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On the Augmented Biot-JKD Equations with Pole-Residue Representation of the Dynamic Tortuosity
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On the Augmented Biot-JKD Equations with Pole-Residue Representation of the Dynamic Tortuosity

Miao-Jung Yvonne Ou and Hugo J. Woerdeman
Interpolation and Realization Theory with Applications to Control Theory, pp 307-328
09 Apr 2019
DOI: https://doi.org/10.1007/978-3-030-11614-9_12
url
http://arxiv.org/abs/1805.00335View
SubmittedOpen Access (License Unspecified),  Open

Abstract

30E10 35R30 41A21 76S05 Biot-JKD equations pole-residue approximation Stieltjes function tortuosity two-sided residue interpolation
In this paper, we derive the augmented Biot-JKD equations, where the memory terms in the original Biot-JKD equations are dealt with by introducing auxiliary dependent variables. The evolution in time of these new variables are governed by ordinary differential equations whose coefficients can be rigorously computed from the JKD dynamic tortuosity function TD(ω) by utilizing its Stieltjes function representation derived in [19], where an approach for computing the pole-residue representation of the JKD tortuosity is also proposed. The two numerical schemes presented in the current work for computing the poles and residues representation of TD(ω) improve the previous scheme in the sense that they interpolate the function at infinite frequency and have much higher accuracy than the one proposed in [19].

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