Publications
Articles in peer-reviewed journals
Fictitious domain method for acoustic waves through a granular suspension of movable rigid spheres
Journal of Computational Physics 280 p. 676-691, 2015Abstract Access to the full article
We develop a model to couple acoustic waves and the motion of rigid movable grains in a submerged suspension. To do so, we use the fictitious domain method based on distributed Lagrange multipliers to enforce the natural jump condition of the wave equation and a rigidity constraint. One can then model the granular medium with Molecular Dynamics or related methods. Both dynamic and acoustic numerical results are compared with analytic solutions of acoustics and an estimation of the error is given. We show energy transfers between two submerged grains separated by water and linked to their own spring while oscillating. The model is applied at large scale with a suspension of many grains to foresee its future possibilities.
Fictitious domain method to model a movable rigid body in a sound wave
Journal of Numerical Mathematics 20(3-4) p. 267-285, 2012Abstract Access to the full article
Motivated by experiments on the acoustics of submerged granular media, we have developed a new fictitious domain method that combines the acoustic wave equation with the equations of motion of a rigid body. The coupling is realized through the natural boundary conditions of the wave equation on the surface of the body and enforced with boundary Lagrange multipliers. The method is validated using analytic solutions for a movable rigid sphere in a sound wave. Results show that the method is promising because numerical results and analytic solutions are close for long wavelengths, although some deviations occur when the wavelength is smaller to the sphere radius. This method permits us to use a discrete element method for particle motion and interaction, and finite elements for wave propagation in the fluid.
Thesis
Propagation d'ondes acoustiques dans une suspension de grains mobiles immergés : couplage de modèles discret et continu par la méthode des domaines fictifs
PhD thesis, University of Rennes 1, France, , 2013
Abstract Download the pdf (french) Go to the "Theses" portal
When an acoustic wave propagates through a granular medium, it causes the grains to move, usually very slightly. In the same way, the movement of a grain embedded in a fluid matrix generates an acoustic wave. In both cases, acoustic energy is transmitted by the fluid and by the inter-granular contacts. We have developed a new numerical model for simulating wave propagation in submerged granular media that takes into account these two modes of energy transport. For the case of dry granular media, the grains are embedded in air whose inertia is so low that the energy it carries can be neglected. These media can be modeled with "Molecular Dynamics" or related methods. On the contrary, when granular media are submerged in water, the energy carried by the fluid cannot be neglected, rendering their modelization much more difficult. We use the fictitious domain method with distributed Lagrange multipliers to couple the equation of motion of the grains to the wave equation of the fluid. We use finite elements to propagate the wave in the fluid, and the grains are modeled in 2D by rigid, incompressible spheres compatible with the hypotheses of Molecular Dynamics. To validate the model, we perform series of numerical experiments whose results are compared to analytic solutions from acoustics. We also perform a simulation with hundreds of grains under an incident wave to demonstrate the possibilities of the model.
Communications
Propagation of uncertainties for an evaluation of the Azores-Gibraltar Fracture Zone tsunamigenic potential
European Geosciences Union (EGU) General Assembly
Vienna, Austria, April 17th to 22nd, 2016
Uncertainty on seismic sources and bathymetry for tsunami modelling
International Union of Geodesy and Geophysics (IUGG)
Prague, Czech Republic, June 22th to July 2nd, 2015
Abstract Download pdf
We show and quantify connections between the uncertainty on specific geological parameters of the generation process of tsunamis, numerical bathymetric parameters and the inundation hazard due to tsunamis. Our work is part of the French project TANDEM which aim is to provide guidance for Tsunami risk assessment on the Atlantic Ocean coastlines. Within this framework, we couple our software, which models tsunamis due to earthquakes, and the Promethee software (http://promethee.irsn.org), which propagates uncertainty through numerical models. On one hand, Our model uses Okada's analytic formulation to model the water surface deformation due to earthquakes in order to generate the tsunami. Then, the shallow water equations are discretized using the finite difference method to propagate the tsunami towards the coast. On the other hand, Promethee is used to propagate sources of uncertainties through the physical model and to perform a global sensitivity analysis. To do so, it runs and analyses a large number of simulations while changing parameters to examine all possible scenarios of the tsunami propagation. We present a preliminary uncertainty analysis of Okada's model parameters such as location, dimensions, orientation of the rupture zone, or shear modulus. We also quantify the effects of the numerical precision of bathymetric grids on the uncertainty of relevant output data for the tsunami warning such as the maximum water height at the coast.
1755 Lisbon tsunami towards the French Atlantic coasts: propagation of uncertainties
International Union of Geodesy and Geophysics (IUGG)
Prague, Czech Republic, June 22th to July 2nd, 2015
Northern Caribbean Tsunami Hazard: Tsunamis induced by the 2010 Haïti Earthquake
European Geosciences Union (EGU) General Assembly
Vienna, Austria, April 12th to 17th, 2015
Abstract
Northern Caribbean Tsunami Hazard: Tsunamis induced by the 2010 Haïti Earthquake.
