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International audience; In this paper, we present a mesh h-adaptation strategy suited for the discontinuous Galerkin formulation of the compressible Navier-Stokes equations on unstructured grids, based on the simplicial remeshing library MMG. A novel a posteriori error estimator, combining the measure of the energy associated with the highest-order modes and the inter-element jumps, is used to build the metric field. The performance of the developed mesh adaptation algorithm is assessed for steady laminar viscous flows past a square cylinder and past a NACA0012 airfoil, and for the unsteady laminar viscous flow past a circular cylinder. The gain in accuracy for a given number of degrees of freedom (DoFs) is demonstrated for = 1, = 2 and = 3 polynomial degrees, with respect to uniformly refined simulations.

International audience; This article presents a formulation that extends the multiscale modelling for compressible large-eddy simulation to a vast family of compact nodal numerical methods represented by the high-order flux reconstruction scheme. The theoretical aspects of the proposed formulation are laid down via mathematical derivations which clearly expose the underlying assumptions and approximations and provide sufficient details for accurate reproduction of the methodology. The final form is assessed on a Taylor–Green vortex benchmark with Reynolds number of 5000 and compared to filtered direct numerical simulation data. These numerical experiments exhibit the important role of sufficient de-aliasing, appropriate amount of upwinding from Roe’s numerical flux and large/small scale partition, in achieving better agreement with reference data, especially on coarse grids, when compared to the baseline implicit large-eddy simulation.

In this paper, we present h- and hp-adaptative strategies suited for the discontinuous Galerkin formulation of the compressible laminar and Reynolds-averaged Navier–Stokes equations on unstructured grids, relying on a metric-based simplicial remeshing approach. An a posteriori error estimator, combining the measure of the energy associated with the highest-order modes and the inter-element jumps, is used to build both the metric field and the polynomial degree distribution map. The choice of refining either in h or p is driven by a smoothness indicator based on the decay of modal coefficients in each element. The performance of the developed adaptation algorithms is assessed for the 2D laminar viscous flow past a NACA0012 airfoil, and for the 3D laminar viscous flows past a sphere and past a delta wing. The adaptive hp-strategy is applied to a 3D turbulent jet issued from a nozzle. Finally, the gain in accuracy provided by the adaptive algorithms with respect to uniformly refined simulations, for a given number of degrees of freedom with polynomial degrees p = 1 , 2 , 3 , is demonstrated.

International audience; This work focuses upon the development of a wavelet‐based variant of the variational multiscale method (VMS) for accurate and efficient large eddy simulation (LES) called wavelet‐based VMS‐LES (WMS‐LES). This approach has been incorporated within the framework of a high‐order incompressible flow solver based upon the pressure‐stabilized discontinuous Galerkin finite element method (DG‐FEM). The VMS approach is designed to produce an a priori scale separation of the governing equations, in a manner which makes no assumptions on either the boundary conditions or the mesh uniformity. Using second‐generation wavelets (SGWs) elementwise for scale separation ensures, on one hand, the preservation of the computational compactness of the DG‐FEM scheme and, on the other hand, the ability to achieve scale separation in wavenumber space. The optimal space‐frequency localization property of the SGW provides an improvement over the commonly used Legendre polynomials. The suitability of the elementwise SGW scale‐separation operation as a tool for error indication has been demonstrated in an h‐adaptive computation of the reentrant corner test case. Finally, the DG‐FEM solver and the WMS‐LES method have been assessed through simulations upon the three‐dimensional Taylor‐Green vortex test case. Our results indicate that the WMS‐LES approach exhibits a distinct improvement over the monolevel LES approach. This effect is not produced by a change in the magnitude of the subgrid dissipation but rather by the redistribution of the subgrid dissipation in wavenumber space.

The variational multiscale (VMS) approach based on a high-order discontinuous Galerkin (DG) method is used to perform LES of the sub-critical flow past a circular cylinder at Reynolds 3 900, 20 000 and 140 000. The effect of the numerical flux function on the quality of the LES solutions is also studied in the context of very coarse discretizations of the TGV configuration at R e = 20 000 . The potential of using p-adaption in combination with DG-VMS is illustrated for the cylinder flow at R e = 140 000 by considering a non-uniform distribution of the polynomial degree based on a recently developed error estimation strategy [57]. The results from these tests demonstrate the robustness of the DG-VMS approach with increasing Reynolds number on a highly curved geometrical configuration.

