LMA - Laboratoire de Mécanique et d’Acoustique


Directeur de Recherche, CNRS

DIRECTEUR ADJOINT du LMA depuis janvier 2018

Research interests

  • Waves in continuous media
  • Dynamic homogenization
  • Nonlinear acoustics, solitons, softening
  • Numerical methods for hyperbolic systems
  • Fractional calculus


  • 1973 : born in Lyon (France)
  • 1994-1997 : Ecole Supérieure d’Ingénieurs de Marseille (now Ecole Centrale Marseille)
  • 2002 : PhD in mechanics, speciality acoustics (Aix-Marseille, France)
  • 2002-2003 : post-doc at the Departamento de Matematica Aplicada (Valencia, Spain)
  • 2003 – present : CNRS researcher at the Laboratoire de Mécanique et Acoustique (Marseille, France)
  • 2010 : habilitation thesis

PhD students

  • Marie Touboul, "Acoustic and elastic wave propagation in microstructured media with interfaces : homogenization, simulation and optimization", codir Cédric Bellis (2018-2021). Manuscript.
  • Harold Berjamin, "Modeling wave propagation in nonlinear solids with slow dynamics", codir Guillaume Chiavassa and Nicolas Favrie (2015-2018). Manuscript.
  • Romain de Monchy, "Développement et évaluation d’une théorie de milieu effectif combinée à un facteur de structure polydisperse pour la caractérisation ultrasonore de l’agrégation érythrocytaire", codir Emilie Franceschini (2013-2016). Manuscript.
  • Emilie Blanc, "Time-domain numerical modeling of poroelastic waves : the Biot-JKD model with fractional derivatives", codir Guillaume Chiavassa (2010-2013). Manuscript.


49 - R. Cornaggia, B. Lombard, "An homogenized model accounting for dispersion, interfaces and source points for transient waves in 1D periodic media", ESAIM : Mathematical Modelling and Numerical Analysis 57 (2023), 1413-1444. Preprint

48 - N. Favrie, B. Lombard, "A hyperbolic generalized Zener model for nonlinear viscoelastic waves", Wave Motion 116 (2023), 103086. Preprint

47 - D. Colas, C. Bellis, B. Lombard, R. Cottereau, "Crossover between quantum and classical waves and high-frequency localization landscapes", Physical Review B 106 (2022), 184210. Preprint

46 - M. Touboul, X. Gao, B. Lombard, "Damping in a row of locally-resonant inclusions : dynamic homogenization and scattering of transient shear waves", Wave Motion 107 (2021), 102811. Preprint

45 - S. Guenneau, B. Lombard, C. Bellis, “Time-domain investigation of an external cloak for antiplane elastic waves", Applied Physics Letters 118 (2021), 191102. Preprint

44 - L. Schwan, N. Favrie, R. Cottereau, B. Lombard, "Extended stress gradient elastodynamics : Wave dispersion and micro-macro identification of parameters", International Journal on Solids and Structures 219-220 (2021), 34-50. Preprint

43 - C. Bellis, B. Lombard, M. Touboul, R. Assier, "Effective dynamics for low-amplitude transient elastic waves in a 1D periodic array of non-linear interfaces", Journal of the Mechanics and Physics of Solids 149 (2021), 104321. Preprint

42 - R. Assier, M. Touboul, B. Lombard, C. Bellis, "High-frequency homogenisation in periodic media with imperfect interfaces", Proceedings Royal Society London A, 476 (2020), 20200402. Preprint

41 - S. Bourgeois, N. Favrie, B. Lombard, "Dynamics of a regularized and bistable Ericksen bar using an extended Lagrangian approach", International Journal on Solids and Structures 207 (2020), 55-69. Preprint

40 - M. Touboul, K. Pham, A. Maurel, J.J. Marigo, B. Lombard, C. Bellis , "Effective resonant model and simulations in the time domain of wave scattering from a periodic row of highly-contrasted inclusions", Journal of Elasticity 142 (2020), 53-82. Preprint

39 - M. Touboul, B. Lombard, C. Bellis, "Time-domain simulation of wave propagation across resonant meta-interfaces", Journal of Computational Physics 414 (2020), 109474. Preprint

38 - S. Junca, B. Lombard, "Analysis of a Sugimoto model of nonlinear acoustics in an array of Helmholtz resonators", SIAM Journal on Applied Mathematics 80-4 (2020), 1704-1722. Preprint

