Generating Functions for the Exact Solution of the Transport Equation. II. Time‐Dependent with Anisotropic Scattering

1968 ◽  
Vol 9 (12) ◽  
pp. 1993-2001 ◽  
Author(s):  
I. K. Abu‐Shumays ◽  
E. H. Bareiss
Keyword(s):  
Exact Solution ◽  
Transport Equation ◽  
Generating Functions ◽  
Anisotropic Scattering ◽  
Time Dependent

Generating Functions for the Exact Solution of the Transport Equation. I

1968 ◽  
Vol 9 (10) ◽  
pp. 1722-1731 ◽  
Author(s):  
I. K. Abu‐Shumays ◽  
E. H. Bareiss
Keyword(s):  
Exact Solution ◽  
Transport Equation ◽  
Generating Functions

Time-dependent albedo problem for quadratic anisotropic scattering

Kerntechnik ◽  
2007 ◽  
Vol 72 (1-2) ◽  
pp. 59-65 ◽  
Author(s):  
R. G. Türeci ◽  
D. Türeci
Keyword(s):  
Anisotropic Scattering ◽  
Time Dependent ◽  
Albedo Problem

scholarly journals The Two-Phase Hell-Shaw Flow: Construction of an Exact Solution

2013 ◽  
Vol 18 (1) ◽  
pp. 249-257
Author(s):  
K.R. Malaikah
Keyword(s):  
Exact Solution ◽  
Velocity Potential ◽  
Time Dependent ◽  
Computational Domain ◽  
Phase Problem ◽  
Complex Velocity ◽  
Two Phase ◽  
Interface Evolution ◽  
Complex Velocity Potential ◽  
Branch Cuts

We consider a two-phase Hele-Shaw cell whether or not the gap thickness is time-dependent. We construct an exact solution in terms of the Schwarz function of the interface for the two-phase Hele-Shaw flow. The derivation is based upon the single-valued complex velocity potential instead of the multiple-valued complex potential. As a result, the construction is applicable to the case of the time-dependent gap. In addition, there is no need to introduce branch cuts in the computational domain. Furthermore, the interface evolution in a two-phase problem is closely linked to its counterpart in a one-phase problem

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