Purpose The purpose of this paper is to investigate a new cooling process of a heated cylinder with confined impacting air jet. Design/methodology/approach To do this the authors used experience-numerical and numerical-numerical comparisons. The experimental facility, designed and built at the Pau University, consists in air jets impacting around a heated circular cylinder. As the inlet velocity magnitude is low (Vin=4.37 m/s – Machin=0.0125), using a compressible solver for numerical simulations presents a number of difficulties. For this low Mach number configuration, the authors compare the performance of three different solvers in this paper. Two of them are compressible, one based on the finite volume approach and the other on a discontinuous Galerkin method, and the third one is an incompressible solver. Some of the numerical results are compared to experimental data. Findings Comparisons between the results from 3D and 2D computations support the relevance of 2D models. Some of the numerical results are compared to experimental data. Research limitations/implications The confined aspect of the set-up reduces experimental measurement to intrusive measures. It should be noted that the temperature measurement given by thermocouples is always considered as “global” or “average”. Originality/value Future aircraft technology will increasingly rely on electrical power. The substitution of mechanical energy by electrical energy will lead to an increasing amount of heat power that need be evacuated. Innovative cooling processes have to be set up according to constraints imposed by the technological design.

The variational multiscale (VMS) approach based on a modal discontinuous Galerkin (DG) method is used to perform LES of the sub-critical flow past a circular cylinder at Reynolds numbers 20 000 and 140 000, based on the cylinder diameter. The potential of using p-adaption in combination with DG-VMS is illustrated for the case at Re = 140 000 by considering a non-uniform distribution of the polynomial degree based on a recently developed error estimation strategy [15]., The variational multiscale (VMS) approach based on a modal discontinuous Galerkin (DG) method is used to perform LES of the sub-critical flow past a circular cylinder at Reynolds numbers 20 000 and 140 000, based on the cylinder diameter. The potential of using p-adaption in combination with DG-VMS is illustrated for the case at Re = 140 000 by considering a non-uniform distribution of the polynomial degree based on a recently developed error estimation strategy

International audience; Some possible future High Fidelity CFD codes for LES simulation of turbomachinery are compared on several test cases increasing in complexity , starting from a very simple inviscid Vortex Convection to a multistage axial experimental compressor. Simulations were performed between 2013 and 2016 b y major Safran partners (Cenaero, Cerfacs, CORIA and Onera) and various numerical methods compared : Finite Volume, Discontinuous Galerkin, Spectral Differences. Comparison to analytical results, to experimental data or to RANS simulations are performed to check and measure accuracy. CPU efficiency versus accuracy are also presented. It clearly appears that the level of maturity could be different between codes and numerical approaches. In the end, advantages and disadvantages of every codes obtained during this project are presented.

International audience; This paper presents an analysis of refinement indicators for the numerical solution of the Euler and the Navier-Stokes equations using a p-adaptive discontinuous Galerkin (DG) method. Residual error, discretiza-tion error and feature-based indicators are studied in the context of p-adaptive DG simulations of two inviscid flow configurations, namely, the flow over a Gaussian bump and the flow past a circular cylinder. As expected, the superiority of local p-refinement as compared to uniform p-refinement is clearly observed. The results obtained highlight the efficiency of the considered refinement indicators with respect to an indicator based on the local entropy error. In particular, they identify regions where numerical errors are being produced and not those where errors are being convected. Finally the p-adaptive algorithm is applied to the simulation of the laminar flow past a circular cylinder at Re = 40. The great potential of the spectral decay 1 and VMS 2 indicators, which combine accuracy and computational efficiency, is also demonstrated.

This paper outlines the development of a wavelet based adaptive discontinuous Galerkin spectral element method (DG-SEM) for unsteady incompressible flows. The proposed approach possesses arbitrary high formal accuracy and permits adaptivity in a way that is computationally cheap and efficient. An element wise discretisation of the domain is performed. Two sets of basis functions are employed per element—the Lagrange polynomials at the Gauss-Legendre-Lobatto (GLL) points which acts as the nodal basis for the DG-SEM method and the second generation wavelets (SGW) which can be looked upon as either a nodal or modal basis, subject to convenience, and is responsible for facilitating the adaptivity. The projection of the signal onto the wavelet space provides information about the local frequency content of the signal. An accumulation of high frequency components acts as an indicator for dynamic mesh refinement via thresholding. The main advantage of using the SGW basis is the low cost of the transform, O(N) per direction.

