Study of interpolation methods for high-accuracy computations on overlapping grids

Overset strategy can be an efficient way to keep high-accuracy discretization by decomposing a complex geometry in topologically simple subdomains. Apart from the grid assembly algorithm, the key point of overset technique lies in the interpolation processes which ensure the communications between the overlapping grids. The family of explicit Lagrange and optimized interpolation schemes is studied. The a priori interpolation error is analyzed in the Fourier space, and combined with the error of the chosen discretization to highlight the modification of the numerical error. When high-accuracy algorithms are used an optimization of the interpolation coefficients can enhance the resolvality, which can be useful when high-frequency waves or small turbulent scales need to be supported by a grid. For general curvilinear grids in more than one space dimension, a mapping in a computational space followed by a tensorization of 1-D interpolations is preferred to a direct evaluation of the coefficient in the physical domain. A high-order extension of the isoparametric mapping is accurate and robust since it avoids the inversion of a matrix which may be ill-conditioned. A posteriori error analyses indicate that the interpolation stencil size must be tailored to the accuracy of the discretization scheme. For well discretized wavelengthes, the results show that the choice of a stencil smaller than the stencil of the corresponding finite-difference scheme can be acceptable. Besides the gain of optimization to capture high-frequency phenomena is also underlined. Adding order constraints to the optimization allows an interesting trade-off when a large range of scales is considered. Finally, the ability of the present overset strategy to preserve accuracy is illustrated by the diffraction of an acoustic source by two cylinders, and the generation of acoustic tones in a rotor–stator interaction. Some recommandations are formulated in the closing section

Study of interpolation methods for high-accuracy computations on overlapping grids

Overset strategy can be an efficient way to keep high-accuracy discretization by decomposing a complex geometry in topologically simple subdomains. Apart from the grid assembly algorithm, the key point of overset technique lies in the interpolation processes which ensure the communications between the overlapping grids. The family of explicit Lagrange and optimized interpolation schemes is studied. The a priori interpolation error is analyzed in the Fourier space, and combined with the error of the chosen discretization to highlight the modification of the numerical error. When high-accuracy algorithms are used an optimization of the interpolation coefficients can enhance the resolvality, which can be useful when high-frequency waves or small turbulent scales need to be supported by a grid. For general curvilinear grids in more than one space dimension, a mapping in a computational space followed by a tensorization of 1-D interpolations is preferred to a direct evaluation of the coefficient in the physical domain. A high-order extension of the isoparametric mapping is accurate and robust since it avoids the inversion of a matrix which may be ill-conditioned. A posteriori error analyses indicate that the interpolation stencil size must be tailored to the accuracy of the discretization scheme. For well discretized wavelengthes, the results show that the choice of a stencil smaller than the stencil of the corresponding finite-difference scheme can be acceptable. Besides the gain of optimization to capture high-frequency phenomena is also underlined. Adding order constraints to the optimization allows an interesting trade-off when a large range of scales is considered. Finally, the ability of the present overset strategy to preserve accuracy is illustrated by the diffraction of an acoustic source by two cylinders, and the generation of acoustic tones in a rotor–stator interaction. Some recommandations are formulated in the closing section

Techniques de recouvrement de maillages pour le calcul direct en aéroacoustique

La mise en œuvre d'un calcul direct en aéroacoustique se révèle difficile lorsque la configuration est complexe. Une solution est de décomposer le domaine de calcul en plusieurs, de topologie plus simple, se recouvrant et communiquant grâce à des interpolations : c'est une technique de recouvrement de maillages. L'ordre et la méthode de ces interpolations seront l'objet de cette étude

Calcul direct du rayonnement acoustique généré par une cavité cylindrique sous une aile d'avion

Les sources de bruit d'origine aérodynamique sont multiples pour un avion. A l'atterrissage, la source prépondérante est le bruit dû à l'écoulement autour de la voilure, du fuselage et du train d'atterrissage. Sous l'impulsion d'Airbus, le projet AEROCAV (Aéroacoustique des cavités) s'intéresse au bruit généré par des cavités cylindriques qui se situent sous les ailes des avions pour évacuer un éventuel surplus de carburant. Elles émettent un rayonnement acoustique intense et très marqué en fréquence. Afin d'étudier les mécanismes de génération sonore, des simulations numériques du rayonnement acoustique dû à l'écoulement affleurant une cavité cylindrique sont réalisées par calcul direct du bruit. Ce type de simulation requiert des algorithmes numériques de haute précision afin de résoudre la turbulence fine échelle et le rayonnement acoustique associé de faible amplitude. Afin de gérer la géométrie complexe, une technique de recouvrement de maillages a été développée. Le point principal est le choix d'une interpolation compatible avec ces schémas de haute précision pour la communication entre les différentes grilles. Un travail spécifique est réalisé sur les méthodes de génération d'une condition d'entrée turbulente afin de reproduire de façon réaliste les conditions de la soufflerie. Deux Simulations des Grandes Échelles sont réalisées pour une cavité de diamètre et profondeur de 100 mm et une vitesse amont de 70 m/s, l'un avec la nouvelle condition d'entrée turbulente et l'autre sans. Ils permettent de reproduire les principales caractéristiques de l'écoulement et du champ acoustique mesurées durant la campagne expérimentale du projet AEROCAV.Aerodynamically generated noise sources are multiple for an airplane. During the landing phase, airframe noise is the main source. At the instigation of Airbus, the project AEROCAV (Aeroacoustics of cavities) deals with the noise produced by cylindrical burst-disk cavities located under the wings. An intense tonal noise is emitted. Numerical simulations of the noise generated by these cylindrical cavities are performed to investigate the noise source mechanisms by using Direct Noise Computation. Such simulations require high-accuracy numerical algorithms in order to compute the fine-scale turbulence together with the very weak associated noise radiation. An overset grid method is developed to tackle the complex geometry of interest. The main point is to choose an interpolation method preserving the high-accuracy of the numerical schemes in order to ensure the communication between the different grids. Turbulent inflow methods based on synthetic turbulence, recycling techniques, or bypass transition are investigated to reproduce the flow conditions of the wind tunnel. Two Large Eddy Simulations are conducted for a cavity with a diameter and a height of 100 mm, and a freestream velocity of 70 m/s, with the turbulent inflow method for one of these computations. The characteristics of the flow and noise, as measured in the AEROCAV experimental campaign, are satisfactorily reproduced by the direct noise computations.PARIS-Arts et Métiers (751132303) / SudocSudocFranceF

A database of validation cases for tsunami numerical modelling

This work has been performed by a French national consortium within the framework of the nationalproject Tandem, with aim to improve knowledge about tsunami risk on the French coasts. Workpackage#1 of this project was the opportunity to build a database of benchmark cases to assess the capabilitiesof 18 codes, solving various set of equations with different numerical methods. 14 test cases were definedfrom the existing literature with validation data from reference simulations, theoretical solutions or lab experiments.They cover the main stages of tsunami life: 1) generation, 2) propagation, 3) run-up and submersion,and 4) impact. For each case several of the numerical codes were compared in order to identify the forces andweaknesses of the models, to quantify the errors that these models may induce, to compare the various modellingmethods, and to provide users with recommendations for practical studies. In this paper, 3 representativecases are selected and presented with an analysis of the results.Tsunamis en Atlantique et MaNche : Définition des Effets par Modélisatio