scholarly journals Shells analysis in orthogonal curvilinear coordinate system with variation-difference method

2019 ◽  
Vol 675 ◽  
pp. 012066
Author(s):  
V N Ivanov ◽  
A A Shmeleva
Keyword(s):  
Coordinate System ◽  
Difference Method ◽  
Curvilinear Coordinate System ◽  
Curvilinear Coordinate ◽  
Orthogonal Curvilinear Coordinate System

Tutorial / Article didactique Derivatives of curvilinear coordinate unit vectors: A concise matrix-vector approach

2000 ◽  
Vol 77 (12) ◽  
pp. 969-983
Author(s):  
P Mohazzabi
Keyword(s):  
Angular Velocity ◽  
Coordinate System ◽  
Time Evolution ◽  
Curvilinear Coordinate System ◽  
Curvilinear Coordinate ◽  
Orthogonal Curvilinear Coordinate System ◽  
Matrix Vector ◽  
Derivatives Of ◽  
Unit Vectors ◽  
Vector Approach

The time evolution of a curvilinear coordinate system can be identifiedwith an angular velocity matrix or vector, which contains the complete differentiationrule for all unit coordinate vectors of the curvilinear system, providinga concise method for their computations. When generalized the technique provides a powerful tool fordifferentiation, with respect to any parameter, of not only unit coordinate vectors but any vector that remains fixed in a general orthogonal curvilinear coordinate system. Several curvilinear systems, as well as the normal and tangentialcoordinate system are examined.PACS No.: 46.00

Flow Over a Cylinder at a Plane Boundary—A Model Based Upon (k–ε) Turbulence

1989 ◽  
Vol 111 (4) ◽  
pp. 414-419 ◽  
Author(s):  
T. Solberg ◽  
K. J. Eidsvik
Keyword(s):  
Pressure Gradient ◽  
Coordinate System ◽  
Adverse Pressure Gradient ◽  
Plane Boundary ◽  
Length Scale ◽  
Two Dimensional ◽  
Curvilinear Coordinate System ◽  
Recirculating Flow ◽  
Model Based ◽  
Curvilinear Coordinate

A model for two-dimensional flows over a cylinder at a plane boundary is developed. The model, based upon a (k-ε) turbulence closure, is formulated in a curvilinear coordinate system based upon frictionless flow. A length scale modification in areas of adverse pressure gradient and recirculating flow appears to be more realistic than the standard (k-ε) model. The main features of the predicted flow do not depend critically upon the details of the grid or model, which means that a well defined solution is obtained. The solution appears to be reasonable and validated to the extent that the data permits.

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