Angular Momentum preserving cell-centered Lagrangian and Eulerian schemes on arbitrary grids

We address the conservation of angular momentum for cell-centered discretization of compressible fluid dynamics on general grids. We concentrate on the Lagrangian step which is also sufficient for Eulerian discretization using Lagrange+Remap. Starting from the conservative equation of the angular momentum, we show that a standard Riemann solver (a nodal one in our case) can easily be extended to update the new variable. This new variable allows to reconstruct all solid displacements in a cell, and is analogous to a partial Discontinuous Galerkin (DG) discretization. We detail the coupling with a second- order Muscl extension. All numerical tests show the important enhancement of accuracy for rotation problems, and the reduction of mesh imprint for implosion problems. The generalization to axi-symmetric case is detailed

A positive scheme for diffusion problems on deformed meshes

International audienceWe present in this article a positive finite volume method for diffusion equation on deformed meshes. This method is mainly inspired from [50, 52], and uses auxiliary unknowns at the nodes of the mesh. The flux is computed so as to be a two-point nonlinear flux, giving rise to a matrix which is the transpose of an M-matrix, which ensures that the scheme is positive. A particular attention is given to the computation of the auxiliary unknowns. We propose a new strategy, which aims at providing a scheme easy to implement in a parallel domain decomposition setting. An analysis of the scheme is provided: existence of a solution for the nonlinear system is proved, and the convergence of a fixed-point strategy is studied

A one-mesh method for the cell-centered discretization of slide lines

A new method is described to handle slide lines in cell-centered Lagrangian schemes for the modeling of sliding problems between two fluids in the framework of compressible hy- drodynamics. The method is an extension of the one proposed in the reference [1] and is conservative in momentum and total energy. Our method is based on the minimization of an objective function over a specific set that models the sliding constraint. We illustrate on several basic problems

Low-Mach correction for Lagrangian acoustic Riemann solvers on unstructured meshes

We propose a low-Mach correction for cell-centered schemes in Lagrangian frame. After transposing some classical results in Eulerian frame to Lagrangian frame, we show why classical cell-centered schemes in Lagrangian frame are not able to capture the low-Mach regime except by using unreasonably fine meshes. Consequently, we propose a slight modification of the original scheme, which is easy to implement in any scheme using a acoustic Godunov Riemann solver on unstructured mesh, and is costless in term of CPU time. We demonstrate that this modification cures this flaw. The properties of the original semi-discrete scheme (consistence, conservation) are preserved. Particular attention is paid to the entropy condition, proving its compatibility with the modification proposed. We assess this new scheme on several low and high-Mach problems, to demonstrate its good behaviour in all regimes. Last test problem is devoted to the study of the growth rate of instability in convergent configuration. It shows that even if the problem is globally very compressible, the low-Mach correction can have a significant impact on the solution

Reconstruction des fluctuations turbulentes par une approche hybride RANS/LES

Président du jury: P. Sagaut Rapporteurs: J. P. Bertoglio, F. Ducros Examinateurs: P. Moschetti, M. Ravachol, M. TerracolNowadays, unsteady calculation of Navier-Stokes equations thanks to Large Eddy Simulation (LES) and all the more Direct Numerical Simulation (DNS) are still beyond the scope of current supercomputers for industrial interests. On the other hand, statistical methods (RANS) less numerically expensive, don't allow to describe broad band phenomena (for instance acoustic sources). Locally coupled methods make it possible to draw benefit of this two kind of approach (RANS and LES). An original method of this type, which can be seen as an extension of the Non-Linear Disturbance Equation (NLDE), is developped in this work. It consists in a decomposition into three parts of the exact solution of the Navier-Stokes equations : mean flow, resolved fluctuations and unresolved (subgrid) fluctuations. The mean flow is computed using a classical RANS method, while resolved fluctuations are derived from a LES method, only on the critical spots of the flow. The code was implemented on the NEC SX5 supercomputer of ONERA and assesed on several incompressible (plane chanel flow) and compressible (turbine blade, high lift system) application cases. The potentialities of the method are demonstrated and an original boundary condition is developped. The method succeds to predict the correct flow behaviour for all these configurations and can be applied locally, what provide a large reduction of the computational cost.Les méthodes actuelles de calcul instationnaire des équations de Navier-Stokes (Simulation Numérique Directe (SND), Simulation des Grandes Echelles (SGE)) demandent encore un temps de calcul excessif pour pouvoir être utilisées à des fins industrielles. D'autre part, les méthodes statistiques (RANS) moins coûteuses, ne permettent pas de rendre compte des phénomènes à large bande fréquentielle, qui sont à l'origine, par exemple, des ondes acoustiques. Le développement de méthodes localement couplées permet de concilier les avantages des deux types d'approches précités (SGE et RANS). Une méthode originale de ce type à été développée sur la base de la Non-Linear Disturbance Equations (NLDE). Elle consiste à résoudre l'intégralité du champ grâce à un calcul statistique. Ensuite, aux endroits critiques, le complément fréquentiel est calculé en SGE, de manière à enrichir le champ. Le code a été implanté sur le NEC SX5 de l'ONERA et testé sur plusieurs cas d'application en incompressible (canal plan bi-périodique) et en compressible (aube de turbomachine, aile hypersustentée). Ses possibilités ont été testées et des conditions limites spécifiques ont été développées. La méthode se comporte bien dans tous ces cas d'application et peut être utilisée de façon locale, permettant ainsi une nette réduction du temps de calcul

