On the Augmented Biot-JKD Equations with Pole-Residue Representation of the Dynamic Tortuosity
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 , 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 .
KeywordsBiot-JKD equations tortuosity Stieltjes function pole-residue approximation two-sided residue interpolation
Mathematics Subject Classification (2010)35R30 76S05 41A21 30E10
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