Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Wave field simulation for heterogeneous porous media with singular memory drag force
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Numerical modeling of elastic waves across imperfect contacts.
SIAM Journal on Scientific Computing
Numerical modeling of 1D transient poroelastic waves in the low-frequency range
Journal of Computational and Applied Mathematics
Efficient solution of a wave equation with fractional-order dissipative terms
Journal of Computational and Applied Mathematics
Biot-JKD model: Simulation of 1D transient poroelastic waves with fractional derivatives
Journal of Computational Physics
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This paper deals with the numerical modeling of wave propagation in porous media described by Biot's theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range. The coexistence of propagating fast compressional wave and shear wave, and of a diffusive slow compressional wave, makes numerical modeling tricky. To avoid restrictions on the time step, the Biot's system is splitted into two parts: the propagative part is discretized by a fourth-order ADER scheme, while the diffusive part is solved analytically. Near the material interfaces, a space-time mesh refinement is implemented to capture the small spatial scales related to the slow compressional wave. The jump conditions along the interfaces are discretized by an immersed interface method. Numerical experiments and comparisons with exact solutions confirm the accuracy of the numerical modeling. The efficiency of the approach is illustrated by simulations of multiple scattering.