Theoretical study of the separation of subcritical and supercriticalturbulent boundary layers by the method of integral equations

1969 ◽  
Author(s):  
J. DER
Keyword(s):  
Integral Equations ◽  
Boundary Layers ◽  
Theoretical Study ◽  
Method Of Integral Equations

Digital Modeling of Electromagnetic Processes in Technological Induction Devices

2021 ◽  
Vol 7 (7) ◽  
pp. 26-32
Author(s):  
Viktor B. DEMIDOVICH ◽  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Integral Equations ◽  
Transverse Magnetic ◽  
Combined Method ◽  
Method Of Integral Equations ◽  
Leading Role ◽  
Casting Aluminum ◽  
Point To Point ◽  
Element Method

Development of an electrical calculation method plays the leading role in simulating induction devices. In modeling electrical devices and complexes, it is often necessary to simultaneously solve both chain and field problems, i.e., to deal with both lumped and distributed parameters. The article considers the method of integral equations for induction systems with non-magnetic and ferromagnetic loading, which is based on the theory of long-range action. The method’s key statement is that the field at any point is determined as the sum of the fields produced by all sources, including primary and secondary ones. Another finite element method is based on the theory of short-range action, which describes the electromagnetic wave propagation from point to point, its refraction and reflection at the boundaries of media. The article substantiates the development of a combined method based on using the method of integral equations for calculating the input parameters of inductors (an external problem) and the finite element method for calculating the field distribution in the load (an internal problem). The combined method has well proven itself in modeling induction heating and melting of metals and oxides, heating a tape in a transverse magnetic field, induction plasmatrons, and casting aluminum into an electromagnetic crystallizer.

On the Heaving Motion of Cylinders of Shallow Draft

1961 ◽  
Vol 5 (04) ◽  
pp. 34-43
Author(s):  
R. C. MacCamy
Keyword(s):  
Integral Equations ◽  
Circular Disk ◽  
Finite Width ◽  
Two Dimensional ◽  
Virtual Mass ◽  
Method Of Integral Equations ◽  
First Approximation ◽  
Strip Theory ◽  
Considerable Simplification ◽  
Special Case

A perturbation procedure is developed for the two-dimensional motion produced by a long ship in heave when the draft is assumed small. The procedure reduces the shallow draft problem to a series of problems for a "raft" of zero draft. A considerable simplification in the method of integral equations is found to occur. For the first approximation, that is, a raft of finite width, the integral equations are solved numerically to determine pressure, virtual mass and damping. The problem of heave of a circular disk of zero draft is treated by the same methods so that an evaluation of strip theory in this special case is possible.

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