Axisymmetric Solutions in Elastostatics and Elastic Wave Propagation by Ascent Methods

1984 ◽  
Vol 51 (3) ◽  
pp. 630-635
Author(s):  
F. R. Norwood
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Three Dimensional ◽  
Elastic Wave Propagation ◽  
Laplacian Operator ◽  
Dimensional Problem ◽  
Axisymmetric Problems ◽  
Axisymmetric Solutions ◽  
Transfer Problems ◽  
Theoretical Results

In the present paper a method of ascent for axisymmetric problems is developed. It is shown that, for problems where the vector or scalar Laplacian operator specifies the space behavior of the potential functions, the three-dimensional axisymmetric problems may be solved by operating on the solution to an associated two-dimensional problem. Hence, the theoretical results presented here may be applied to heat transfer problems, to problems in elastostatics, and to elastic wave propagation problems.

The relationship between two- and three-dimensional elastic-wave propagation

1971 ◽  
Vol 61 (6) ◽  
pp. 1583-1588 ◽  
Author(s):  
C. N. G. Dampney
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Three Dimensional ◽  
Elastic Wave Propagation ◽  
Simple Relationship ◽  
Two Dimensional ◽  
Intrinsic Interest ◽  
Cylindrically Symmetric ◽  
The Relationship ◽  
Dimensional Wave

abstract A technique similar to inverting Abel's equation is used to invert the descent of dimensions method between three-dimensional, cylindrically-symmetric and two-dimensional wave propagation. The end result is a very simple relationship between the two types of wave propagation. Apart from its intrinsic interest, the large number of two-dimensional studies reported in the literature could now be related to their three-dimensional counterparts.

A Methodology to Solve 2D and Axisymmetric Radiative Transfer Problems Using a General 3D Solver

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
P. Kumar ◽  
V. Eswaran
Keyword(s):  
Radiative Transfer ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Special Treatment ◽  
Dimensional Problem ◽  
Scattering Media ◽  
Special Cases ◽  
Axisymmetric Problems ◽  
Transfer Problems ◽  
Benchmark Solutions

A method to solve the radiative transfer equation (RTE) for absorbing-emitting and/or scattering media for 2-D and axisymmetric geometries using a general 3-D solver with a special treatment of the boundary condition in the third direction is presented. It allows a choice of first- or second- order schemes and can be used with non-orthogonal hexahedral grids for complex domains. Two-dimensional or axisymmetric problems are treated as different special cases of a three-dimensional problem. The method is tested on axisymmetric problems with absorbing-emitting and/or scattering media and on a 2D planar problem with a transparent medium and validated by comparisons with benchmark solutions.

Sign in / Sign up

Export Citation Format

Share Document