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- Joël Piraux, Joseph Aiguier
- 2004

A new numerical method, called the Explicit Simplified Interface Method (ESIM), is developed in the context of acoustic wave propagation in heterogeneous media. Equations of acoustics are written as a first-order linear hyperbolic system. Away from interfaces, a standard scheme (Lax-Wendroff, TVD, WENO...) is used in a classical way. Near interfaces, the… (More)

- B. Lombard, J. Piraux, C. Gélis, J. Virieux
- 2008

SUMMARY A method is proposed for accurately describing arbitrary-shaped free boundaries in finite-difference schemes for elastodynamics, in a time-domain velocity-stress framework. The basic idea is as follows: fictitious values of the solution are built in vacuum, and injected into the numerical integration scheme near boundaries. The most original feature… (More)

- Bruno Lombard, Joël Piraux
- SIAM J. Scientific Computing
- 2003

Elastic wave propagation is studied in a heterogeneous 2-D medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident wavelength is similar to the radius of the inclusions. A purely numerical methodology is presented, with which the… (More)

- Bruno Lombard, Joël Piraux
- 2005

The propagation of elastic waves in a fractured rock is investigated, both theoretically and numerically. Outside the fractures, the propagation of compressional waves is described in the simple framework of one-dimensional linear elastodynam-ics. The focus here is on the interactions between the waves and fractures: for this purpose, the mechanical… (More)

Propagation of monochromatic elastic waves across cracks is investigated in 1D, both theoretically and numerically. Cracks are modeled by nonlinear jump conditions. The mean dilatation of a single crack and the generation of harmonics are estimated by a perturbation analysis, and computed by the harmonic balance method. With a periodic and finite network of… (More)

- Bruno Lombard, Joël Piraux
- SIAM J. Scientific Computing
- 2006

A numerical method is described for studying how elastic waves interact with imperfect contacts such as fractures or glue layers existing between elastic solids. These contacts have been classicaly modeled by interfaces, using a simple rheological model consisting of a combination of normal and tangential linear springs and masses. The jump conditions… (More)

- Guillaume Chiavassa, Bruno Lombard, Joël Piraux
- J. Computational Applied Mathematics
- 2010

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… (More)

- Bruno Lombard, Joël Piraux
- J. Comput. Physics
- 2011

A 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… (More)