Parallel Anisotropic Unstructured Grid Adaptation

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

Durée de vie d'un composite en fatigue statique sous un gradient de contrainte et de température = Composite lifetime, in static fatigue, under non-uniform stress and temperature fields

National audienceUn modèle mécanique est proposé pour le calcul de la durée de vie du composite dans des conditions où champs de température et de contrainte sont non uniformes. Le modèle prend en compte le phénomène de cicatrisation matricielle et les 3 principaux processus d'endommagement en fatigue, identifiés par fractographie M.E.B : fissuration lente des fibres, rupture fragile locale de fibre et rupture par paquet de fibres [1, 2, 3]. Il s'agit d'un modèle multi-échelle fondé sur la rupture des fibres et des fils. Le modèle est confronté à des résultats expérimentaux obtenus en fatigue à 800°C pour un composite SiC/SiC. L'aboutissement du modèle est double. D'une part, il conduit à l'établissement d'une distribution spatiale des durées de vie, en fatigue statique, au sein de la pièce ou de l'éprouvette. Cette loi permet de localiser les zones critiques où la durée de vie est minimale, et de prévoir la durée de vie en fonction de la géométrie. D'autre part, ce modèle permet la définition d'une géométrie en fonction d'une distribution spatiale fixée de durée de vie

Recent Improvements on Cavity-Based Operators for RANS Mesh Adaptation

International audienceIf anisotropic mesh adaptation has been a reliable tool to predict inviscid flows, its use with viscous flows at high Reynolds number remains a tedious task. Indeed many issues tends to limit the efficiency of standard remeshing algorithms based on local modifications. First, the high Reynolds number require to handle a very high level of anisotropy O(1 : 10 6) near the geometry. In the range of anisotropy, interpolation of metric fields or the projection on geometry are typical components that may fail during an adaptive step. The need for high-resolution near the geometry imposes to use an accurate geometry description, and optimally, be linked to a continuous CAD geometries. However, the boundary layer sizing may become smaller than typical CAD tolerance. We present a simple hierarchical geometry approximation where the newly created points are projected linearly, then using a cubic approximation then the CAD data. Finally, the accuracy, speed of convergence of the flow solver highly depends on the topology of the grids. Typical quasi-structured grids are preferred in the boundary layer while this kind of grids are complicated to generate with typical anisotropic meshing algorithm. We discuss in this paper, new developments in metric-orthogonal approach where an advancing points techniques is used to propose new points. Then these newly created points are inserted by using the cavity operator

Unstructured Mesh Generation and Adaptation

International audienceWe first describe the well established unstructured mesh generation methods as involved in the computational pipeline, from geometry definition to surface and volume mesh generation. These components are always a preliminary and required step to any numerical computations. From an historical point of view, the generation of fully unstructured mesh generation in 3D has been a real challenge so as to the design of robust and accurate second order schemes on such unstructured meshes. If the issue of generating volume meshes for geometries of any complexity is now mostly solved, the emergence of robust numerical schemes on unstructured meshes has paved the way to adaptivity. Indeed, unstructured meshes in contrast with structured or block structured grids have the necessary flexibility to control the discretization both in size and orientation. In the second part, we review the main components to perform adaptative computations: (i) anisotropic mesh prescription via a metric field tensor (ii) anisotropic error estimates, and (iii) anisotropic mesh generation. For each component, we focus on a particularly simple method to implement. In particular, we describe a simple but robust strategy for generating anisotropic meshes. Each adaptation entity, ie surface, volume or boundary layers, relies on a specific metric tensor field. The metric-based surface estimate is then used to control the deviation to the surface and to adapt the surface mesh. The volume estimate aims at controlling the interpolation error of a specific field of the flow. Several 3D examples issued from steady and unsteady simulations from systems of hyper-bolic laws are presented. In particular, we show that despite the simplicity of the introduced adaptive meshing scheme a high level of anisotropy can be reached. This includes the direct prediction of the sonic boom of an aircraft by computing the flow from the cruise altitude to the ground, the interaction between shock waves and boundary layer, or the prediction of complex unsteady phenomena in 3D

Towards goal-oriented mesh adaptation for fluid-structure interaction

In order to address fluid-structure interaction, we present an a priori analysis for an ALE compressible flow model. This analysis is the key for an anisotropic metricbased mesh adaptation

Anisotropic, Adaptive Finite Elements for a Thin 3D Plate

International audienceAn adaptive, anisotropic finite element algorithm is proposed to solve the 3D linear elasticity equations in a thin 3D plate. Numerical experiments show that adaptive computations can be performed in thin 3D domains having geometrical aspect ratio 1:1000

Developments on the P2{P^2} cavity operator and Bézier Jacobian correction using the simplex algorithm.

International audienceThis paper describes developments on the ${P^2}$ cavity operator stemming from a new Bézier untangling algorithm. Both surface and volume are adapted to an anisotropic solution field with the cavity operator as the low-level driver handling all topological changes to the mesh. The ${P^2}$ extension of the cavity operator handles curvature through Riemannian curved edge length minimization in the volume and geometry projection on the surface. In particular, the anisotropy conserving log-euclidean metric interpolation scheme was extended to high-order elements to facilitate differentiating edge length in the metric field. As a step forward from previous iterations of the ${P^2}$ cavity operator, validity is now enforced through optimization of Jacobian coefficients using the simplex algorithm for linear programs. This is made possible by the fact that Jacobian control coefficients are linear with regards to each control point and enables the global optimization of the minimum of all control coefficients surrounding an edge at once. Numerical results illustrate the ability of metric-induced curving to relatively quickly curve 3D meshes with complex geometries involved in Computational Fluid Dynamics (CFD) using only local schemes. This framework allow us to curve highly anisotropic meshes with around 10 million elements within minutes

Shrimp User Guide. A Fast Mesh Renumbering and Domain Partionning Method

This technical note describes the main features of Shrimp, a software that renumbers mesh entities and splits mesh domain and handle the parallelization of adaptive mesh generators. The aim of the software, the input and the output files and the list of options are given in this document. Shrimp has been developed within the GAMMA research project at INRIA Paris-Rocquencourt. This document describes the features of the current version: release V1.0 (January 2009)

Geometry Modeling for Unstructured Mesh Adaptation

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

P2 Cavity Operator with Metric-Based Volume and Surface Curvature

International audienceThis paper describes theoretical developments and algorithms involved in the design of a P2 cavity operator to generate anisotropic curved meshes. Both volume and surface are adapted. A high-level approach is chosen, such that the existing P1 cavity operator is used as-is to handle topology. The P2 extension performs the curving process and ensures geometric validity. Volume curvature is based on Riemannian edge length minimization, first requiring a description of the metric field along a Bézier edge: this leads to the proposed high-order extension of the log-Euclidean scheme and differentiation of geometrical quantities in this framework. Surface curvature is based on similar principles, with the added difficulty of CAD or CAD surrogate projection. Numerical results illustrating the P2 cavity operator’s ability to recover curvature, from surface geometry to boundary layers to metric fields are presented. Examples are based on 3D real-world geometries encountered in Computational Fluid Dynamics (CFD). This framework allow us to curve highly anisotropic meshes with around 10 million elements within minutes