37 - H. Berjamin, B. Lombard, G. Chiavassa, N. Favrie, "Plane-strain waves in nonlinear elastic solids with softening", Wave Motion, 89 (2019), 65-78. Preprint

36 - C. Bellis, B. Lombard, "Simulating transient wave phenomena in acoustic metamaterials using auxiliary fields", Wave Motion, 86 (2019), 175-194. Preprint

35 - P. Vigué, C. Vergez, B. Lombard, B. Cochelin, "Continuation of periodic solutions for systems with fractional derivatives", Nonlinear Dynamics, 95-1 (2019), 479-493. Preprint

34 - H. Berjamin, B. Lombard, G. Chiavassa, N. Favrie, "A finite-volume approach to nonlinear longitudinal elastic waves : application to slow dynamics", Acta Acustica united with Acustica, 104 (2018), 561-570. Preprint.

33 - H. Berjamin, B. Lombard, G. Chiavassa, N. Favrie, "Modeling longitudinal wave propagation in nonlinear viscoelastic solids with softening", International Journal on Solids and Structures, 141-142 (2018), 35-44. Preprint.

32 - H. Berjamin, B. Lombard, G. Chiavassa, N. Favrie, "Analytical solution to 1D nonlinear elastodynamics with general constitutive laws", Wave Motion, 74 (2017), 35-55. Preprint.

31 - H. Berjamin, N. Favrie, B. Lombard, G. Chiavassa, "Nonlinear waves in solids with slow dynamics : an internal-variable model", Proceedings Royal Society London A, 473 (2017), 20170024. Preprint.

30 - J.F. Mercier, B. Lombard, "A two-way model for nonlinear acoustic waves in a non-uniform lattice of Helmholtz resonators", Wave Motion, 72 (2017), 260-275. Preprint.

29 - B. Lombard, A. Maurel, J.J. Marigo, "Numerical modeling of the acoustic wave propagation across an homogenized rigid microstructure in the time domain", Journal of Computational Physics, 335 (2017), 558-577. Preprint.

28 - H. Berjamin, B. Lombard, C. Vergez, E. Cottanceau, “Time-domain modeling of brass instruments including nonlinear wave propagation, viscothermal losses, and lips vibration”, Acta Acustica united with Acustica, 103 (2017), 117-131. Preprint.

27 - B. Lombard, D. Matignon, "Diffusive approximation of a time-fractional Burger’s equation in nonlinear acoustics", SIAM Journal on Applied Mathematics, 76-5 (2016), 1765-1791. Preprint.

26 - E. Blanc, D. Komatitsch, E. Chaljub, B. Lombard, Z. Xie, “Highly-accurate stability-preserving optimization of the Zener viscoelastic model, with application to wave propagation in the presence of attenuation“, Geophysical Journal International, 205 (2016), 427-439. Preprint.

25 - S. Bilbao, R. Harrison, J. Kergomard, B. Lombard, C. Vergez, “On passive models of wave propagation in acoustic tubes”, Journal of the Acoustical Society of America, 138-2 (2015), 555-558. Preprint.

24 - B. Lombard, J.F. Mercier, O. Richoux, “Numerical investigation of acoustical solitons”, Proceedings of the Estonian Academy of Sciences, 64-3 (2015), 304-310. Preprint.

23 - N. Favrie, B. Lombard, C. Payan, “Fast and slow dynamics in a nonlinear elastic bar excited by longitudinal vibrations”, Wave Motion, 56 (2015), 221-238. Preprint.

22 - O. Richoux, B. Lombard, J.F. Mercier, “Generation of acoustic solitary waves in a lattice of Helmholtz resonators”, Wave Motion, 56 (2015), 85-99. Preprint.

21 - E. Blanc, G. Chiavassa, B. Lombard, “Wave simulation in 2D heterogeneous transversely isotropic porous media with fractional attenuation : a Cartesian grid approach”, Journal of Computational Physics, 275 (2014), 118-142. Preprint.

20 - A. Ben Jazia, B. Lombard, C. Bellis, “Wave propagation in a fractional viscoelastic Andrade medium : diffusive approximation and numerical modeling”, Wave Motion, 51 (2014), 994-1010. Preprint.

19 - S. Junca, B. Lombard, “Stability of a nonlinear critical neutral differential delay equation”, Journal on Differential Equations, 256 (2014), 2368-2391. Preprint.

