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Papers by Nathalie Glinsky

HAL (Le Centre pour la Communication Scientifique Directe), 2018

A two-year seismological experiment in Rognes (South Eastern France) confirms the site effects re... more A two-year seismological experiment in Rognes (South Eastern France) confirms the site effects responsible for the severe damage experienced during the 1909 Provence earthquake. Many experimental and numerical studies have been dedicated to quantify and understand the effect of topography on seismic ground motion. However, these local amplifications depend on many parameters and their causes are not yet fully known. Numerical simulation is an interesting tool to try to explain these phenomena and simplified models are helpful for parametric analysis. For this, we use a discontinuous Galerkin finite element method to study the amplification along 2D profiles. First, an extensive numerical study considering an idealized hill topography investigates the combined effects of the steepness, heterogeneity and the angle of incidence on the surface response and focuses in particular on strong amplifications recorded in gentle slope configurations. Secondly, simulations are applied to a realistic 2D profile of the Rognes area. The confrontation of these numerical results with data from a seismological survey help to confirm the influence of both the topography and in-depth geology.

HAL (Le Centre pour la Communication Scientifique Directe), Aug 30, 2010

Journal of Computational Physics, Feb 1, 2018

We propose a nodal high-order discontinuous Galerkin method for 1D wave propagation in nonlinear ... more We propose a nodal high-order discontinuous Galerkin method for 1D wave propagation in nonlinear media. We solve the elastodynamic equations written in the velocity-strain formulation and apply an upwind flux adapted to heterogeneous media with nonlinear constitutive behavior coupling stress and strain. Accuracy, convergence and stability of the method are studied through several numerical applications. Hysteresis loops distinguishing loading and unloading-reloading paths are also taken into account. We investigate several effects of nonlinearity in wave propagation, such as the generation of high frequencies and the frequency shift of resonant peaks to lower frequencies. Finally, we compare the results for both nonlinear models, with and without hysteresis, and highlight the effects of the former on the stabilization of the numerical scheme.

ESAIM, 2009

We are interested in the simulation of P-SV seismic wave propagation by a high-order Discontinuou... more We are interested in the simulation of P-SV seismic wave propagation by a high-order Discontinuous Galerkin method based on centered fluxes at the interfaces combined with a leapfrog time-integration. This non-diffusive method, previously developed for the Maxwell equations [4, 9, 20], is particularly well adapted to complex topographies and fault discontinuities in the medium. We prove that the scheme is stable under a CFL type condition and that a discrete energy is preserved on an infinite domain. Convergence properties and efficiency of the method are studied through numerical simulations in two and three dimensions of space. Résumé. Nous nous intéressonsà la propagation d'ondes sismiques de types P et SV par une méthode de Galerkin Discontinue d'ordreélevé basée sur des flux centrés aux interfaces combinésà un schéma saute-mouton en temps. Cette méthode non-dissipative, précédemment développée pour leséquations de Maxwell [4, 9, 20], est particulièrement bien adaptéeà des milieux présentant une topographie complexe ou contenant des failles. On prouve la stabilité du schéma sous une condition de type CFL ainsi que la conservation d'une energie discrète dans un domaine infini. L'efficacité de la méthode est illustrée par des simulations numériques en deux et trois dimensions d'espace.

Comptes Rendus Mathematique, Feb 1, 2003

On considère les équations de Navier-Stokes compressibles pour des gaz régis par des lois général... more On considère les équations de Navier-Stokes compressibles pour des gaz régis par des lois générales de pression et de température, celles-ci étant compatibles avec l'existence d'une entropie et les relations de Gibbs. On étend la méthode de relaxation introduite pour les équations d'Euler par Coquel et Perthame. En conservant les mêmes conditions « souscaractéristiques » pour les flux hyperboliques et grâce à une décomposition consistante des flux diffusifs basée sur une température globale, on montre la stabilité du système relaxé via le signe de la production d'une certaine entropie. Une analyse asymptotique au premier ordre autour des états d'équilibre confirme le résultat de stabilité. On présente enfin une implémentation numérique de la méthode. Pour citer cet article : E.

Geophysical Journal International, Mar 25, 2015

We present an extension of the nodal discontinuous Galerkin method for elastic wave propagation t... more We present an extension of the nodal discontinuous Galerkin method for elastic wave propagation to high interpolation orders and arbitrary heterogeneous media. The high-order lagrangian interpolation is based on a set of nodes with excellent interpolation properties in the standard triangular element. In order to take into account highly variable geological media, another set of suitable quadrature points is used where the physical and mechanical properties of the medium are defined. We implement the methodology in a 2-D discontinuous Galerkin solver. First, a convergence study confirms the hp-convergence of the method in a smoothly varying elastic medium. Then, we show the advantages of the present methodology, compared to the classical one with constant properties within the elements, in terms of the complexity of the mesh generation process by analysing the seismic amplification of a soft layer over an elastic half-space. Finally, to verify the proposed methodology in a more complex and realistic configuration, we compare the simulation results with the ones obtained by the spectral element method for a sedimentary basin with a realistic gradient velocity profile. Satisfactory results are obtained even for the case where the computational mesh does not honour the strong impedance contrast between the basin bottom and the bedrock.

EGUGA, Apr 1, 2013

We present a novel technique for solving extension problems such as the extension velocity, by re... more We present a novel technique for solving extension problems such as the extension velocity, by reformulating the problem into an elliptic differential equation. We introduce a novel discretization using an upwind flux without any additional stabilization. This leads to a triangular matrix structure, which can be solved using a marching algorithm and high-order accuracy, even in the presence of singularities.

Journal of theoretical and computational acoustics, Sep 1, 2018

We present a higher-order discretization scheme for the compressible Euler and Navier-Stokes equa... more We present a higher-order discretization scheme for the compressible Euler and Navier-Stokes equations with immersed boundaries. Our approach makes use of a Discontinuous Galerkin (DG) discretization in a domain that is implicitly defined by means of a level set function. The zero iso-contour of this level set function is considered as an additional domain boundary where we weakly enforce boundary conditions in the same manner as in boundary-fitted cells. In order to retain the full order of convergence of the scheme, it is crucial to perform volume and surface integrals in boundary cells with high accuracy. This is achieved using a linear moment-fitting strategy. Moreover, we apply a non-intrusive cell-agglomeration technique that averts problems with very small and ill-shaped cuts. The robustness, accuracy and convergence properties of the scheme are assessed in several two-dimensional test cases for the steady compressible Euler and Navier-Stokes equations. Approximation orders range from zero to four, even though the approach directly generalizes to even higher orders. In all test cases with a sufficiently smooth solution, the experimental order of convergence matches the expected rate for DG schemes.

68th EAGE Conference and Exhibition incorporating SPE EUROPEC 2006, 2006

For seismic wave propagation, we propose a complete reanalysis of the finite-volume approach base... more For seismic wave propagation, we propose a complete reanalysis of the finite-volume approach based on unstructured triangular meshes. Triangular control volumes are particularly well adapted to the propagation of elastic waves in heterogeneous media. We consider a non-staggered pseudo-conservative formulation as time variation is controlled by fluxes on edges of the element and we implement in a 2D geometry both source excitation and absorbing boundary conditions as PML zones. Simple illustrations show that this method could be a competitor of more traditional finite-difference methods.

A nodal high-order discontinuous Galerkin method for elastic wave propagation in arbitrary hetero... more A nodal high-order discontinuous Galerkin method for elastic wave propagation in arbitrary heterogeneous media