Comparing goal-oriented RANS error estimates applied to high-lift configuration computations

International audienceThis presentation discusses an anisotropic adaptive strategy in the context of the 3rd AIAA high-lift prediction workshop. If anisotropic mesh adaptation has proven its reliability for inviscid flows [1, 2], additional challenges remain to be solved to have the full gain of adaptivity, including early asymptotic (spatial second) order convergence, early capturing of the scales of then physical phenomena,. .. Several (fundamental) modifications are needed in the classical adaptive loop to address complex viscous effects. This includes the way error estimates are evaluated, how viscous solutions are interpolated between (anisotropic) meshes, and finally the generation of the boundary layer mesh to comply with the metric size prescription. Addressing fully each of this component remains a challenge on itself. In this presentation, we propose two error estimates to address the RANS equations, this implies in particular to treat appropriately the considered turbulence model. Here, we only consider the one equation Spalart-Allmaras turbulence model

Comparing anisotropic adaptive strategies on the 2nd AIAA sonic boom workshop geometry

International audienceThe recent release of the 2nd AIAA sonic boom geometry offers the opportunity to review the classical anisotropic adaptive strategies for complex geometries. The design of Mach-aligned tailored grids is also a great challenge to see how adaptivity can compete with user-defined tailored grids. Two classical adaptive strategies, multi-scale and goal-oriented, are compared with the results obtained on tailored grids. For the flow solver, we discuss several low-dissipation numerical schemes of order 4th and 6th with respect to regular 2nd order scheme both on inviscid and RANS flow conditions. We finally perform a non-linear error analysis to assess the convergence of the sequence of adaptive meshes with respect to tailored grids. All results and discussions are based on the C25D baseline geometry

Nonlinear corrector for RANS equations

International audienceThe scope of this paper is to present a nonlinear error estimation and correction for Navier-Stokes and RANS equations. This correction is obtained by deducing a source term from the evaluation of the residual of the solution interpolated on the h/2 mesh. To avoid the generation of the h/2 mesh (which is prohibitive for realistic applications), the residual at each vertex is computed by local refinement only in the neighborhood of the considered vertex. It successfully improves solution predictions and yields a sharp estimate of the numerical error

Adaptation de maillage pour des approximations k-exact en CFD

This paper illustrates the application of error estimates based on k-exactness of approximation schemes for building mesh adaptive approaches able to produce better numerical convergence to continuous solution. The cases of k = 1 and k = 2, i.e. second-order and third-order accurate approximations with steady and unsteady flows are considered.Cet article illustre l’application d’estimations d’erreur, basées sur les schémas d’approximation k-exactitude, pour la construction d’approches adaptatives en maillage permettant de produire une meilleure convergence numérique en solution continue. Les cas de k = 1 et k = 2, c'est-à-dire les approximations précises des deuxième et troisième ordres avec des écoulements stables et instables sont prises en compte

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. Laminar flow over a delta wing and turbulent flow over an ONERA M6 wing are verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and a moment. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. The wing adaptation cases in the current study document a clear improvement to existing grid adaptation procedures. The stage is set for the infusion of verified grid adaptation into production fluid flow simulations

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. Laminar flow over a delta wing is verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and pitching moment

Adjoint Based Anisotropic Mesh Adaptation for Turbomachinery Applications

International audienceAdaptive methods have been widely used in aeronautics to improve the predictions while minimizing the CPU cost. They are used to deal with complex phenomena (sonic-boom, vortices,. . .), or to guarantee the optimal (second) order of convergence of the numerical scheme, especially when discontinuities (shocks waves) are present in the flow field [1]. Mesh adaptation now tends to spread in industrial applications but its application to turbomachinery applications is limited to a few attempts due to some particularities of these applications. Turbomachinery involves different complex flows of very small scale (jets, boundary-layers, shock,...) with a strong impact on performance[3]. These flow features are not known a priori and require an appropriate discretization of the domain. Mesh adaptation is thus particularly appropriate for such applications and becomes even more practical when many meshes are required as for design optimisation and performances study. However, in order to handle all these features together, a special care must be taken in the whole adaptation cycle. The periodicity, rotating frames and RANS equations have to be taken into account in the primal and adjoint solver and in the error estimators to prescribe an appropriate mesh size. The periodicity also has to be taken into account in the mesh adaptation step to guarantee the periodicity of the computational domain. Any modification of the mesh on one side of the domain has to be applied to the other side, which has strong impacts on traditional mesh operators (smoothing, boundary layer generation,...) We will show how mesh adaptation can be applied to RO37 and LS89 test cases, improving solutions quality and the inherent difficulties of periodic mesh adaptation and how they can be resolved. REFERENCES [1] A. Loseille, A. Dervieux, P.J. Frey and F. Alauzet, Achievement of global second-order mesh convergence for discontinuous flows with adapted unstructured meshes

Comparing anisotropic adaptive strategies on the 2nd AIAA sonic boom workshop geometry

International audienceThe recent release of the 2nd AIAA sonic boom geometry offers the opportunity to review the classical anisotropic adaptive strategies for complex geometries. The design of Mach-aligned tailored grids is also a great challenge to see how adaptivity can compete with user-defined tailored grids. Two classical adaptive strategies, multi-scale and goal-oriented, are compared with the results obtained on tailored grids. For the flow solver, we discuss several low-dissipation numerical schemes of order 4th and 6th with respect to regular 2nd order scheme both on inviscid and RANS flow conditions. We finally perform a non-linear error analysis to assess the convergence of the sequence of adaptive meshes with respect to tailored grids. All results and discussions are based on the C25D baseline geometry

Mesh adaptation strategies using wall functions and low-Reynolds models

International audienceThe scope of this paper is to determine an optimal mesh adaptation strategy to compute turbulent flows in presence of solid bodies using RANS models. To this end we propose to use additionally model specific wall functions when the low-Reynolds turbulence model is not sufficiently resolved. Such wall functions degenerate to the low-Reynolds turbulence model they mimic when the mesh size tends to 0. This significantly improves solutions on coarse initial grids and fasten computations toward the final solution

Corretru nonlineaire pour les equations RANS

International audienceThe scope of this paper is to present a nonlinear error estimation and correction for Navier-Stokes and RANS equations. This correction is obtained by deducing a source term from the evaluation of the residual of the solution interpolated on the h/2 mesh. To avoid the generation of the h/2 mesh (which is prohibitive for realistic applications), the residual at each vertex is computed by local refinement only in the neighborhood of the considered vertex. It successfully improves solution predictions and yields a sharp estimate of the numerical error.L'objectif de cet article est de présenter une estimation et une correction d'erreur non linéaire pour les équations de Navier-Stokes et RANS. Cette correction est obtenue en déduisant un terme source de l'évaluation du résidu de la solution interpolée sur le maillage h / 2. Pour éviter la génération du maillage h / 2 (ce qui est prohibitif pour des applications réalistes), le résidu à chaque sommet est calculé par raffinement local uniquement au voisinage du sommet considéré. Il améliore avec succès les prévisions de solution et fournit une estimation précise de l'erreur numérique