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Rainer Friedrich, Wolfgang Rodi's Advances in LES of Complex Flows (Fluid Mechanics and Its PDF

By Rainer Friedrich, Wolfgang Rodi

ISBN-10: 0306483831

ISBN-13: 9780306483837

ISBN-10: 1402004869

ISBN-13: 9781402004865

Comprises the court cases of the EUROMECH Colloquium, held in Munich, Germany. Articles concentrate on new advancements within the box of large-eddy simulation of advanced flows concerning the subjects of modeling and research of subgrid scales, numerical matters in LES, and combustion and magnetohydrodynamics.

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Extra resources for Advances in LES of Complex Flows (Fluid Mechanics and Its Applications) (v. 65)

Example text

These are the allowed multipoles. Other multipoles, which must be completely absent, are the forbidden multipoles. We can derive a simple expression for the allowed multipoles in a magnet designed with symmetry for a multipole of order n. Consider an additional multipole (a systematic error) in this field, of order m. By the principle of superposition, the total field can be written as By + iBx = |Cn | eiϕn rn−1 ei(n−1)θ + |Cm | eiϕm rm−1 ei(m−1)θ . 83) By design, the geometry is such that under a rotation about the z axis through π/n, the magnet looks the same, except that all currents have reversed direction: therefore the field simply changes sign.

In some ways, this is a very convenient representation, since it is the one usually provided directly by a magnetic modelling code: further processing is usually required to arrive at other representations. However, while a numerical field map in two dimensions is often a practical representation, in three dimensions the amount of data in even a relatively simple magnet can become extremely large, especially if a high resolution is required for the mesh. A multipole representation, on the other hand, provides the description of a magnetic field as a relatively small set of coefficients, from which the field components at any point can be reconstructed using the basis functions.

The fact that the allowed higher-order multipoles have an order given by an odd integer multiplied by the order of the main multipole is a consequence of the fact that magnetic poles always occur in north–south pairs: to maintain the correct rotational symmetry (with the field changing sign under a rotation through π/2) the first higher-order multipole must be constructed by ‘splitting’ each main pole into three, then into five, and so on. The field in a real magnet will contain all higher-order multipoles, not just the ones allowed by symmetry.

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Advances in LES of Complex Flows (Fluid Mechanics and Its Applications) (v. 65) by Rainer Friedrich, Wolfgang Rodi


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