Multiple-correction hybrid k -exact schemes for high-order compressible RANS-LES simulations on fully unstructured grids

A Godunov's type unstructured finite volume method suitable for highly compressible turbulent scale-resolving simulations around complex geometries is constructed by using a successive correction technique. First, a family of k-exact Godunov schemes is developed by recursively correcting the truncation error of the piecewise polynomial representation of the primitive variables. The keystone of the proposed approach is a quasi-Green gradient operator which ensures consistency on general meshes. In addition, a high-order single-point quadrature formula, based on high-order approximations of the successive derivatives of the solution, is developed for flux integration along cell faces. The proposed family of schemes is compact in the algorithmic sense, since it only involves communications between direct neighbors of the mesh cells. The numerical properties of the schemes up to fifth-order are investigated, with focus on their resolvability in terms of number of mesh points required to resolve a given wavelength accurately. Afterwards, in the aim of achieving the best possible trade-off between accuracy, computational cost and robustness in view of industrial flow computations, we focus more specifically on the third-order accurate scheme of the family, and modify locally its numerical flux in order to reduce the amount of numerical dissipation in vortex-dominated regions. This is achieved by switching from the upwind scheme, mostly applied in highly compressible regions, to a fourth-order centered one in vortex-dominated regions. An analytical switch function based on the local grid Reynolds number is adopted in order to warrant numerical stability of the recentering process. Numerical applications demonstrate the accuracy and robustness of the proposed methodology for compressible scale-resolving computations. In particular, supersonic RANS/LES computations of the flow over a cavity are presented to show the capability of the scheme to predict flows with shocks, vortical structures and complex geometries.A Godunov's type unstructured finite volume method suitable for highly compressible turbulent scale-resolving simulations around complex geometries is constructed by using a successive correction technique. First, a family of k-exact Godunov schemes is developed by recursively correcting the truncation error of the piecewise polynomial representation of the primitive variables. The keystone of the proposed approach is a quasi-Green gradient operator which ensures consistency on general meshes. In addition, a high-order single-point quadrature formula, based on high-order approximations of the successive derivatives of the solution, is developed for flux integration along cell faces. The proposed family of schemes is compact in the algorithmic sense, since it only involves communications between direct neighbors of the mesh cells. The numerical properties of the schemes up to fifth-order are investigated, with focus on their resolvability in terms of number of mesh points required to resolve a given wavelength accurately. Afterwards, in the aim of achieving the best possible trade-off between accuracy, computational cost and robustness in view of industrial flow computations, we focus more specifically on the third-order accurate scheme of the family, and modify locally its numerical flux in order to reduce the amount of numerical dissipation in vortex-dominated regions. This is achieved by switching from the upwind scheme, mostly applied in highly compressible regions, to a fourth-order centered one in vortex-dominated regions. An analytical switch function based on the local grid Reynolds number is adopted in order to warrant numerical stability of the recentering process. Numerical applications demonstrate the accuracy and robustness of the proposed methodology for compressible scale-resolving computations. In particular, supersonic RANS/LES computations of the flow over a cavity are presented to show the capability of the scheme to predict flows with shocks, vortical structures and complex geometries

Une stratégie de maillage hybride structurée/non structurée pour la simulation numérique aérodynamique d'effets technologiques pour des configurations complexes de turbomachines

International audienceThis paper presents a hybrid grid strategy for the CFD modeling of complex technological effects which can be encountered on turbomachinery applications. It consists in mixing within the computational domain structured and non structured zones which are connected with conformal matching frontiers. The main channel flow path is meshed with a classical structured approach, while non structured grids enable to mesh the technological components. The application of this grid strategy with the ONERA CFD code elsA is illustrated on two industrial applications: a multi-row film-cooled turbine blade and a multistage compressor including labyrinth seals.Cet article présente une stratégie de maillage hybride structurée/non structurée pour la simulation numérique en aérodynamique d'effets technologiques complexes rencontrés dans des turbomachines. Le principe consiste à faire cohabiter au sein d'un même domaine de calcul des zones structurées et non structurées, qui sont raccordées par des frontières coincidentes. Le canal principal de la veine est maillée avec une topologie classique de maillage structuré, alors que les composants technologiques sont maillés avec des éléments non structurés. L'application de cette stratégie de maillage avec le code elsA de l'ONERA est illustrée sur deux applications industrielles: une aube de turbine refroidie et un compresseur multi-étage

Conservative and accurate method for turbomachinery stage interfaces

Une méthode d'ordre élevé et conservative pour le traitement des conditions des interfaces inter-étage dans les turbomachines est développée en utilisant des reconstructions k-exactes de la solution dans le plan r - Ѳ . Les résultats obtenus pour la configuration d’ étage de turbine à haute pression BRITE démontrent l’intérêt de l’approche proposée par rapport aux méthodes standard d’ordre faible

