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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; An accurate determination of the catalytic property of thermal protection materi- als is crucial to design reusable atmospheric entry vehicles. This property is deter- mined by combining experimental measurements and simulations of the reactive boundary layer near the material surface. The inductively-driven Plasmatron fa- cility at the von Karman Institute for Fluid Dynamics provides a test environment to analyze gas-surface interactions under effective hypersonic conditions. In this study, we develop an uncertainty quantification methodology to rebuild values of the gas enthalpy and material catalytic property from Plasmatron experiments. A non-intrusive spectral projection method is coupled with an in-house boundary- layer solver, to propagate uncertainties and provide error bars on the rebuilt gas enthalpy and material catalytic property, as well as to determine which uncer- tainties have the largest contribution to the outputs of the experiments. We show that the uncertainties computed with the methodology developed are significantly reduced compared to those determined using a more conservative engineering ap- proach adopted in the analysis of previous experimental campaigns.

We construct a third order multidimensional upwind residual distribution scheme for the system of the Navier–Stokes equations. The underlying approximation is obtained using standard P2 Lagrange finite elements. To discretise the inviscid component of the equations, each element is divided in sub-elements over which we compute a high order residual defined as the integral of the inviscid fluxes on the boundary of the sub-element. The residuals are distributed to the nodes of each sub-element in a multi-dimensional upwind way. To obtain a discretisation of the viscous terms consistent with this multi-dimensional upwind approach, we make use of a Petrov–Galerkin analogy. The analogy allows to find a family of test functions which can be used to obtain a weak approximation of the viscous terms. The performance of this high-order method is tested on flows with high and low Reynolds number.

This article deals with the discretization of linearized Euler equations by multidimensional upwind residual distribution methods. Linearized Euler equations are applied to model the propagation of sound in the domain where no source of sound is present and where the analogy methods such as Ffowcs―Williams can not be used because of gradients in the mean flow. The residual distribution method leads to a class of schemes that shares properties of both finite element method and finite volume method. In particular, the schemes used here are multidimensional upwind, which make them very attractive because of their low cross-dissipation. First, the discretization method is introduced as an alternative method for computational aeroacoustic applications on unstructured grids. The residual distribution method is then analyzed analytically for wave propagation. Next it is applied to linearized Euler equations with proper acoustic boundary conditions, and finally verifiedon test cases having exact solution.

Residual distribution schemes on curved geometries are discussed in the context of higher order spatial discretization for hyperbolic conservation laws. The discrete solution, defined by a Finite Element space based on triangular Lagrangian Pk elements, is globally continuous. A natural sub-triangulation of these elements allows to reuse the simple distribution schemes previously developed for linear P1 triangles. The paper introduces curved elements with piecewise quadratic and cubic approximation of the boundaries of the domain, using standard sub- or isoparametric transformation. Numerical results for the Euler equations confirm the predicted order of accuracy, showing the importance of a higher order approximation of the geometry.

International audience; We discuss preliminary results on the construction of uniformly high-order residual distribution $(\cal RD)$ type discretizations for steady advection-diffusion on unstructured grids. A properly designed scaling of the $(\cal RD)$ upwind stabilization with the physical viscosity allows to obtain schemes with uniform and arbitrary accuracy, on a very compact stencil. Second- and third-order examples are given to illustrate the potential of the approach.

In the first part, an extension of upwind residual distribution schemes for high-order accurate solution of hyperbolic problems is introduced, based on the use of spatially varying distribution matrices. Following this, the application to adjoint-based error estimation for steady compressible flow is presented. Finally the resolution of acoustic wave propagation by a space-time residual distribution is discussed. The accuracy of the methodology is demonstrated on several test cases.

In this article, the results of aeroacoustic cases obtained by high-order methods are presented. One internal and one external case are considered. The internal case is a transonic cavity. It has been computed by three parters, namely FOI-LiU (Linkoping University), University of Stuttgart (USTUTT) and Dassault Aviation (DASSAV). FOI-LiU has computed with their higher order accurate finite difference solver using a block structured grid. Comparisons are made to reference calculations using an unstructured grid with Edge. USTUTT uses a high order discontinuous Galerkin spectral element code for the final high-order computations and a mixed modal/nodal DG code for the baseline computations. Dassault Aviation uses their in-house stabilized finite element code Aether, both for the reference and the higher-order computations. In both instances unstructured tetrehedral grids are used. The external case is a quasi-two dimensional generic wing and flap configuration defined in the VALIANT FP7 project. Two institutions were involved in the high-order simulation of this low-Mach number test case, M = 0.15, Central Institute of Aero- and Hydrodynamics, TsAGI, and the von Karman Institute, VKI. In the following, the acoustic predictions corresponding to the two test cases will be described.

The paper investigates a new methodology to rebuild freestream conditions for the trajectory of a reentry vehicle from stagnation-point measurements. Uncertainties due to measurements and model parameters are taken into account, and a Bayesian setting supplied with metamodels is used to solve the associated stochastic inverse problem. A sensitivity analysis based on a stochastic spectral framework is first investigated to study the impact of uncertain input data on stagnation-point measurements. An original backward uncertainty propagation method is then proposed, for which only the uncertainties that have the most impact are retained.

