Optimizing the geometrical accuracy of curvilinear meshes

This paper presents a method to generate valid high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a linear mesh, that is subsequently curved without taking care of the validity of the high order elements. An optimization procedure is then used to both untangle invalid elements and optimize the geometrical accuracy of the mesh. Standard measures of the distance between curves are considered to evaluate the geometrical accuracy in planar two-dimensional meshes, but they prove computationally too costly for optimization purposes. A fast estimate of the geometrical accuracy, based on Taylor expansions of the curves, is introduced. An unconstrained optimization procedure based on this estimate is shown to yield significant improvements in the geometrical accuracy of high order meshes, as measured by the standard Haudorff distance between the geometrical model and the mesh. Several examples illustrate the beneficial impact of this method on CFD solutions, with a particular role of the enhanced mesh boundary smoothness.Comment: Submitted to JC

Variabilité génétique de la performance de nage chez l'alevin de Truite fario (Salmo trutta)

International audienc

A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows

Both compressible and incompressible Navier-Stokes solvers can be used and are used to solve incompressible turbulent flow problems. In the compressible case, the Mach number is then considered as a solver parameter that is set to a small value, $\mathrm{M}\approx 0.1$, in order to mimic incompressible flows. This strategy is widely used for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. The present work raises the question regarding the computational efficiency of compressible DG solvers as compared to a genuinely incompressible formulation. Our contributions to the state-of-the-art are twofold: Firstly, we present a high-performance discontinuous Galerkin solver for the compressible Navier-Stokes equations based on a highly efficient matrix-free implementation that targets modern cache-based multicore architectures. The performance results presented in this work focus on the node-level performance and our results suggest that there is great potential for further performance improvements for current state-of-the-art discontinuous Galerkin implementations of the compressible Navier-Stokes equations. Secondly, this compressible Navier-Stokes solver is put into perspective by comparing it to an incompressible DG solver that uses the same matrix-free implementation. We discuss algorithmic differences between both solution strategies and present an in-depth numerical investigation of the performance. The considered benchmark test cases are the three-dimensional Taylor-Green vortex problem as a representative of transitional flows and the turbulent channel flow problem as a representative of wall-bounded turbulent flows

Development of a Data-Driven Wall Model for Separated flows

Large Eddy Simulations (LES) are of increasing interest for turbomachinery design since they provide a more reliable prediction of flow physics and component behavior. However, they remain prohibitively expensive at high Reynolds numbers or actual complex geometries. Most of the cost is associated with the resolution of the boundary layer, and therefore, to save computational resources, wall-modeled LES (wmLES) has become a valued tool. However, wall models are not yet reliable in predicting the complex flow configurations occurring in turbomachinery passages. Most existing analytical wall models assume the flow to be fully turbulent, attached, flow aligned, and near-equilibrium. These assumptions no longer hold when different flow regimes and complex flow features coexist. Although significant progress has been made in recent years (e.g., non-equilibrium models using pressure gradients), they have not always brought a clear benefit for such realistic flows. This paper proposes an innovative data-driven wall model to treat separated flows. Among the many possibilities to solve this complex regression problem, deep neural networks have been selected for their universal approximation capabilities~\cite{hornik_approximation_1991}. In the present framework, the two-dimensional periodic hill problem is selected as a reference test case featuring the separation of a fully turbulent boundary layer. Gaussian Mixture Neural networks (GMN) and Convolutional Neural Networks (CNN) combined with a self-attention layer~\cite{Vaswani_sel_attention_2017} are trained to predict the wall-parallel components of the wall shear stress using instantaneous flow quantities and geometric parameters. The \textit{a priori} and \textit{a posteriori} validation of such data-driven wall models on the periodic hill problem will be presented.9. Industry, innovation and infrastructur