Stabilization of cell-centered compressible Lagrangian methods using subzonal entropy

International audienc

Contributions au développement de schémas volumes finis pour l'hydrodynamique lagrangienne

The purpose of this document is to report on some recent advances in finite volumes schemes (also called centered or collocated) for Lagrangian hydrodynamics. It is structured in three parts. The first part, introductory, is an overview of the elements of modeling and numerical analysis that motivated the development of centered schemes. The second part is a quick description of these methods. It gives most of the keys to apprehend the third part. The latter describes some of the recent work carried out since 2010 around these schemes and which can be grouped into four themes: extension to the Arbitrary-Lagrangian-Eulerian frame (ALE), improvement of the robustness, improvement of the precision and extensions to new physical and numerical models. This report is not intended to be exhaustive, but provides entry points in the form of abstracts and bibliographic notes, leaving the reader to refer to the corresponding articles to deepen the topics of his choice. This work has benefited from collaboration with other CEA or university laboratories. In particular, the authors would like to warmly thank Gilles Carre, Philippe Hoch and Isabelle Marmajou, as well as Bruno Despres (Jacques-Louis Lions Laboratory, Sorbonne University). Finally, note that, for ten years, the literature around these schemes has been very abundant. The purpose of this document is not to review it, and many of these works are not cited, without having to see a judgment on their value. Some terms appear in color in the document, which means that information are provided either in the form of inserts in the body of the document or in the glossary (at the end of the report).Ce document a pour but de rendre compte de quelques avancees recentes concernant les schemas volumes finis (dits egalement centres ou colocalises) pour l'hydrodynamique Lagrangienne. Il est structure en trois parties. La premiere partie, introductive, est un survol des elements de modelisation et d'analyse numerique qui ont motive le developpement des schemas centres. La seconde partie est une description rapide de ces methodes. Elle donne l'essentiel des cles permettant d'apprehender la troisieme partie. Cette derniere decrit certains des travaux recents realises depuis 2010 autour de ces schemas et qui peuvent etre regroupes en quatre themes: extension au referentiel Euler-Lagrange-Arbitraire (ALE), amelioration de la robustesse, amelioration de la precision et extensions a de nouveaux modeles physico-numeriques. Ce rapport ne pretend pas etre exhaustif, mais fournit des points d'entrees sous forme de resumes et de notes bibliographiques, laissant la charge au lecteur de se referer aux articles correspondants pour approfondir les sujets de son choix. Ce travail a beneficie de la collaboration avec d'autres laboratoires du CEA ou universitaires. En particulier, les auteurs tiennent a chaleureusement remercier Gilles Carre, Philippe Hoch et Isabelle Marmajou, ainsi que Bruno Despres (Laboratoire Jacques-Louis Lions, Sorbonne universite). Enfin, notons que, depuis dix ans, la litterature autour de ces schemas a ete tres abondante. L'objectif de ce document n'est pas d'en faire une revue, et beaucoup de ces travaux ne sont pas cites, sans qu'il faille y voir un jugement sur leur valeur. Certains termes apparaissent en couleur dans le document, cela signifie que des informations les concernant sont fournies, soit sous formes d'encarts inseres dans le corps du document, soit dans le glossaire (a la fin du rapport)

Reconstruction des fluctuations turbulentes par une approche hybride RANS/SGE

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