On the augmented BiotJKD equations with PoleResidue representation of the dynamic tortuosity
Abstract
In this paper, we derive the augmented BiotJKD equations, where the memory terms in the original BiotJKD 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 $T^D(\omega)$ by utilizing its Stieltjes function representation derived in \cite{ou2014onreconstructi}, where an algorithm for computing the poleresidue 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 $T^D(\omega)$ 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 \cite{ou2014onreconstructi}.
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1805.00335
 Bibcode:
 2018arXiv180500335O
 Keywords:

 Mathematics  Numerical Analysis;
 Mathematics  Complex Variables