International audience; A high-order discontinuous Galerkin (DG) approach is used for the DNS and LES of the flow over periodically arranged hills. In order to assess the capacity of the DG method to capture the Reynolds-number dependent features of the flow, four Reynolds numbers are considered: 2800, 10 595, 19 000, and 37 000. The DG solutions are compared with the reference data available in the literature. For Reb = 10595 the no-model and the WALE LES approaches are compared. The hp-convergence analyses performed for the DNS demonstrate the superior performance of increasing the polynomial order as compared to refining the mesh. It appears from this study that the use of a subgrid modelling approach together with an appropriate level of local hp-refinement could greatly improve the solution without penalising the computational cost of the simulation.

We assess the performance of a high-order discontinuous Galerkin (DG) approach to simulate wall-bounded turbulent flows for a range of Reynolds numbers. First, a plane channel flow configuration with turbulent heat transfer at R e τ = 640 is considered. Second, a detached flow configuration is investigated. This configuration represents the flow over periodically arranged hills. Four bulk Reynolds numbers Re b are considered: 2800, 10 595, 19 000, and 37 000. For R e b = 2800 direct numerical simulation (DNS) is used. Large-eddy simulations (LES) based on the WALE subgrid-scale model are carried out for the higher Re b . The simulation results are compared to reference data from CFD and experiment. hp -convergence analyses are performed which demonstrate the superior performance of increasing the polynomial order as compared to refining the mesh. It appears from this work that the use of a subgrid modelling approach together with local hp-adaptation could greatly improve the accuracy of the solution without penalising the computational cost of the simulation.

This paper presents details of the solver Aghora for the simulation of unsteady compressible turbulent flows. Different modelling levels are used: Reynolds averaged Navier-Stokes equations coupled with turbulence transport equations, variational multiscale formulation of large-eddy simulation, and direct numerical simulation. The space discretization is based on a high-order discontinuous Galerkin method with representation of curved boundaries. High-order explicit and implicit Runge-Kutta methods are used for the time integration. The performance of the solver will be assessed in various examples of compressible turbulent ow numerical simulation in three space dimensions.

A modal Discontinuous Galerkin (DG) method is assessed for the Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) of freely decaying turbulence. We consider as benchmark test case the TaylorGreen vortex flow. Inviscid computations show the conservation and dissipation properties of the DG scheme in the context of 3D non-linear flow problems. DG DNS computations carried at low and moderate Reynolds numbers (Re = 400 and Re = 1600, respectively) show good agreement with a reference solution generated using a Fourier pseudo-spectral code. LES computations are carried out at larger Reynolds number (Re = 3000), and compared to a reference filtered DNS. The Variational Multiscale Simulation framework, which can be straightforwardly implemented in a modal DG code is compared to the classical Smagorinsky approach for LES.

Over the past few years, ONERA has been working on the extension of the multiblock structured solver elsA to hybrid-grid con gurations. By hybrid grids, we mean those in which structured (ijk-based) and unstructured blocks coexist within the same computational domain. We have called the new solver elsA-H. This approach has a number of advantages which are highlighted in this work. In this paper, we review the hybrid-grid algorithms upon which elsA-H relies, focusing on the particular handling of matching-grid interfaces. We also report recent progress on the parallelisation of such algorithms, as well as on the development of an appropriate hybrid-grid load-balancing tool. Finally, we present preliminary work on the implementation of a hybrid multigrid algorithm into elsA-H. A number of simulation results for several unstructured and hybrid-grid con gurations are reported in this paper.

A new fully integrated environment for compressible ow simulation on structured and unstructured zones coexisting within the same hybrid mesh is presented. This environment originates from the existing elsA a CFD software tool, developed by ONERA and CERFACS for structured grids, and widely used both in industry and research. Some con gurations can not be easily addressed with a fully structured mesh approach. An e cient way to overcome this drawback is to combine structured and unstructured zones in a single hybrid mesh. Structured zones are kept for sake of accuracy in boundary layers, wall clock e ciency and low memory consumption. Unstructured zones enable an easier mesh generation / adaptation process. This paper describes the extension of elsA to unstructured multi-element zones composed of hexahedra, tetrahedra, prisms and pyramids. A key feature is the treatment of structured / unstructured zone interfaces, performed with a mismatched abutting grid interface algorithm. We demonstrate that the Object-Oriented (OO) programming approach is useful and e cient to integrate unstructured data structures and numerical methods into the original software to form a single computational CFD kernel. Software design, numerical algorithm, structured/unstructured block interface treatment, CPU e ciency and parallel scalability, are discussed. Finally, validation examples demonstrating the project status are given.