Machine Learning for wall modeling in LES of separating flows

Large Eddy Simulations (LES) are of increasing interest for turbomachinery design since they provide a more reliable prediction of flow physics and component behavior than standard RANS simulations. However, they remain prohibitively expensive at high Reynolds numbers or realistic geometries. The cost of resolving the near-wall region has justified the development of wall-modeled LES (wmLES), which uses a wall model to account for the effect of the energetic near-wall eddies. The classical assumptions of algebraic wall models do not hold for more complex flow patterns that frequently occur in turbomachinery passages (i.e., misalignment, separation). This work focuses on the extension of wall models to the separation phenomenon. Among possibilities to solve the complex regression problem (i.e., predicting the wall-parallel components of the shear stress from instantaneous flow data and geometrical parameters), neural networks have been selected for their universal approximation capabilities. Since DNS and LES perform well on academic and several industrial configurations, they are used to produce databases to train various neural networks. In the present work, we investigate the possibility of using neural networks to improve wall-shear stress models for flows featuring severe pressure gradients and separation. The database is composed of three building-blocks flows: (1) a flow aligned turbulent boundary layer at equilibrium; (2) a turbulent boundary layer subjected to a moderate pressure gradient; and (3) a turbulent boundary layer that separates and reattaches from a curved wall. These building blocks are referred to as a channel flow at a friction Reynolds number of 950 and the two walls (i.e., the flat upper surface and the curved lower one) of the two-dimensional periodic hill at a bulk Reynolds number of $10{,}595$, respectively. This work is constructed around three main questions: which input points should be considered for the data-driven wall model, how should one normalize the in- and output data to obtain a unified and consistent database, and which neural networks are considered

Connectivity-change moving mesh methods for high-order meshes: Toward closed advancing-layer high-order boundary layer mesh generation

International audienceCurved mesh generation starting from a P1 mesh and closed advancing-layer boundary layer mesh generation both rely on mesh deformation and mesh optimization techniques. The approach presented in this work is to generalize connectivity-change moving mesh methods to high-order meshes. This approach is based on a high-order linear elasticity solver for the mesh deformation and on high-order mesh optimization operators such as mesh smoothing and generalized swapping. Thanks to this method, Pk meshes are generated from P1 meshes and closed advancing-layer boundary layer mesh generation will soon be possible

P2 mesh optimization operators

International audienceCurved mesh generation starting from a P1 mesh relies on mesh deformation and mesh optimization techniques. Mesh optimization techniques consist in locally modifying the mesh in order to improve it with respect to a given quality criterion. This work presents the generalization of two mesh quality-based optimization operators to P2 meshes. The generalized operators consist in mesh smoothing and generalized swapping. With the use of these operators, P2 mesh generation starting from a P1 mesh is more robust and P2 connectivity-change moving mesh methods for large displacements are now possible

An efficient discontinuous Galerkin method for aeroacoustic propagation

An efficient discontinuous Galerkin formulation is applied to the solution of the linearized Euler equations and the acoustic perturbation equations for the simulation of aeroacoustic propagation in two-dimensional and axisymmetric problems, with triangular and quadrilateral elements. To improve computational efficiency, a new strategy of variable interpolation order is proposed in addition to a quadrature-free approach and parallel implementation. Moreover, an accurate wall boundary condition is formulated on the basis of the solution of the Riemann problem for a reflective wall. Time discretization is based on a low dissipation formulation of a fourth-order, low storage Runge-Kutta scheme. Along the far-field boundaries a perfectly matched layer boundary condition is used. For the far-field computations, the integral formulation of Ffowcs Williams and Hawkings is coupled with the near-field solver. The efficiency and accuracy of the proposed variable order formulation is assessed for realistic geometries, namely sound propagation around a high-lift airfoil and the Munt problem

Functional architecture and specifications for Tolerancing Data and Knowledge Management

Part 1: Knowledge ManagementInternational audienceThe paper deals with the Computer-Aided Tolerancing and Product Data Management. It is especially focus on data and knowledge management system to support and improve the tolerancing tasks in product development process. The first part of the paper introduces an overview about the recent developments related to tolerancing supports and data management systems. Based on a literature survey and industrial issues, the second part proposes a functional architecture and specifications of the data and knowledge manage-ment system addressing the numerous needs clarified by tolerancing experts