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\begin{document}

\title{Time-domain numerical modeling of wave propagation in poroelastic media
with rational approximation of the fractional attenuation}



\author[1]{Jiangming Xie}%
\author[2]{Maojun Li}%
\author[3]{Miao-Jung Ou}%
\affil[1]{Tsinghua University}%
\affil[2]{University of Electronic Science and Technology of China}%
\affil[3]{University of Delaware}%


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  \date{May 04, 2024}


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\begin{abstract}
n this work, we investigate the poroelastic waves by solving the
time-domain Biot-JKD equation with an efficient numerical method. The
viscous dissipation occurring in the pores depends on the square root of
the frequency and is described by the Johnson-Koplik-Dashen (JKD)
dynamic tortuosity/permeability model. The temporal convolutions of
order 1/2 shifted fractional derivatives are involved in the time-domain
Biot-JKD model, causing the problem to be stiff and challenging to be
implemented numerically. Based on the best relative approximation of the
square-root function, we design an efficient algorithm to approximate
and localize the convolution kernel by introducing a finite number of
auxiliary variables that satisfy a local system of ordinary differential
equations. The imperfect hydraulic contact condition is used to describe
the interface boundary conditions and the Runge-Kutta discontinuous
Galerkin (RKDG) method together with the splitting method is applied to
compute the numerical solutions. Several numerical examples are
presented to show the accuracy and efficiency of our approach.%
\end{abstract}%



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