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Computational Fluid Dynamics (CFD) has become critical to the design and analysis of aerospace vehicles. Parallel grid adaptation that resolves multiple scales with anisotropy is identified as one of the challenges in the CFD Vision 2030 Study to increase the capacity and capability of CFD simulation. The Study also cautions that computer architectures are undergoing a radical change and dramatic increases in algorithm concurrency will be required to exploit full performance. This paper reviews four different methods to parallel anisotropic grid generation. They cover both ends of the spectrum: (i) using existing state-of-the-art software optimized for a single core and modifying it for parallel platforms and (ii) designing and implementing scalable software with incomplete, but rapidly maturating functionality. A brief overview for each grid adaptation system is presented in the context of a telescopic approach for multilevel concurrency. These methods employ different approaches to enable parallel execution, which provides a unique opportunity to illustrate the relative behavior of each approach. Qualitative and quantitative metric evaluations are used to draw lessons for future developments in this critical area for parallel CFD simulation.

Discretization error is a common source of uncertainty in computational fluid dynamics (CFD) analyses. Traditional means of controlling discretization error through fixed-mesh refinement studies ha...

A new strategy for high-fidelity unsteady mesh adaptation dealing with fluid–structure interaction (FSI) problems is presented using a partitioned approach. The Euler equations are solved by an edge-based Finite-Volume solver whereas the linear elasticity equations are solved by the finite-element method using the Lagrange $${\mathbb {P}}_1$$ elements. The coupling between both codes is realized by imposing suitable boundary conditions on conforming meshes even at the fluid–structure interface. Small displacements of the structure are assumed and so the mesh is not deformed. The unsteady mesh adaptation process is based on a unique cavity operator which can handle non-manifold geometry, the fluid–structure interface in this work. The computation of a well-documented two-dimensional test case is finally carried out to perform validation of this new strategy as well as a three-dimensional test case to demonstrate our ability to treat complex three-dimensional test cases.

International audience; ViZiR 4 is an interactive visualization software that uses OpenGL 4 graphic pipeline. It can be used to analyze large meshes with possibly solutions and in this paper the focus is made with results from the 4th AIAA CFD High Lift Prediction Workshop. To perform such simulations, it is necessary to have fast, precise and interactive tools to analyze, check and validate the numerical results obtained. Fast I/O and rendering is important to inspect results and comparisons with ParaView show that ParaView is much slower (ratio between 5 and 50). Many post-processing tools, such as picking, hiding surfaces by reference, isolines rendering and clip planes generation, allow to quickly investigate meshes and solutions. Pixel exact rendering permits to have a precise preview of solutions and tessellations on GPU are used to render high-order and curved elements. Some scripting tools allow to generate quickly images and go over sequences of several meshes that is useful when mesh adaptation is involved. All along the paper, results from the workshop are shown to illustrate the capabilities of ViZiR 4.

International audience; This papers points out some weaknesses of the solution-adapted process. They have been solved by improving the Newton's method of the flow solver enabling convergence to machine zero at each run of the solution adaptive process. This work also presents the benefits of using metric-based anisotropic mesh adaptation for the numerical simulation of high lift configurations. For instance, we reconsider the CRM-HL geometry of the 3rd AIAA CFD High Lift Prediction Workshop and we obtain a prediction of the lift value similar to that of the x-fine mesh generated with the best practices (206 million vertices) with an adapted mesh composed only of 2.7 million vertices. This represents a reduction in the mesh size by a factor of 75.

International audience; We present a strategy for the generation of mixed-element quasi-structured meshes. This strategy is based on the tools of metric-based mesh adaptation. Using metricorthogonal point placement, we can generate a pattern of points following the underlying structure of the metric-field, from which we generate a quasi structured triangular or mixed-element mesh. This paper presents some enhancement of the adaptation loop towards the generation of quad-dominant meshes. Especially, since this method highly depends on the prescribed metric-field, we present a tailored gradation process that favors the formation of structured elements. We also explore two processes to recover the quadrilaterals: an indirect method based on combining right triangles from a preliminary orthogonal triangular mesh, and a quadrilateral detection at the point-placement step.

