A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes

This document presents an interpolation operator on unstructured tetrahedral meshes that satisfies the properties of mass conservation, P1-exactness (order 2) and maximum principle. Interpolation operators are important for many applications in scientific computing. For instance, in the context of anisotropic mesh adaptation for time-dependent problems, the interpolation stage becomes crucial as the error due to solution transfer accumulates throughout the simulation. This error can eventually spoil the overall solution accuracy. When dealing with conservation laws in CFD, solution accuracy requires enforcement of mass preservation throughout the computation, in particular in long time scale computations. In the proposed approach, the conservation property is achieved by local mesh intersection and quadrature formulae. Derivatives reconstruction is used to obtain a second order method. Algorithmically, our goal is to design a method which is robust and efficient. The robustness is mandatory to obtain a reliable method on real-life applications and to apply the operator to highly anisotropic meshes. The efficiency is achieved by designing a matrix-free operator which is highly parallel. A multi-thread parallelization is given in this work. Several numerical examples are presented to illustrate the efficiency of the proposed approach

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)

Estimateur d'erreur géométrique et métriques anisotropes pour l'adaptation de maillage: Partie II : exemples d'applications

Ce rapport présente quelques résultats relatifs à l'adaptation de maillages anisotropes non structurés, en dimensions deux et trois. Dans la partie I de ce rapport, on a décrit un estimateur d'erreur géométrique a posteriori basé sur une majoration de l'erreur d'interpolation. A l'aide de cet estimateur on peut construire une carte de métriques basée sur une approximation discrète du hessien de la solution qui va servir à générer un maillage unité vis-à-vis de cette carte de métriques. Plusieurs exemples analytiques sont d'abord fournis pour valider l'estimateur d'erreur proposé. Ensuite un exemple en mécanique des fluides est montré

Continuous Mesh Model and Well-Posed Continuous Interpolation Error Estimation

Rapport de recherche INRIAIn the context of mesh adaptation, Riemannian metric spaces have been used to prescribe orientation, density and stretching of anisotropic meshes. Such structures are used to compute lengths in adaptive mesh generators. In this report, a Riemannian metric space is shown to be more than a way to compute a distance. It is proven to be a reliable continuous mesh model. In particular, we demonstrate that the linear interpolation error can be derived continuously for a continuous mesh. In its tangent space, a Riemannian metric space reduces to a constant metric tensor so that it simply spans a metric space. Metric tensors are then used to continuously model discrete elements. On this basis, geometric invariants have been extracted. They connect a metric tensor to the set of all the discrete elements which can be represented by this metric. As the behavior of a Riemannian metric space is obtained by patching together the behavior of each of its tangent spaces, the global mesh model arises from gathering together continuous element models. We complete the continuous-discrete analogy by providing a continuous interpolation error estimate and a well-posed definition of the continuous linear interpolate. The later is based on an exact relation connecting the discrete error to the continuous one. From one hand, this new continuous framework freed the analysis of the topological mesh constraints. On the other hand, powerful mathematical tools are available and well defined on the space of continuous meshes: calculus of variations, differentiation, optimization, ..., whereas these tools are not defined on the space of discrete meshes

Estimateur d'erreur géométrique et métriques anisotropes pour l'adaptation de maillage. Partie I : aspects théoriques

Ce rapport traite de l'adaptation de maillages anisotropes non structurés. Il présente en détails un estimateur d'erreur géométrique a posteriori basé sur une majoration de l'erreur d'interpolation. A l'aide de cet estimateu- r on construit une carte de métriques (définie aux sommets du maillage) basée sur une approximation discrète du hessien de la solution. Le maillage est adapté en utilisant cette carte de métriques, ce qui revient à construire un maillage unité vis-à-vis de cette carte de métriques. Quelques exemples analytiques seront présentés dans la seconde partie de ce rapport pour illustrer l'approche proposée

Optimisation 3D du nez d'un SuperSonic Business Jet basée sur l'adaptation de maillages. Application à la réduction du bang sonique

Ce rapport traite d'un problème d'optimisation de forme 3D du nez d'un SuperSonic Business Jet (SSBJ) sous des contraintes aérodynamiques et accoustiques. La contrainte accoustique concerne la génération du bang sonique par l'avion. On présente une méthode d'optimisation de faible dimension pour analyser l'impact du nez sur ces contraintes. Plus précisément, après avoir paramétrisé le nez de l'avion, on échantillonne l'espace de contrôle, puis on construit la surface de réponse qui nous donne l'optimum global. La simulation se décompose en deux étapes : (i) l'écoulement autour du profil modélisé par les équations d'Euler et (ii) la propagation des ondes de pression au sol, qui a pour condition initiale la solution Euler, par un modèle de transport d'onde non-linéaire. Afin d'avoir une meilleure prédiction du bang sonique et donc une meilleur évaluation de la fonction coût, le calcul de l'écoulement en mécanique des fluides est couplée avec l'adaptation de maillages pour obtenir une solution plus précise

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

Multi-Scale Anisotropic Mesh Adaptation for Time-Dependent Problems

This paper deals with anisotropic mesh adaptation applied to unsteady inviscid CFD simulations. Anisotropic metric-based mesh adaptation is an efficient strategy to reduce the extensive CPU time currently required by time-dependent simulations from the perspective of performing this kind of computations on a daily basis in an industrial context. In this work, we detail the time-accurate extension of multi-scale anisotropic mesh adaptation for steady flows, i.e., a control of the interpolation error in Lp norm, to unsteady flows based on a space-time error analysis and an enhanced version of the fixed-point algorithm. We also show that each stage - remeshing, metric field computation, solution transfer, and flow solution - is important to design an efficient time-accurate anisotropic mesh adaptation process. The parallelization of the whole mesh adaptation platform is also discussed. The efficiency of the approach is emphasized on three-dimensional problems with convergence analysis and CPU data

Optimization of P2 meshes and applications

International audienceMesh optimization techniques are a way to locally modify the mesh in order to improve it with respect to a given quality criterion. To this end, 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