The wavelet-based multi-resolution analysis technique is used to develop a novel approach to the modelling of the sub-grid terms in the large-eddy simulation equations. This new approach is called WaveLES. A numerical framework for the solution of the projected equations is developed for one and three-dimensional problems. The WaveLES method is assessed in a priori tests on an atmospheric turbulent time series, and a direct numerical simulation. A posteriori tests are carried out for the Burgers equation.

In this work we perform a-priori analyses of the Discontinuous Galerkin (DG) Variational Multiscale (VMS) method for Large Eddy Simulation (LES). An analytical framework is introduced to study the ideal energy transfer between resolved and unresolved scales. The proposed frame work is consistent with the discretization employed for the DG-LES simulations. The concept of modal eddy viscosity is also introduced which can be employed for the a-priori analysis of the DG-VMS method or spectral vanishing viscosity approaches. The developed framework is then applied to the analysis of the energy transfer in DG-LES by employing a DNS database of the Taylor-Green Vortex (TGV) at Re = 5 000, 20 000 and 40 000. A-priori analyses are carried out for three variants of the DG-VMS approach: the small-small and all-all variants. The performed analysis demonstrates that when the DG-LES resolution limit falls at the beginning of the dissipation range the assumption of large scales free of interaction with the unresolved scales is valid and the DG-VMS approach can replicate the ideal SGS dissipation spectrum. For coarser resolutions, typical of LES at high Reynolds numbers, the DG-VMS approach is unable to replicate the ideal energy transfer mechanism at the large-resolved scales. It is shown, a-priori, that a more accurate agreement can be obtained by employing a mixed Smagorinsky and DG-VMS approach with a fixed value of the scale-fraction parameter.

This thesis focuses on the development of an accurate and efficient method for performing Large-Eddy Simulation (LES) of turbulent flows. An LES approach based upon the Variational Multiscale (VMS) method is considered. VMS produces an a priori scale-separation of the governing equations, in a manner which makes no assumptions on the boundary conditions and mesh uniformity. In order to ensure that scale-separation in wavenumber is achieved, we have chosen to make use of the Second Generation Wavelets (SGW), a polynomial basis which exhibits optimal space-frequency localisation properties. Once scale-separation has been achieved, the action of the subgrid model is restricted to the wavenumber band closest to the cuto. We call this approach wavelet-based VMS-LES (WAV-VMS-LES). This approach has been incorporated within the framework of a high-order incompressible flow solver based upon pressure-stabilised discontinuous Galerkin FEM (DG-FEM). The method has been assessed by performing highly under-resolved LES upon the 3D Taylor-Green Vortex test case at two different Reynolds numbers.; Cette thèse se concentre sur le développement d’une méthode précise et efficace pour la simulation des grandes échelles (LES) des écoulements turbulents. Une approche de la LES basée sur la méthode variationnelle multi-échelles (VMS) est considérée. La VMS applique aux équations de la dynamique des fluides une séparation d’échelles a priori sans recours à des hypothèses sur les conditions aux limites ou sur l’uniformité du maillage. Afin d’assurer effectivement une séparation d’échelles dans l’espace des nombres d’onde associé, nous choisissons d’utiliser les ondelettes de deuxième génération (SGW), une base polynomiale qui présente des propriétés de localisation spatiale-fréquence optimales. A partir de la séparation d’échelles ainsi réalisée, l’action du modèle sous-maille est limitée à un intervalle de nombres d’onde proche de la coupure spectrale. Cette approche VMS-LES basée sur les ondelettes est désignée par WAV-VMS-LES. Elle est incorporée dans un solveur d’ordre élevé pour la simulation des écoulements incompressibles sur la base d’une méthode de Galerkin discontinue (DG-FEM) stabilisée pour la pression. La méthode est évaluée par réalisation de LES sur des maillages fortement sous-résolus pour le cas test du tourbillon de Taylor-Green 3D à deux nombres de Reynolds différents.

