Absorbing boundaries for wave propagation problems
Journal of Computational Physics
Discrete-time signal processing (2nd ed.)
Discrete-time signal processing (2nd ed.)
Wave propagation in media with singular memory
Mathematical and Computer Modelling: An International Journal
Matrix approach to discrete fractional calculus II: Partial fractional differential equations
Journal of Computational Physics
Numerical modeling of 1D transient poroelastic waves in the low-frequency range
Journal of Computational and Applied Mathematics
A local high-order doubly asymptotic open boundary for diffusion in a semi-infinite layer
Journal of Computational Physics
A Fast Time Stepping Method for Evaluating Fractional Integrals
SIAM Journal on Scientific Computing
Time domain numerical modeling of wave propagation in 2D heterogeneous porous media
Journal of Computational Physics
Least-Squares Spectral Method for the solution of a fractional advection-dispersion equation
Journal of Computational Physics
Biot-JKD model: Simulation of 1D transient poroelastic waves with fractional derivatives
Journal of Computational Physics
Numerical modeling of nonlinear acoustic waves in a tube connected with Helmholtz resonators
Journal of Computational Physics
Hi-index | 31.48 |
The objective of this paper is to use Biot's theory and the Johnson-Koplik-Dashen dynamic permeability model in wave field simulation of a heterogeneous porous medium. The Johnson-Koplik-Dashen dynamic permeability model was originally formulated in the frequency domain. In this paper, the time domain drag force expression of the model is expressed in terms of the shifted fractional derivative of the relative fluid velocity. In contrast to the exponential-type viscous relaxation models, the convolution operator in the Johnson-Koplik-Dashen dynamic permeability model cannot be replaced by memory variables satisfying first-order relaxation differential equations. A new method for calculating the shifted fractional derivative without storing and integrating the entire velocity histories is developed. Using the new method to calculate the fractional derivative, the governing equations for the two-dimensional porous medium are reduced to a system of first-order differential equations for velocities, stresses, pore pressure and the quadrature variables associated with the drag forces. Spatial derivatives involved in the first-order differential equations system are calculated by Fourier pseudospectral method, while the time derivative of the system is discretized by a predictor-corrector method. For the demonstration of our method, some numerical results are presented. .