Papers by Sébastien Terrana
Méthodes Galerkin discontinues hybridables pour la propagation des ondes élastiques et acoustiques dans des milieux géophysiques complexes
Aujourd'hui les reseaux d'observation sismologique peuvent combiner des capteurs sismique... more Aujourd'hui les reseaux d'observation sismologique peuvent combiner des capteurs sismiques large-bande, hydrophones et micro-barometres. Exploiter l'ensemble de ces donnees necessite l'utilisation de simulations numeriques capables de modeliser la propagation des ondes dans des milieux acoustiques et elastiques, avec un couplage aux interfaces fluide-solide. Avec cette these, nous proposons une methode numerique de type Galerkin Discontinue Hybridable (HDG), d'ordre arbitrairement eleve en espace, permettant de modeliser la propagation des ondes elastodynamiques et acoustiques. Dans un premier temps, des conditions de transmission entre des milieux heterogenes elastiques et acoustiques sont construites en utilisant les relations de Rankine-Hugoniot. Ces conditions sont ensuite utilisees pour etablir les raccords inter-elements dans le cadre d'une methode HDG modelisant de maniere unifiee les propagation d'ondes mecaniques dans les deux milieux. Nous propo...
An HDG method for dissimilar meshes
IMA Journal of Numerical Analysis, 2021
We present a hybridizable discontinuous Galerkin (HDG) method for dissimilar meshes. The method i... more We present a hybridizable discontinuous Galerkin (HDG) method for dissimilar meshes. The method is devised by formulating HDG discretizations on separate meshes and gluing these HDG discretizations through appropriate transmission conditions that weakly enforce the continuity of the numerical trace and the numerical flux across the dissimilar interfaces. The transmission conditions are based upon transferring the numerical flux from the first mesh to the second mesh and the numerical trace from the second mesh to the first one. The transfer of the numerical trace/flux from one mesh to the other relies on the extrapolation of the approximate flux, and is made to be consistent with the HDG methodology for conforming meshes. Stability of the HDG method is shown and the error analysis of the HDG method is established. Numerical results are presented to validate the theoretical results.
Wall-resolved implicit large eddy simulation of transonic buffet over the OAT15A airfoil using a discontinuous Galerkin method
AIAA Scitech Forum, 2020
We present a wall-resolved implicit large eddy simulation (WRILES) of transonic buffet over the O... more We present a wall-resolved implicit large eddy simulation (WRILES) of transonic buffet over the OAT15A supercritical airfoil at at Mach number 0.73, angle of attack $3.5^{\rm o}$ and Reynolds number $3 \times 10^6$. The simulation is performed using a high-order discontinuous Galerkin (DG) method and a diagonally implicit Runge-Kutta (DIRK) scheme on graphics processor units (GPUs). In order to effectively resolve the boundary layers at high Reynolds numbers, we develop a LES mesh refinement strategy to provide adequate resolution in the normal and streamwise/crossflow directions while keeping the aspect ratio of the elements below 20. Without yhe need for subgrid scale or wall models, the WRILES method successfully predicts the buffet onset, the buffet frequency, and turbulence statistics. Various turbulence phenomena are predicted and demonstrated, such as periodical low-frequency oscillations of shock wave in the streamwise direction, strong shear layer detached from the shock wave due to shock wave boundary layer interaction (SWBLI) and small scale structures broken down by the shear layer instability in the transition region, and shock-induced flow separation. The pressure coefficient, the root mean square (RMS) of fluctuating pressure and streamwise range of shock wave oscillation agree well with experimental data. The results demonstrate the capability of the WRILES method for predicting the buffet phenomena at high Reynolds numbers.