This thesis focuses on the development of an accurate and efficient method for performing Large-Eddy Simulation (LES) of turbulent flows. An LES approach based upon the Variational Multiscale (VMS) method is considered. VMS produces an a priori scale-separation of the governing equations, in a manner which makes no assumptions on the boundary conditions and mesh uniformity. In order to ensure that scale-separation in wavenumber is achieved, we have chosen to make use of the Second Generation Wavelets (SGW), a polynomial basis which exhibits optimal space-frequency localisation properties. Once scale-separation has been achieved, the action of the subgrid model is restricted to the wavenumber band closest to the cuto. We call this approach wavelet-based VMS-LES (WAV-VMS-LES). This approach has been incorporated within the framework of a high-order incompressible flow solver based upon pressure-stabilised discontinuous Galerkin FEM (DG-FEM). The method has been assessed by performing highly under-resolved LES upon the 3D Taylor-Green Vortex test case at two different Reynolds numbers., Cette thèse se concentre sur le développement d’une méthode précise et efficace pour la simulation des grandes échelles (LES) des écoulements turbulents. Une approche de la LES basée sur la méthode variationnelle multi-échelles (VMS) est considérée. La VMS applique aux équations de la dynamique des fluides une séparation d’échelles a priori sans recours à des hypothèses sur les conditions aux limites ou sur l’uniformité du maillage. Afin d’assurer effectivement une séparation d’échelles dans l’espace des nombres d’onde associé, nous choisissons d’utiliser les ondelettes de deuxième génération (SGW), une base polynomiale qui présente des propriétés de localisation spatiale-fréquence optimales. A partir de la séparation d’échelles ainsi réalisée, l’action du modèle sous-maille est limitée à un intervalle de nombres d’onde proche de la coupure spectrale. Cette approche VMS-LES basée sur les ondelettes est désignée par WAV-VMS-LES. Elle est incorporée dans un solveur d’ordre élevé pour la simulation des écoulements incompressibles sur la base d’une méthode de Galerkin discontinue (DG-FEM) stabilisée pour la pression. La méthode est évaluée par réalisation de LES sur des maillages fortement sous-résolus pour le cas test du tourbillon de Taylor-Green 3D à deux nombres de Reynolds différents.

This work focuses on the development of the Discontinuous Galerkin (DG) method for the large-eddy simulation (LES) of turbulents flows. The DG method shows some interesting properties for LES : high-order of accuracy, compact stencil, unstructured meshes and amodal polynomial basis which can be used to implement multiscale turbulence models. We consider in this work the Variational Multiscale approach (VMS), which consists in splitting the resolved scales into two components using the modal basis in order to restrict the action of the model to a given range of small scales. The models have been tuned using the transfer functions of the DG hp-discretizations. The accuracy of the DG method for the representation of turbulent phenomena has been assessed through DNS of free and wall-bounded canonical flows. Finally, the VMS/DG approach has been assessed for simple configurations at high Reynolds numbers. We have shown that this particular approach allows for an accurate representation of turbulent flows for coarse discretizations.; Cette thèse vise à développer et évaluer la méthode de Galerkin discontinue (DG) pour la simulationdes grandes échelles (LES) des écoulements turbulents. L’approche DG présente un nombre d’avantages intéressants pour la LES : ordre élevé, stencil compact, prise en compte des maillages non structurés et expression de la solution numérique dans une base de polynômes permettant l’utilisation de modèles de turbulence multi-échelle. Parmi ce type de modèles, nous nous sommes intéressés ici à la méthode Variational Multiscale (VMS) qui consiste à séparer les échelles résolues dans la base de polynômes pour restreindre l’influence du modèle à une gamme réduite d’échelles. Les modèles considérés ont été paramétrés en prenant en compte les fonctions de transfert spécifiques aux discrétisations DG. La précision de la méthode pour la représentation de phénomènes turbulents variés a été évaluée à travers la réalisation de DNS de configurations académiques. Enfin, l’approche VMS/DGa été éprouvée sur des configurations simples à haut nombre de Reynolds. Il apparaît que cette méthodologie permet la représentation précise des phénomènes turbulents pour un coût réduit en terme de degrés de liberté.