Multisymplectic formulation of fluid dynamics using the inverse map
Cotter, C. J., Holm, D. D. and Hydon, P. E. (2007) Multisymplectic formulation of fluid dynamics using the inverse map Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463 (2086). pp. 2671-2687.
An asymptotic Green's function in homogeneous anisotropic viscoelastic media is derived. The Green's function in viscoelastic media is formally similar to that in elastic media, but its computation is more involved. The stationary slowness vector is, in general, complex valued and inhomogeneous. Its computation involves finding two independent real-valued unit vectors which specify the directions of its real and imaginary parts and can be done either by iterations or by solving a system of coupled polynomial equations. When the stationary slowness direction is found, all quantities standing in the Green's function such as the slowness vector, polarization vector, phase and energy velocities and principal curvatures of the slowness surface can readily be calculated.
The formulae for the exact and asymptotic Green's functions are numerically checked against closed-form solutions for isotropic and simple anisotropic, elastic and viscoelastic models. The calculations confirm that the formulae and developed numerical codes are correct. The computation of the P-wave Green's function in two realistic materials with a rather strong anisotropy and absorption indicates that the asymptotic Green's function is accurate at distances greater than several wavelengths from the source. The error in the modulus reaches at most 4% at distances greater than 15 wavelengths from the source.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|Date :||8 October 2007|
|Identification Number :||https://doi.org/10.1098/rspa.2007.1862|
|Uncontrolled Keywords :||anisotropy, attenuation, Green's function, viscoelasticity|
|Additional Information :||Published in Proceedings of the Royal Society A, 463, 2671-2687. Copyright 2007 The Royal Society.|
|Depositing User :||Mr Adam Field|
|Date Deposited :||27 May 2010 14:41|
|Last Modified :||23 Sep 2013 18:33|
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