An Educational Two-Dimensional Interactive Dynamic Grid Generator

1996 ◽  
Vol 24 (4) ◽  
pp. 279-290 ◽  
Author(s):  
M. Darwish ◽  
H. Diab ◽  
F. Moukalled
Keyword(s):  
Vector Fields ◽  
Three Dimensional ◽  
Object Oriented ◽  
Object Oriented Programming ◽  
Two Dimensional ◽  
Coordinate Systems ◽  
Curvilinear Grids ◽  
Windows Applications ◽  
Interactive Dynamic ◽  
Dimensional Domain

This paper describes IDGG, an Interactive Dynamic Grid Generator, for use as an educational tool by students studying computational fluid dynamics. The package is a Windows applications and runs on IBM PC, or compatible, computers. It is written in Pascal and built using object-oriented programming. The computer program allows the user to generate boundary-fitted curvilinear grids in any two-dimensional domain. The procedure adopted requires the user to perform the transformation step by step allowing him/her to easily grasp the concept of boundary-fitted coordinate systems. In addition, IDGG may be used by CFD researchers to display results graphically in the form of vector fields, contours, and two- and three-dimensional plots. The examples provided show the effectiveness of the package as a teaching aid.

Large-scale vortex structures in turbulent wakes behind bluff bodies. Part 1. Vortex formation processes

1987 ◽  
Vol 174 ◽  
pp. 233-270 ◽  
Author(s):  
A. E. Perry ◽  
T. R. Steiner
Keyword(s):  
Large Scale ◽  
Vector Fields ◽  
Vortex Formation ◽  
Three Dimensional ◽  
Point Theory ◽  
Shear Stresses ◽  
Bluff Bodies ◽  
Two Dimensional ◽  
Mean Flow ◽  
Turbulent Wakes

An investigation of turbulent wakes was conducted and phase-averaged velocity vector fields are presented, as well as phase-averaged and global Reynolds normal and shear stresses. The topology of the phase-averaged velocity fields is discussed in terms of critical point theory. Here in Part 1, the vortex formation process in the cavity region of several nominally two-dimensional bluff bodies is investigated and described using phase-averaged streamlines where the measurements were made in a nominal plane of symmetry. It was found that the flows encountered were always three-dimensional and that the mean-flow patterns in the cavity region were quite different from those expected using classical two-dimensional assumptions.

scholarly journals NONORIENTABLE MANIFOLDS IN THREE-DIMENSIONAL VECTOR FIELDS

2003 ◽  
Vol 13 (03) ◽  
pp. 553-570 ◽  
Author(s):  
HINKE M. OSINGA
Keyword(s):  
Vector Field ◽  
Periodic Orbit ◽  
Vector Fields ◽  
Invariant Manifolds ◽  
Three Dimensional ◽  
Period Doubling ◽  
Building Blocks ◽  
Two Dimensional ◽  
Dimensional Vector ◽  
Three Dimensional Vector Field

It is well known that a nonorientable manifold in a three-dimensional vector field is topologically equivalent to a Möbius strip. The most frequently used example is the unstable manifold of a periodic orbit that just lost its stability in a period-doubling bifurcation. However, there are not many explicit studies in the literature in the context of dynamical systems, and so far only qualitative sketches could be given as illustrations. We give an overview of the possible bifurcations in three-dimensional vector fields that create nonorientable manifolds. We mainly focus on nonorientable manifolds of periodic orbits, because they are the key building blocks. This is illustrated with invariant manifolds of three-dimensional vector fields that arise from applications. These manifolds were computed with a new algorithm for computing two-dimensional manifolds.

Numerical Solution to a Two-Dimensional Conduction Problem Using Rectangular and Cylindrical Body-Fitted Coordinate Systems

1981 ◽  
Vol 103 (4) ◽  
pp. 753-758 ◽  
Author(s):  
A. Goldman ◽  
Y. C. Kao
Keyword(s):  
Temperature Distribution ◽  
Coordinate System ◽  
Numerical Solution ◽  
Rectangular Plate ◽  
Three Dimensional ◽  
Cylindrical Body ◽  
Two Dimensional ◽  
Coordinate Systems

The temperature distribution in a rectangular plate with a circular void at the center was calculated using a body-fitted coordinate system. Three different transformed geometries were considered: rectangular-rectangular, cut-line, and cylindrical. Problems involving insulated outer surfaces could not be solved using the rectangular-rectangular transformation but could be solved with both the cut-line and cylindrical transformations. The cylindrical transformation also appears to have the capability of being extended to three-dimensional problems.

3D-2D asymptotic analysis of an optimal design problem for thin films

1998 ◽  
Vol 1998 (505) ◽  
pp. 173-202 ◽  
Author(s):  
Irene Fonseca ◽  
Gilles Francfort
Keyword(s):  
Optimal Design ◽  
Design Problem ◽  
Bulk Material ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Optimal Design Problem ◽  
Two Phase ◽  
Energy Bounds ◽  
Optimal Material ◽  
Dimensional Domain

Abstract The Gamma-limit of a rescaled version of an optimal material distribution problem for a cylindrical two-phase elastic mixture in a thin three-dimensional domain is explicitly computed. Its limit is a two-dimensional optimal design problem on the cross-section of the thin domain; it involves optimal energy bounds on two-dimensional mixtures of a related two-phase bulk material. Thus, it is shown in essence that 3D-2D asymptotics and optimal design commute from a variational standpoint.

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