2, etc.

So in general, plugging into (18) we expect ds2 = g 11dq 2File Size: KB. Gradient For a given scalar function (q 1;q 2;q 3) in a orthogonal coordinates q i, let the gradient of be O = f 1~e 1 + f 2~e 2 + f 3~e 3; (13) here ~e 1;~e 2;~e 3 is the corresponding orthonormal basis for fq 1;q 2;q 3gand f iare some unknown functions of fq igNow using eq.

6, we have d = O d~r= f 1h 1dq 1 + f 2h 2dq 2 + f 3h 3dq 3: (14) On ther other hand, one can show d = @ @q 1 dqFile Size: KB.

equivalent to the polar coordinate position 2, p/4). It is a simple matter of trigonometry to show that we can transform x,y coordinates to r,f coordinates via the two transformation equations: x =rcos f and y =rsin f (1) Clearly the same point will have two very different coordinate addresses when defined in different coordinate systems, but isFile Size: 64KB.

Tensor Analysis and Curvilinear Coordinates Phil Lucht Rimrock Digital Technology, Salt Lake City, Utah last update: Maple code is available upon request.

Comments and errata are welcome. The material in this document is copyrighted by the Size: 3MB. Introduction of generalized curvilinear coordinates to spectral nodal Galerkin methods for irregular-shaped two-dimensional sound field analysis.

Acoustical Science and Technology, 39 (1), Introduction of generalized curvilinear coordinates to spectral nodal Galerkin methods for irregular-shaped two-dimensional sound field : Yozo Araki, Toshiya Samejima.

In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian coordinates by using a transformation that is locally invertible (a one-to-one map) at each point. This means that one can convert a point given in a Cartesian coordinate system to its curvilinear coordinates.

The various non-rectangular coordinate systems have given rise to a generalization of the concept of a coordinate system in the idea of a generalized (curvilinear) coordinate system employing curvilinear coordinates as follows.

Curvilinear coordinates. Consider the. Generalized Curvilinear Coordinates in Hybrid and Electromagnetic Codes 81 where the grid point indices are speciﬁed by i, j, k and n is the time level. The x-component of l 2 can be computed from the table specifying the location of the coordinate points and is given by l 2x = q x (i, j +1,k,2)−q x (i, j,k,2).

(5) The unit basis vectors. Multidomain pseudospectral time-domain (MPSTD) algorithm, previously proposed for a Cartesian coordinates system, is extended to Maxwell's equations in a curvilinear coordinates system and applied.

2 Gradient in curvilinear coordinates Given a function f(u;v;w) in a curvilinear coordinate system, we would like to nd a form for the gradient operator. In order to do so it is convenient to start from the expression for the function di erential.

We have either, df= rfdr (9) or, expanding dfusing curvilinear coordinates, df= @f @u du+ @f @v. Generalized source method in curvilinear coordinates for 2D grating diffraction simulation Alexey A.

Shcherbakov and Alexandre V. Tishchenko Journal of Quantitative Spectroscopy and Radiative Transfer. Crossref. Impact of different stochastic line edge roughness patterns on measurements in scatterometry - a simulation studyCited by: In this work, a spectral difference lattice Boltzmann method (SDLBM) is developed and applied for an accurate simulation of two-dimensional inviscid compressible flows on structured grids.

The compressible form of the discrete Boltzmann–BGK equation is used in which multiple particle speeds have to be employed to correctly model the compressibility in a thermal by: 6. A generalized curvilinear coordinate formulation for the large-eddy simulation (LES) that centers on the fact that two spatial operations are necessary to complete the derivation is proposed.

The recommended order of operations is to transform the full resolution system prior to by: Orthogonal curvilinear coordinate systems corresponding to singular spectral curves A.E. Mironov y I.A. Taimanov z 1 Introduction In this paper we study the limiting case of the Krichever construction of orthog-onal curvilinear coordinate systems when the spectral curve becomes singular.

We study the limiting case of the Krichever construction of orthogonal curvilinear coordinate systems when the spectral curve becomes singular.

We show that when the curve is reducible and all its irreducible components are rational curves, the construction procedure reduces to solving systems of linear equations and to simple computations with elementary by: 9.An integral-collocation-based ﬁctitious domain the transformation of the governing equation into generalized curvilinear coordinates at the beginning, limits the application of pseudo-spectral techniques to problems deﬁned in simple geometries.

There .Geometrically they can be lengths along straight lines, or arc lengths along curves, or angles; not necessarily Cartesian coordinates or other standard orthogonal coordinates. There is one for each degree of freedom, so the number of generalized coordinates equals the number of .