The post§ight analysis of a space mission requires accurate determination of the free-stream conditions for the trajectory. The Mach number, temperature, and pressure conditions can be rebuilt from the heat §ux and pressure measured on the spacecraft by means of a Flush Air Data System (FADS). This instrumentation comprises a set of sensors §ush mounted in the thermal protection system to measure the static pressure (pressure taps) and heat §ux (calorimeters). Knowing that ex

The paper investigates a new methodology to rebuild freestream conditions for the trajectory of a re-entry vehicle from measurements of stagnation-point pressure and heat flux. Uncertainties due to measurements and model parameters are taken into account and a Bayesian setting is used to solve the associated stochastic inverse problem. A sensitivity analysis based on a stochastic spectral framework is first investigated to study the impact of uncertain input data on stagnation-point measurements. An original backward uncertainty propagation method is then proposed, for which only the uncertainties that have the most impact are retained.

Imposing subsonic outlet boundary conditions for compressible ow simulations is still a challenging problem, since spurious re ections are occurring if unsteady disturbances leaving the domain. Most of the non-re ecting boundary conditions can be found in the literature performing very well if only acoustic perturbations are considered, but they are less e ective if there are vortical structures passing through the boundaries. This issue is true for both inlets and outlets, but in the current paper just outlets are considered in 2D and 3D. In the literature these spurious waves due to unsteady perturbation passing though the boundaries are called re ections. However, if a vortical structure is leaving the domain, the acoustic waves propagating back to the solution domain are rather created. In this sense, the original characteristic equations are modi ed such that the source terms responsible for these spurious waves could be identi ed and deactivated. In such a way, the vortical disturbances can pass the boundaries and therefore no more bu er zone is needed. In this paper, we used this approach to design non-re ecting outlet using residual distribution schemes to solve the bulk ow. We have developed the new boundary condition for both Linearized Euler Equations and Navier-Stokes Equations.

boundary conditions are applied for subsonic outlet in order to adjust it to the multidimensional upwind discretization of Residual Distribution Method. The article analyzes boundary conditions from the litera- ture and gives suggestions of improvement based on physical considerations. The dierent formulations are compared through analytical problems.

This article is dedicated to the design of high order residual distributive schemes for unsteady problems. We use a space-time strategy, which means that the time is considered as a third dimension. To achieve high order both in space and in time, we use prismatic elements having (k+1) levels, each level being a P k element. The first section is dedicated to the deign of space-time schemes on such elements. The second section presents the performances on different type of problems. In particular, we look at a discontinuous problem on Euler equations and two problems of propagation of sound using Linearised Euler equations.

We present an extension of the multidimensional upwind distributive schemes to high order solution spaces. We look into different high-order discretization issues such as: quadratic and cubic boundary curvature; monotonicity of the schemes in presence of solutions with discontinuities; discretisation of temporal terms for unsteady applications and discretization of diffusive fluxes. Results of test cases representative of all these issues are presented.

This article deals with the discretization of Linearized Euler Equations (LEEs) by multidimensional upwind Residual Distribution methods. Linearized Euler equations are applied in the domain where there is no source of sound and the analogy methods such as Ffowcs-Williams can not be used because of gradients in the mean flow. Residual distribution method is a class of schemes that is in between finite-element and finite-volume. In particular, the schemes that we use are multidimensional upwind which make them very attractive because of their very low cross-dissipation. First, we define the formulation of the LEEs that we choose to use. Then, we focus on the residual schemes and we describe two ways of discretizing unsteady problems. The third part presents a wave number of those schemes. Finally, we show the advantage of these schemes on several acoustic problems.

We review a class of compact methods to approximate steady solutions to $$\frac{\partial u}{\partial t}+\nabla\cdot{\cal F}(u)=\nabla\cdot(\nu\nabla u)\quad \forall(x,y)\in\Omega$$ (1)

International audience; This article deals with the latest development in the construction of monotone high-order residual distribution schemes (RDS) on quadrilateral meshes. In the first part we give some generalities about the way upwind high-order RDS is designed. In the second part, some standard schemes are described. Then, the design of a stabilization to help the convergence is shown. The last part of this article is dedicated to the results obtained with these schemes.

The COOLFluiD (Computational Object Oriented Libraries for Fluid Dynamics) project, officially started in 2002, has lead to the creation of a world-class, extremely modular collaborative platform for high-performance scientific computing and multi-physics modeling. Target applications include Space Weather modeling, aeroacoustics, turbulence, aerothermodynamics for aerospace problems ranging from incompressible regime to hypersonics, steady and unsteady flows, etc. COOLFluiD features a unique collection of parallel numerical solvers for unstructured meshes, where each physical model (set of PDE’s, variable transformation, aerothermochemical properties, etc.) or numerical algorithm (space discretization, time discretization, coupling strategy, linear system solver interface, etc.) is enclosed in a separate module which is loaded dynamically at run-time. The paper presents a concise description about the main design strengths of the platform, an overview of current capabilities (in terms of numerical methods and physical models) and a gallery of the most challenging applications tackled so far. Particular attention is devoted to the computational modeling of aerothermodynamics and plasma flows, including atmospheric re-entry flows and numerical simulation of experiments in high-enthalpy facilities.