LMA - Laboratoire de Mécanique et d’Acoustique

Blanc Emilie

Degree : PhD student

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PDF +33 4 91 16 40 80

Mail : eblanc@lma.cnrs-mrs.fr

Secretary : M.Madeleine MORANO

Research team : Waves and Imaging

Numerical modeling of poroelastic transient waves

PhD from October, 2010 to October, 2013, with PhD supervisors Guillaume Chiavassa (M2P2, Marseille, gchiavassa@centrale-marseille.fr) and Bruno Lombard (LMA, Marseille, lombard@lma.cnrs-mrs.fr).


Abstract of the thesis






  • 2007-2010 General engineer Ecole Centrale Marseille : Fluid, Energy, Transport, Environment, Health
  • 2009-2010 Master’s degree at IRPHE (Marseille) : Fluid mechanics and non-linear physics
  • October, 2010-October, 2013 PhD mechanics and acoustics at LMA : Numerical modeling of poroelastic transient waves


I investigate the propagation of poroelastic waves described by the Biot’s model in the time-domain. Most of the existing methods have been developed in the low-frequency range. The aim of my thesis is to derive some numerical methods in all the domain of validity of the Biot’s model. In the high-frequency range, the effects of the viscous boundary layer inside the pores must be taken into account. The model of dynamic permeability of Johnson-Koplik-Dashen (JKD) is used. In this case, some coefficients of the Biot-JKD’s model are proportional to the square root of the frequency. In the time-domain, fractional derivatives are therefore introduced into the evolution partial differential equations.

Two strategies exist to calculate these fractional derivatives. The first strategy is to compute the involved convolution integral. However, it requires to store the past of the solution, which is too penalizing in term of computational memory. The second strategy, which I implement, is based on a diffusive representation of the convolution kernel. The latter is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. The coefficients of the diffusive representation are determined by optimization on the frequency range of interest.

The properties of the Biot-JKD’s model with diffusive representation are analysed : decay of energy, error of the model. A numerical modeling is proposed, based on a splitting strategy : a propagative part is discretized by a fourth-order ADER scheme on a Cartesian grid, whereas a diffusive part is solved exactly. The properties of this algorithm are analysed. Numerical solutions are compared to analytical ones, with physical parameters representative of real media.

Propagation across a porous medium including 15 ellipsoidal scatterers


1. E. Blanc, G. Chiavassa, B. Lombard, "Biot-JKD model : simulation of 1D transient poroelastic waves with fractional derivatives", Journal of Computational Physics, 237 (2013), 1-20. Version PDF

2. E. Blanc, G.Chiavassa, B. Lombard, "A time-domain numerical method for Biot-JKD poroelastic waves in 2D heterogeneous media", accepted and to be published at Journal of Acoustical Society of America (2013).Version PDF


  • Review : European Journal of Control


1. XXIIème Journées d’Acoustique Physique Sous-Marine et Ultrasonore (2011).

2. Recent Developments in Wave Physics of Complex Media (2011).

3. Symposium on the Acoustics of Poro-Elastic Materials (2011).

4. 11ème Congrès Français d’Acoustique and 2012 Annual IOA Meeting (2012). Version PDF

5. Wave propagation in complex media and applications (2012).

6. 41ème Congrès National d’Analyse Numérique (2012).


  • General courses in mathematics (5h)
  • Teaching assistant in numerical analysis (20h)
  • Scilab practicals (14h)
  • Teaching assistant in probability and statistics (30h)