Algorithmic Differentiation for an effcient CFD solver

We illustrate the benefits of Algorithmic Differentiation (AD) for the development of aerodynamic flow simulation software. In refining the architecture of the elsA CFD solver, developed jointly by ONERA and Safran, we consider AD as a key technology to cut development costs of some derivatives of interest, namely the tangent, adjoint, and Jacobian. We first recall the mathematical background of CFD applications which involve these derivatives. Then, we briefly present the software architecture of elsA (Cambier et al. [12]) and the design choices which give it its HPC capability while highlighting how these choices strongly constrain the applicability of AD. To meet our efficiency requirements, we select the Source-Transformation approach to AD through the Tapenade tool which is justified by a series of experiments and benchmarks. Finally, we present results on large scale configurations

Méthodes de volumes finis d'ordre élevé en maillages non coïncidents pour les écoulements dans les turbomachines

A high-order and conservative method is developed for the numerical treatment of interface conditions in patched grids, based on the use of a ctitious grid methodology. The proposed approach is compared with a non-conservative interpolation of the state variables from the neighbouring domain for selected internal fow problems.Les travaux de cette thèse, réalisés au sein de l’équipe CLEF/DMFN de l’ONERA (Office National d’ Etudes et de Recherches Aérospatiales) en partenariat avec le laboratoire DynFluid et le CIRT (Consortium Industrie-Recherche en Turbomachines) s’inscrivent dans une demarche d’amélioration des outils de simulations pour les turbomachines. Compte tenu de ce contexte, l’objectif de cette étude est de développer de nouvelles méthodes pour le traitement des raccords non coincidents dans les turbomachines qui soit à la fois d’ordre elevé et conservatifs. Les développements proposés sont validés et composés de configurations de difficulté croissante

High-order finite volume with conservative mismatch interface for turbomachinery flows

Les travaux de cette thèse, réalisés au sein de l’équipe CLEF/DMFN de l’ONERA (Office National d’ Etudes et de Recherches Aérospatiales) en partenariat avec le laboratoire DynFluid et le CIRT (Consortium Industrie-Recherche en Turbomachines) s’inscrivent dans une demarche d’amélioration des outils de simulations pour les turbomachines. Compte tenu de ce contexte, l’objectif de cette étude est de développer de nouvelles méthodes pour le traitement des raccords non coincidents dans les turbomachines qui soit à la fois d’ordre elevé et conservatifs. Les développements proposés sont validés et composés de configurations de difficulté croissante.A high-order and conservative method is developed for the numerical treatment of interface conditions in patched grids, based on the use of a ctitious grid methodology. The proposed approach is compared with a non-conservative interpolation of the state variables from the neighbouring domain for selected internal fow problems

Méthodes de volumes finis d'ordre élevé en maillages non coïncidents pour les écoulements dans les turbomachines

A high-order and conservative method is developed for the numerical treatment of interface conditions in patched grids, based on the use of a ctitious grid methodology. The proposed approach is compared with a non-conservative interpolation of the state variables from the neighbouring domain for selected internal fow problems.Les travaux de cette thèse, réalisés au sein de l’équipe CLEF/DMFN de l’ONERA (Office National d’ Etudes et de Recherches Aérospatiales) en partenariat avec le laboratoire DynFluid et le CIRT (Consortium Industrie-Recherche en Turbomachines) s’inscrivent dans une demarche d’amélioration des outils de simulations pour les turbomachines. Compte tenu de ce contexte, l’objectif de cette étude est de développer de nouvelles méthodes pour le traitement des raccords non coincidents dans les turbomachines qui soit à la fois d’ordre elevé et conservatifs. Les développements proposés sont validés et composés de configurations de difficulté croissante

Multiple-correction hybrid k -exact schemes for high-order compressible RANS-LES simulations on fully unstructured grids

A Godunov's type unstructured finite volume method suitable for highly compressible turbulent scale-resolving simulations around complex geometries is constructed by using a successive correction technique. First, a family of k-exact Godunov schemes is developed by recursively correcting the truncation error of the piecewise polynomial representation of the primitive variables. The keystone of the proposed approach is a quasi-Green gradient operator which ensures consistency on general meshes. In addition, a high-order single-point quadrature formula, based on high-order approximations of the successive derivatives of the solution, is developed for flux integration along cell faces. The proposed family of schemes is compact in the algorithmic sense, since it only involves communications between direct neighbors of the mesh cells. The numerical properties of the schemes up to fifth-order are investigated, with focus on their resolvability in terms of number of mesh points required to resolve a given wavelength accurately. Afterwards, in the aim of achieving the best possible trade-off between accuracy, computational cost and robustness in view of industrial flow computations, we focus more specifically on the third-order accurate scheme of the family, and modify locally its numerical flux in order to reduce the amount of numerical dissipation in vortex-dominated regions. This is achieved by switching from the upwind scheme, mostly applied in highly compressible regions, to a fourth-order centered one in vortex-dominated regions. An analytical switch function based on the local grid Reynolds number is adopted in order to warrant numerical stability of the recentering process. Numerical applications demonstrate the accuracy and robustness of the proposed methodology for compressible scale-resolving computations. In particular, supersonic RANS/LES computations of the flow over a cavity are presented to show the capability of the scheme to predict flows with shocks, vortical structures and complex geometries.A Godunov's type unstructured finite volume method suitable for highly compressible turbulent scale-resolving simulations around complex geometries is constructed by using a successive correction technique. First, a family of k-exact Godunov schemes is developed by recursively correcting the truncation error of the piecewise polynomial representation of the primitive variables. The keystone of the proposed approach is a quasi-Green gradient operator which ensures consistency on general meshes. In addition, a high-order single-point quadrature formula, based on high-order approximations of the successive derivatives of the solution, is developed for flux integration along cell faces. The proposed family of schemes is compact in the algorithmic sense, since it only involves communications between direct neighbors of the mesh cells. The numerical properties of the schemes up to fifth-order are investigated, with focus on their resolvability in terms of number of mesh points required to resolve a given wavelength accurately. Afterwards, in the aim of achieving the best possible trade-off between accuracy, computational cost and robustness in view of industrial flow computations, we focus more specifically on the third-order accurate scheme of the family, and modify locally its numerical flux in order to reduce the amount of numerical dissipation in vortex-dominated regions. This is achieved by switching from the upwind scheme, mostly applied in highly compressible regions, to a fourth-order centered one in vortex-dominated regions. An analytical switch function based on the local grid Reynolds number is adopted in order to warrant numerical stability of the recentering process. Numerical applications demonstrate the accuracy and robustness of the proposed methodology for compressible scale-resolving computations. In particular, supersonic RANS/LES computations of the flow over a cavity are presented to show the capability of the scheme to predict flows with shocks, vortical structures and complex geometries