GPU-accelerated Large Eddy Simulation of Hypersonic Flows
AIAA Scitech Forum, 2020
High-order discontinuous Galerkin (DG) methods have emerged as an attractive approach for large e... more High-order discontinuous Galerkin (DG) methods have emerged as an attractive approach for large eddy simulation of turbulent flows owing to their high accuracy and implicit dissipation properties. However, the application of DG methods for hypersonic flows is still challenging due to the high-computational cost and the lack of robust shock capturing algorithms. In this paper, we adreess the efficiency and robustness of Discontinuous Galerkin methods. To that end we develop a high-order implicit discontinuous Galerkin method for the numerical simulation of hypersonic flows on graphics processors (GPUs). The main ingredients in our approach include: i) implicit high-order DG approximation on unstructured/adapted meshes, ii) shock capturing for hypersonic flows, iii) iterative solution methods with CUDA/MPI implementation on GPU clusters, and iv) effective matrix-free preconditioner with reduced basis approximation of the Jacobian matrix. Numerical results on several test cases are presented to validate our method.
A hybridizable discontinuous Galerkin method for both thin and 3D nonlinear elastic structures
Computer Methods in Applied Mechanics and Engineering, 2019
We present a 3D hybridizable discontinuous Galerkin (HDG) method for nonlinear elasticity which c... more We present a 3D hybridizable discontinuous Galerkin (HDG) method for nonlinear elasticity which can be efficiently used for thin structures with large deformation. The HDG method is developed for a three-field formulation of nonlinear elasticity and is endowed with a number of attractive features that make it ideally suited for thin structures. Regarding robustness, the method avoids a variety of locking phenomena such as membrane locking, shear locking, and volumetric locking. Regarding accuracy, the method yields optimal convergence for the displacements, which can be further improved by an inexpensive postprocessing. And finally, regarding efficiency, the only globally coupled unknowns are the degrees of freedom of the numerical trace on the interior faces, resulting in substantial savings in computational time and memory storage. This last feature is particularly advantageous for thin structures because the number of interior faces is typically small. In addition, we discuss the implementation of the HDG method with arc-length algorithms for phenomena such as snap-through, where the standard load incrementation algorithm becomes unstable. Numerical results are presented to verify the convergence and demonstrate the performance of the HDG method through simple analytical and popular benchmark problems in the literature.
Journal of Scientific Computing, 2018
We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) method... more We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main features, display numerical results to illustrate their performance, and conclude with bibliography notes. The main ingredients in devising these DG methods are (i) a local Galerkin projection of the underlying partial differential equations at the element level onto spaces of polynomials of degree k to parametrize the numerical solution in terms of the numerical trace; (ii) a judicious choice of the numerical flux to provide stability and consistency; and (iii) a global jump condition that enforces the continuity of the numerical flux to obtain a global system in terms of the numerical trace. These DG methods are termed hybridized DG methods, because they are amenable to hybridization (static condensation) and hence to more efficient implementations. They share many common advantages of DG methods and possess some unique features that make them well-suited to wave propagation problems. *
SUMMARY We introduce a time-domain, high-order in space, hybridizable discontinuous Galerkin spec... more SUMMARY We introduce a time-domain, high-order in space, hybridizable discontinuous Galerkin spectral element method (HDG-SEM) for wave equations in coupled elastic-acoustic media. The method is based on a first-order hyperbolic velocity-strain formulation of the wave equations written in conservative form. This method follows the HDG approach by introducing a hybrid unknown, which is the approximation of the velocity on the elements boundaries, as the only globally (i.e inter-element) coupled degrees of freedom. In this article, we first present a hybridized formulation of the exact Riemann solver at the element boundaries, taking into account elastic-elastic, acoustic-acoustic and elastic-acoustic interfaces. We then use this Riemann solver to derive an explicit construction of the HDG stabilization function τ for all the above-mentioned interfaces. We thus obtain a HDG scheme for coupled elastic-acoustic problems. This scheme is then discretized in space on quadrangular/hexahedral meshes using arbitrary high-order polynomial basis for both volumetric and hybrid fields, using an approach similar to the spectral element methods. This leads to a semi-discrete system of algebraic differential equations (ADE), which thanks to the structure of the global conservativity condition can be reformulated easily as a classical system
Uploads
Papers by Sébastien Terrana