Three-dimensional magnetostatic field calculation using integro-differential equation for scalar potential

1996 ◽  
Vol 32 (3) ◽  
pp. 667-670 ◽  
Author(s):  
A.G. Kalimov ◽  
M.L. Svedentsov
Keyword(s):  
Differential Equation ◽  
Scalar Potential ◽  
Three Dimensional ◽  
Field Calculation ◽  
Magnetostatic Field ◽  
Integro Differential Equation

Three dimensional magnetostatic field calculation using equivalent magnetic charge method

1991 ◽  
Vol 27 (6) ◽  
pp. 5010-5012 ◽  
Author(s):  
Y. Xu ◽  
Z. Jiang ◽  
Q. Wang ◽  
X. Xu ◽  
D. Sun ◽  
...  
Keyword(s):  
Magnetic Charge ◽  
Three Dimensional ◽  
Field Calculation ◽  
Magnetostatic Field

On the Theory of Potential Flow About a Ship Advancing in Waves

1992 ◽  
Vol 36 (01) ◽  
pp. 17-29
Author(s):  
Francis Noblesse ◽  
Dane Hendrix
Keyword(s):  
Differential Equation ◽  
Potential Flow ◽  
Theoretical Basis ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Regular Waves ◽  
Integro Differential Equation ◽  
The Mean ◽  
The Green Function ◽  
Subsequent Integration

This study considers the three-dimensional potential flow due to a ship advancing with constant average speed in a train of regular waves. A modified integro-differential equation for determining the velocity potential on the mean position of the hull surface is obtained, and a solid theoretical basis for obtaining a numerical solution of the equation via a panel method is developed following the approach used by Kochin more than 50 years ago. In short, the approach is essentially based on a Fourier representation of the solution of a modified integro-differential equation. This approach circumvents the fundamental difficulties associated with the numerical evaluation of the Green function and its gradient, and their subsequent integration over the panels used to approximate the hull surface of a ship.

Flow around a Triaxial Ellipsoid in a Long Circular Tube

2011 ◽  
Vol 66 (8-9) ◽  
pp. 481-488
Author(s):  
Doo-Sung Lee
Keyword(s):  
Differential Equation ◽  
Fluid Dynamics ◽  
Fluid Flow ◽  
Circular Cylinder ◽  
Circular Tube ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Triaxial Ellipsoid ◽  
Viscous Fluid Flow ◽  
Integro Differential Equation

Abstract This paper deals with the three-dimensional analysis of viscous fluid flow in a long circular cylinder containing an ellipsoidal obstacle. The center of the ellipsoid coincides with that of the cylinder, and the flow is confined to the space between the ellipsoid and the cylinder when the fluid velocity at the large distance from the ellipsoid is uniform. The equations of the classical theory of fluid dynamics are solved in terms of an unknown function which is then shown to be the solution of a boundary integro-differential equation. A numerical solution of the integro-differential equation is obtained and the pressure on the surface of the ellipsoid is presented in graphical forms for various values of the radius of the circular tube.

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