Application of approximate boundary conditions to electromagnetic transient scattering problems

1996 ◽  
Author(s):  
S. Yuferev
Keyword(s):  
Boundary Conditions ◽  
Scattering Problems ◽  
Electromagnetic Transient ◽  
Transient Scattering ◽  
Approximate Boundary Conditions

One-Dimensional Jost Solutions: The S-Matrix Revisited

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Boundary Conditions ◽  
Transmission Coefficient ◽  
Radial Equation ◽  
Scattering Problems ◽  
One Dimensional ◽  
S Matrix ◽  
Jost Functions ◽  
Jost Solutions ◽  
Square Well ◽  
Matrix Problems

This chapter examines the properties of one-dimensional Jost solutions for S-matrix problems. It first considers how the left–right transmission and reflections coefficients can be expressed in terms of the elements of the S-matrix for one-dimensional scattering problems on, focusing on poles of the transmission coefficient. It then uses the radial equation to revisit the problem of the square-well potential from the perspective of the Jost solution, with Jost boundary conditions at r = 0 and as r approaches infinity. It also presents the notations for the Jost functions and the S-matrix before discussing the problem of scattering from a constant spherical inhomogeneity.

The Validity of Approximate Boundary Conditions for Natural Convection With Thermal Radiation in Open Cavities

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Om Singh ◽  
Shireesh B. Kedare ◽  
Suneet Singh
Keyword(s):  
Natural Convection ◽  
Boundary Conditions ◽  
Significant Loss ◽  
Computational Effort ◽  
Computational Domain ◽  
Maximum Difference ◽  
Open Cavities ◽  
Shallow Cavities ◽  
Approximate Boundary Conditions ◽  
The Difference

Abstract The use of approximate boundary conditions at the opening of the cavities leads to restriction of the computational domain and, hence, the reduction in computational effort. However, the accuracy of the restricted domain approach (RDA) had been evaluated only for the natural convection inside open cavities and that too only for one aspect ratio (AR). The validity of the approach had not been evaluated for inclined, as well as, shallow cavities. This study focuses on the analysis of the accuracy of RDA against extended domain approach (EDA) in open cavities of different ARs, at different inclinations and different Rayleigh numbers (Ra). The results show that the difference between the approaches is only significant in very shallow cavities (AR is defined as the height of the hot wall divided by the depth of the cavity) at low Ra. For Ra higher than  106 and an AR greater than 0.2, the maximum difference between the two approaches is around 5% and hence RDA can be recommended in these ranges, resulting in increased computational efficiency without significant loss in the accuracy. Moreover, the maximum difference in the results for the two methods is for intermediate inclinations. Even there, an increase in the difference is more pronounced at lower Ra. Furthermore, distribution of the exit velocity and temperature at the opening as well as the distribution of the Nusselt number at the hot wall is compared for RDA and EDA to explain the behavior of error at different ARs and inclinations.

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