Two-Dimensional Mesh Movement for Rectangular Regions and Other Natural Coordinate Systems.

A numerical method is presented and applied to the solution of two-dimensional steady-state, anisotropic heat conduction problems. The solution method employs the boundary-fitted coordinate system technique which transforms the region under study onto a fixed rectangular domain where computations are done easily. Consequently, the procedure eliminates the shape of the boundary as a complicating factor. The method is quite general and can handle any multiply-connected, arbitrary-shaped region. Two examples, a solid disk and an eccentric annulus, are worked out to demonstrate the utility of the method. Isotherm results check with previously published solutions.

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An Educational Two-Dimensional Interactive Dynamic Grid Generator

International Journal of Mechanical Engineering Education ◽

10.1177/030641909602400406 ◽

1996 ◽

Vol 24 (4) ◽

pp. 279-290 ◽

Cited By ~ 1

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.

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Spatial Rotation of the Fractional Derivative in Two-Dimensional Space

Advances in Mathematical Physics ◽

10.1155/2015/719173 ◽

2015 ◽

Vol 2015 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Ehab Malkawi

Keyword(s):

Fractional Derivative ◽

Physical Interpretation ◽

Fractional Derivatives ◽

Dimensional Space ◽

Two Dimensional ◽

Coordinate Systems ◽

Spatial Rotation ◽

Interaction Terms ◽

Physical Quantities ◽

Shed Light

The transformations of the partial fractional derivatives under spatial rotation inR2are derived for the Riemann-Liouville and Caputo definitions. These transformation properties link the observation of physical quantities, expressed through fractional derivatives, with respect to different coordinate systems (observers). It is the hope that such understanding could shed light on the physical interpretation of fractional derivatives. Also it is necessary to be able to construct interaction terms that are invariant with respect to equivalent observers.

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

Journal of Heat Transfer ◽

10.1115/1.3244537 ◽

1981 ◽

Vol 103 (4) ◽

pp. 753-758 ◽

Cited By ~ 9

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.

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Regular Two-Dimensional Packing of Congruent Objects: Cognitive Analysis of Honeycomb Constructions

Applied Sciences ◽

10.3390/app11115128 ◽

2021 ◽

Vol 11 (11) ◽

pp. 5128

Author(s):

Nikolay N. Klevanskiy ◽

Sergey I. Tkachev ◽

Ludmila A. Voloshchuk ◽

Rouslan B. Nourgaziev ◽

Vladimir S. Mavzovin

Keyword(s):

Cognitive Processes ◽

Honeycomb Structure ◽

Two Dimensional ◽

Coordinate Systems ◽

Convex Polygons ◽

New Approach ◽

Covering Density ◽

Regular Packing ◽

Geometric Objects ◽

Cognitive Visualization

A new approach to investigate the two-dimensional, regular packing of arbitrary geometric objects (GOs),using cognitive visualization, is presented. GOs correspond to congruent non-convex polygons with their associated coordinate system. The origins of these coordinate systems are accepted by object poles. The approach considered is based on cognitive processes that are forms of heuristic judgments. According to the first heuristic judgment, regular packing of congruent GOs on the plane have a honeycomb structure, that is, each GO contacts six neighboring GO, the poles of which are vertices of the pole hexagon in the honeycomb construction of packing. Based on the visualization of the honeycomb constructions a second heuristic judgment is obtained, according to which inside the hexagon of the poles, there are fragments of three GOs. The consequence is a third heuristic judgment on the plane covering density with regular packings of congruent GOs. With the help of cognitive visualization, it is established that inside the hexagon of poles there are fragments of exactly three objects. The fourth heuristic judgment is related to the proposal of a triple lattice packing for regular packing of congruent GOs.

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