Multiple thyrotropin β-subunit and thyrotropin receptor-related genes arose during vertebrate evolution.

Thyroid-stimulating hormone (TSH) is composed of a specific β subunit and an α subunit that is shared with the two pituitary gonadotropins. The three β subunits derive from a common ancestral gene through two genome duplications (1R and 2R) that took place before the radiation of vertebrates. Analysis of genomic data from phylogenetically relevant species allowed us to identify an additional Tshβ subunit-related gene that was generated through 2R. This gene, named Tshβ2, present in cartilaginous fish, little skate and elephant shark, and in early lobe-finned fish, coelacanth and lungfish, was lost in ray-finned fish and tetrapods. The absence of a second type of TSH receptor (Tshr) gene in these species suggests that both TSHs act through the same receptor. A novel Tshβ sister gene, named Tshβ3, was generated through the third genomic duplication (3R) that occurred early in the teleost lineage. Tshβ3 is present in most teleost groups but was lostin tedraodontiforms. The 3R also generated a second Tshr, named Tshrb. Interestingly, the new Tshrb was translocated from its original chromosomic position after the emergence of eels and was then maintained in its new position. Tshrb was lost in tetraodontiforms and in ostariophysians including zebrafish although the latter species have two TSHs, suggesting that TSHRb may be dispensable. The tissue distribution of duplicated Tshβs and Tshrs was studied in the European eel. The endocrine thyrotropic function in the eel would be essentially mediated by the classical Tshβ and Tshra, which are mainly expressed in the pituitary and thyroid, respectively. Tshβ3 and Tshrb showed a similar distribution pattern in the brain, pituitary, ovary and adipose tissue, suggesting a possible paracrine/autocrine mode of action in these non-thyroidal tissues. Further studies will be needed to determine the binding specificity of the two receptors and how these two TSH systems are interrelated

ParaDiGM: a library to handle Parallel Distributed General Meshes

2022During the last decade, the Moore's law has proven to be outdated. The computational power does not double anymore every year for a given cost under the pursuit of the energy efficiency. To address this issue, the High Performance Computing (HPC) industry showed an incredible ingenuity by designing complex architectures. Today, the HPC tends to have more and more cores on each node, possibly with accelerators like General-Purpose Graphics Processing Unit (GPGPU) or Field-Programmable Gate Array (FPGA), and with less and less memory. As a corollary, the developers of scientific computing software need to pay attention and master numerous key concepts, which require great expertise, to hope to extract a reasonable performance. These key concepts include programming on heterogeneous architectures, multithreading programming, Message Passage Interface (MPI) programming, load balancing, asynchronous and non-blocking communications, cache blocking techniques, vectorization or even parallel Input/Output (I/O). It is in this context that the ParaDiGM library was created to provide the developers a progressive framework, which consists of a set of low-, mid- and high-level services usable by many developers of scientific computing software that rely on a mesh, typically when solving partial differential equations on a given domain. The ParaDiGM kernel is based on the key concept of a distributed or partitioned view of data stored in an array. After introducing ParaDiGM and giving some general information in the first section, we shall attach great importance in the second section to describe in details the distributed and the partitioned approaches and their impact on parallel algorithms. For instance, we will show that the partitioned view is not always well suited for parallel algorithms and that the distributed view, even though less intuitive, is better suited for specific algorithms. New MPI communication protocols have been developed to switch from one view to the other. Then, we will present parallel dedicated algorithms for wall distance computation in the third section and isosurfaces computations in the fourth section. In each section, some applications will be shown with a special emphasis on the parallel computational efficiency on several thousand cores