Method of conditional minimization for the numerical solution of a nonstationary problem with free boundaries

1991 ◽  
Vol 31 (2) ◽  
pp. 257-267
Author(s):  
R. Čiegis ◽  
R. Ciupaila
Keyword(s):  
Numerical Solution ◽  
Nonstationary Problem ◽  
Free Boundaries ◽  
Conditional Minimization

Non-linear Convection with Free Boundaries

1970 ◽  
Vol 1 (8) ◽  
pp. 381-382 ◽  
Author(s):  
J. O. Murphy
Keyword(s):  
Rayleigh Number ◽  
Prandtl Number ◽  
Numerical Solution ◽  
Extreme Values ◽  
Fluid Layer ◽  
Free Boundaries ◽  
Non Linear ◽  
Basic Equations ◽  
Horizontal Fluid Layer ◽  
Astrophysical Situation

In an IAU Symposium report, Spiegel has made mention of the basic reasons for the astrophysical interest in the problem of non-linear convection of a horizontal fluid layer heated from below. Unfortunately the two important parameters of this problem—the Prandtl number P and the Rayleigh number R take on ‘extreme’ values in the astrophysical situation and this presents immediate difficulties as far as the numerical solution of the basic equations go.

Numerical treatment of a singularity in a free boundary problem

1972 ◽  
Vol 330 (1583) ◽  
pp. 573-580 ◽  
Keyword(s):  
Free Boundary ◽  
Numerical Solution ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Complex Variable ◽  
Free Boundary Problems ◽  
Separation Point ◽  
Free Boundaries ◽  
Boundary Problems ◽  
A Free Boundary Problem

The numerical solution of free boundary problems gives rise to many computational difficulties. One such difficulty is due to the singularity at the separation point between the fixed and free boundaries. A method is suggested which uses complex variable techniques to determine the shape of the free boundary near to the separation point. This complex variable solution is also used to improve the accuracy of the finite-difference solution in the neighbourhood of the singularity. The analytical study was incorporated into an algorithm for the numerical solution of a particular free boundary problem concerning the percolation of a fluid through a porous dam. Some numerical results for this problem are presented.

Backscattering Analysis of Cylinder Shaped Scatterer in Vegetation Medium: Comparison Between Theories

2020 ◽  
Vol 2 (1) ◽  
pp. 15-18
Author(s):  
Syabeela Syahali ◽  
Ewe Hong Tat ◽  
Gobi Vetharatnam ◽  
Li-Jun Jiang ◽  
Hamsalekha A Kumaresan
Keyword(s):  
Numerical Solution ◽  
Cross Section ◽  
Traditional Method ◽  
Microwave Remote Sensing ◽  
Solution Model ◽  
Complex Nature ◽  
Good Match ◽  
Equivalent Source ◽  
Backscattering Cross Section ◽  
Method Model

This paper analyses the backscattering cross section of a cylinder both using traditional method model and a new numerical solution model, namely Relaxed Hierarchical Equivalent Source Algorithm (RHESA). The purpose of this study is to investigate the prospect of incorporating numerical solution model into volume scattering calculation, to be applied into microwave remote sensing in vegetation area. Results show a good match, suggesting that RHESA may be suitable to be used to model the more complex nature of vegetation medium.

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