18 - B. Lombard, J.F. Mercier, “Numerical modeling of nonlinear acoustic waves in a tube with Helmholtz resonators”, Journal of Computational Physics, 259 (2014), 421-443. Preprint.

17 - E. Blanc, G. Chiavassa, B. Lombard, “A time-domain numerical method of two-dimensional wave propagation in porous media with frequency-dependent dynamic permeability”, Journal of Acoustical Society of America, 134-6 (2013), 4610-4623. Preprint.

16 - 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. Preprint.

15 - G. Chiavassa, B. Lombard, “Wave propagation across acoustic / Biot’s media : a finite-difference method”, Communications in Computational Physics, 13-4 (2013), 985-1012. Preprint.

14 - M. Chekroun, L. Le Marrec, B. Lombard, J. Piraux, “Multiple scattering of elastic waves : a numerical method for computing the effective wavenumbers”, Waves in Random and Complex Media, 22-3 (2012), 398-422. Preprint.

13 - G. Lefeuve-Mesgouez, A. Mesgouez, G. Chiavassa, B. Lombard, “Semi-analytical and numerical methods for computing transient waves in 2D acoustic / poroelastic stratified media”, Wave Motion, 49-7 (2012), 667-680. Preprint.

12 - S. Junca, B. Lombard, “Interaction between periodic elastic waves and two contact nonlinearities”, Mathematical Models and Methods in Applied Sciences, 22-4 (2012). Preprint.

11 - B. Lombard, J. Piraux, “Numerical modeling of transient two-dimensional viscoelastic waves”, Journal of Computational Physics, 230 (2011), 6099-6114. Preprint.

10 - G. Chiavassa, B. Lombard, “Time domain numerical modeling of wave propagation in 2D heterogeneous porous media”, Journal of Computational Physics, 230 (2011), 5288-5309. Preprint.

9 - G. Chiavassa, B. Lombard, J. Piraux, “Numerical modeling of 1-D transient poroelastic waves in the low-frequency range”, Journal of Computational and Applied Mathematics, 234 (2010), 1757-1765. Preprint.

8 - S. Junca, B. Lombard, “Dilatation of a one-dimensional nonlinear crack impacted by a periodic elastic wave”, SIAM Journal on Applied Mathematics, 70-3 (2009), 735-761. Preprint.

7 - B. Lombard, J. Piraux, C. Gélis, J. Virieux, “Free and smooth boundaries in 2-D finite-difference schemes for transient elastic waves”, Geophysical Journal International, 172 (2008), 252-261. Preprint.

6 - B. Lombard, J. Piraux, “Modeling 1-D elastic P-waves in a fractured rock with hyperbolic jump conditions”, Journal of Computational and Applied Mathematics, 204-2 (2007), 292-305. Preprint.

5 - B. Lombard, J. Piraux, “Numerical modeling of elastic waves across imperfect contacts”, SIAM Journal of Scientific Computing, 28-1 (2006), 172-205. Preprint.

4 - B. Lombard, R. Donat, “The Explicit Simplified Interface Method for compressible multicomponent flows”, SIAM Journal of Scientific Computing, 27-1 (2005), 208-230. Preprint.

3 - B. Lombard, J.Piraux, “Numerical treatment of two-dimensional interfaces for acoustic and elastic waves”, Journal of Computational Physics, 195-1 (2004), 90-116. Preprint.

2 - B. Lombard, J. Piraux, “How to incorporate the spring-mass conditions in finite-difference schemes”, SIAM Journal of Scientific Computing, 24-4 (2003), 1379-1407. Preprint.

1 - J. Piraux, B. Lombard, “A new interface method for hyperbolic problems with discontinuous coefficients : one-dimensional acoustic example”, Journal of Computational Physics, 168-1 (2001), 227-248. Preprint.


2 - B. Lombard, "Modélisation numérique de la propagation et de la diffraction d’ondes mécaniques", Habilitation à Diriger des Recherches de l’Université d’Aix-Marseille 2 (8 janvier 2010). Manuscript.

1 - B. Lombard, "Méthodes numériques pour la propagation des ondes mécaniques et acoustiques en présence d’interfaces", Thèse de l’Université d’Aix-Marseille 2 (4 janvier 2002). Manuscript.


  • PROSPERO (PROgramme de Simulation de la Propagation d’ondes en milieu hétEROgène). Web page