A 2D Time domain numerical method for the low frequency biot model

National audienceA numerical method is proposed to simulate the propagation of transient poroelastic waves across 2D heterogeneous media, in the low frequency range. A velocity-stress formulation of Biot's equations is followed, leading to a first-order system of partial differential equations. This system is splitted in two parts: a propagative one discretized by a fourth-order ADER scheme, and a diffusive one that is solved analytically. Near material interfaces, a space-time mesh refinement is implemented to capture the small spatial scales related to the slow compressional wave. Lastly, an immersed interface method is implemented to accurately model the jump conditions between the different media and the geometry of the interfaces. Numerical experiments and comparisons with exact solutions confirm the efficiency and the accuracy of the approach

Numerical modeling of 1-D transient poroelastic waves in the low-frequency range

Propagation of transient mechanical waves in porous media is numerically investigated in 1D. The framework is the linear Biot's model with frequency-independant coefficients. The coexistence of a propagating fast wave and a diffusive slow wave makes numerical modeling tricky. A method combining three numerical tools is proposed: a fourth-order ADER scheme with time-splitting to deal with the time-marching, a space-time mesh refinement to account for the small-scale evolution of the slow wave, and an interface method to enforce the jump conditions at interfaces. Comparisons with analytical solutions confirm the validity of this approach.Comment: submitted to the Journal of Computational and Applied Mathematics (2008

Time domain numerical modeling of wave propagation in 2D heterogeneous porous media

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.Comment: Journal of Computational Physics (March 2011

Numerical modeling of 1-D transient poroelastic waves

International audienc

A time domain numerical method for the low frequency Biot model

National audienceA numerical method is proposed to simulate the propagation of transient poroelastic waves across heterogeneous media, in the low frequency range. A velocity-stress formulation of Biot's equations is followed, leading to a first-order differential system. This system is splitted in two parts: a propagative one discretized by a fourth-order ADER scheme, and a diffusive one that can be solved analytically. Near acoustic sources and media interfaces, a space-time mesh refinement is implemented to capture the small spatial scales related to the diffusive slow compressional wave. Lastly, since the physical parameters are non-homogeneous, an immersed interface method is implemented to accurately model the jump con- ditions between the different media. The resulting method allows to investigate the propagation through porous/porous or fluid/porous media with realistic values of physical parameters. Numerical experiments in two and three dimensions and comparisons with exact solutions confirm that the whole set of compressional and shear waves is efficiently modeled

Enantioselective rhodium-catalyzed addition of arylboronic acids to alkenylheteroarenes

In the presence of a rhodium complex containing a newly developed chiral diene ligand, alkenes activated by a range of π-deficient or π-excessive heteroarenes engage in highly enantioselective conjugate additions with various arylboronic acids