A numerical method for sound waves in a submerged granular medium
International Congress on Ultrasonics (ICU)
Singapore, May 1st to 4th, 2013
Related publication: G. W. Siong, L. S. Piang, and K. B. Cheong editors,
Proceedings of the 2013 International Congress on Ultrasonics, p. P0338Abstract
Different numerical models exist to simulate sound propagation through granular media in a fluid matrix, such as random bead piles. In such models, the granular medium is represented by static arrangements of particles, i.e. neither inter-particle contacts nor interaction between the sound and particle motion are considered. In the present work, we have developed a new numerical model which takes these effects into account by combining two approaches: (1) the "Molecular Dynamics" approach that models the grains as incompressible 2D rigid spheres, manages collisions, and computes inter-particle forces, and (2) the Finite Elements approach that propagates the acoustic wave through the liquid matrix. In order to couple both the particle motion and the acoustic wave equations, we work with the Fictitious Domain method which uses Lagrange multipliers to enforce natural boundary conditions of the wave equation and the rigidity constraint.
In this way, our model can work in two different ways: a sound pulse can be emitted (1) by an active acoustic source as in conventional NDT studies or (2) by a micro-rearrangement of the particles inside the granular medium. In the former case, we apply our model to characterize the state of a granular pile from the acoustic waves backscattered by the particles. The numerical results are compared with previous experiments performed on immersed glass beads and characterized by an original multiscale analysis based on the wavelet response method. The latter case deals with mechanical vibrations originating inside the granular skeleton. We model the acoustic emissions induced by particle rearrangements during a gravitational destabilization: the simulated acoustic wavefield is compared to experimental data where acoustic emissions appear as avalanche precursors.
Simulations acoustiques dans des milieux granulaires immergés
ANR StabInGraM,
Rennes, France, November 26th and 27th, 2012
Modélisation de grains diffusant dans un fluide
Journée des Doctorants de SDLM, poster
Rennes, France, January 18th, 2012
Prize of the best poster
A distributed Lagrange multiplier based / fictitious domain method to model acoustic wave propagation in granular media in a fluid
3rd Workshop on Generic Solvers for PDEs: FreeFem++ and Applications
Paris, France, December 5th to 7th, 2011Abstract Related article
The objective of our work is to simulate the propagation of an acoustic wave through a submerged granular medium where the effect of inter-particle contacts must be taken into account. The particles are modeled as incompressible 2D rigid spheres, and the inter-particle forces will be calculated using "Molecular Dynamics" method. The incident wavelength is much greater than particle radius. To do this, we propose a new fictitious domain method to couple the acoustic wave equation [Bokil and Glowinski 2005] and Newton's second law for point particles [Glowinski et al. 1999]. Using a distributed Lagrange multiplier method, we enforce the rigid-body motion constraint as a side constraint. We also introduce tricks into FreeFEM++ to obtain pseudo-regular meshes and to use real solution functions and real test functions for the point particles equations in the problem definition. A first test consists of fixing one particle to a spring and studying scattered wave and system energy.
Couplage fluide/grains pour modéliser la propagation acoustique en milieu granulaire immergé
GdR Transport Solide Naturel
Rennes, France, November 28th and 29th, 2011
Tips and tricks for finite difference and i/o-less FWI
SEG International Exposition and 81th Annual Meeting
San Antonio, Texas, USA, September 18th to 23rd, 2011
Related publication: SEG Technical Program Expanded Abstracts 2011, p. 3174-3178Abstract Access extended abstract
Thanks to the computer capability grow in the last decade, the FD method reappeared in 3D seismic to simulate the full two-way wave equation, together with 3D reverse time migration (RTM) and full waveform inversion (FWI). In addition to the optimized implementation of 3D stencils, the reverse time migration heavily relies on interconnect and i/o (input/output) subsystem to support domain decomposition communication as well as the necessary snapshots for cross correlation of the forward and backward wave-fields. In this paper, we summarize the different levels of optimization available to speedup stencil computations. We also define a model to estimate the actual efficiency of such algorithm. To optimize the FWI algorithm we revisit check-pointing algorithms based on Griewank (1992) that were already used in Computational fluid dynamics and in seismic (Symes, 2007) to avoid or limit the i/o. Such techniques are implemented using main memory and/or disk as a checkpoint device at the cost of some recomputation of the forward propagation. The key point is to use a fast i/o device. We also show that a dedicated hybrid parallel implementation using MPI and OpenMP can help to extend this model to larger workload and to keep almost all data in memory, still achieving good scalability: Instead of using large parallel filesystem, local fast i/o devices based on SSD technology can ensure the extra i/o needs.
Modélisation des propriétés acoustiques des milieux granulaires immergés
2ème Journée des Jeunes Chercheurs de l'INSA de Rennes - MMS, poster
Rennes, France, June 23rd, 2011
2nd prize of the best poster
Training reports
Imagerie sismique 3D de structures complexes
Master 2 training report, University of Rennes 1 & Geosciences Research Center of MINES ParisTech, 2010
Inversion de données ultrasonores pour la caractérisation de soudures hétérogènes
Master 1 training report, University of Rennes 1 & IRMAR (JRU 6625 CNRS), 2009