Predicting shock/shock and shock/boundary-layer interactions in gas flows that surround high-speed vehicles is key in aerodynamic design. Under typical hypersonic conditions, these flow structures are influenced by complex nonequilibrium phenomena leading to high-temperature effects. In this work, the conceptual Bedford wing-body vehicle is studied to analyze flow patterns in shock/shock and shock/boundary-layer interactions with thermochemical nonequilibrium. A parametric computational fluid dynamics study is carried out for different hypersonic operating conditions, with respect to the freestream Mach number. Simulations are performed with the SU2-NEMO solver coupled to the Mutation++ library, which provides all the necessary thermodynamic, kinetic, and transport properties of the mixture and chemical species. The Adaptive Mesh Generation library is used for automatic anisotropic mesh adaptation. Numerical results show that increasing the freestream Mach number from 4 to 10 leads to changes in the shock layer, locations of shock impingement, and regions of boundary-layer separation. Despite these changes, the change in freestream Mach number has little impact on the overall shock interaction structures.

International audience; With the increasing use of high-order methods and high-order meshes, scientific visualization software need to adapt themselves to reliably render the associated meshes and numerical solutions. In this paper, a novel approach, based on OpenGL 4 framework, enables a GPU-based rendering of high-order meshes as well as an almost pixel-exact rendering of high-order solutions. Several aspects of the OpenGL Shading Language and in particular the use of dedicated shaders (GPU programs) allows to answer this visualization challenge. Fragment shaders are used to compute the exact solution for each pixel, made possible by the transfer of degrees of freedom and shape functions to the GPU with textures. Tessellation shaders, combined with geometric error estimates, allow us to render high-order curved meshes by providing an adaptive subdivision of elements on the GPU directly. A convenient way to compute bounds for high-order solutions is described. The interest of using Bézier basis instead of Lagrange functions lies in the existence of fast and robust evaluation of polynomial functions with de Casteljau algorithm. A technique to plot highly nonlinear isolines and wire frames with a desired thickness is derived. It is based on a finite difference scheme performed on GPU. In comparison with standard techniques, we remove the use of any linear interpolation step and the need to generate a priori a fixed subdivided mesh. This reduces the memory footprint, improves the accuracy and the speed of the rendering. Finally, the method is illustrated with various 3D examples.

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.

Unstructured grid adaptation is a technology that holds the potential to improve the automation and accuracy of computational fluid dynamics and other computational disciplines. Difficulty producing the highly anisotropic elements necessary for simulation on complex curved geometries that satisfies a resolution request has limited this technology's widespread adoption. The Unstructured Grid Adaptation Working Group is an open gathering of researchers working on adapting simplicial meshes to conform to a metric field. Current members span a wide range of institutions including academia, industry, and national laboratories. The purpose of this group is to create a common basis for understanding and improving mesh adaptation. We present our first major contribution: a common set of benchmark cases, including input meshes and analytic metric specifications, that are publicly available to be used for evaluating any mesh adaptation code. We also present the results of several existing codes on these benchmark cases, to illustrate their utility in identifying key challenges common to all codes and important differences between available codes. Future directions are defined to expand this benchmark to mature the technology necessary to impact practical simulation workflows.

International audience; The scope of this paper is to present a nonlinear error estimation and correction for Navier-Stokes and Reynolds-averaged Navier-Stokes equations. This nonlinear corrector enables better solution or functional output predictions at fixed mesh complexity and can be considered in a mesh adaptation process. After solving the problem at hand, a corrected solution is obtained by solving again the problem with an added source term. This source term is deduced from the evaluation of the residual of the numerical 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. One of the main feature of this approach is that it automatically takes into account all the properties of the considered numerical method. The numerical examples point out that it successfully improves solution predictions and yields a sharp estimate of the numerical error. Moreover, we demonstrate the superiority of the nonlinear corrector with respect to linear corrector that can be found in the literature.

The quantification and control of discretization error is critical to obtaining reliable simulation results. Adaptive mesh techniques have the potential to automate discretization error control, but have made limited impact on production analysis workflow. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic mesh adaptation mechanics. However, the poor integration of initial mesh generation and adaptive mesh mechanics to typical sources of geometry has hindered adoption of adaptive mesh techniques, where these geometries are often created in Mechanical Computer- Aided Design (MCAD) systems. The difficulty of this coupling is compounded by two factors: the inherent complexity of the model (e.g., large range of scales, bodies in proximity, details not required for analysis) and unintended geometry construction artifacts (e.g., translation, uneven parameterization, degeneracy, self-intersection, sliver faces, gaps, large tolerances be- tween topological elements, local high curvature to enforce continuity). Manual preparation of geometry is commonly employed to enable fixed-grid and adaptive-grid workflows by reducing the severity and negative impacts of these construction artifacts, but manual process interaction inhibits workflow automation. Techniques to permit the use of complex geometry models and reduce the impact of geometry construction artifacts on unstructured grid workflows are models from the AIAA Sonic Boom and High Lift Prediction are shown to demonstrate the utility of the current approach.