Adaptive mesh refinements for thin shells whose middle surface is not exactly known

A strategy concerning mesh refinements for thin shells computation is presented. The geometry of the shell is given only by the reduced information consisting in nodes and normals on its middle surface corresponding to a coarse mesh. The new point is that the mesh refinements are defined from several criteria, including the transverse shear forces which do not appear in the mechanical energy of the applied shell formulation. Another important point is to be able to construct the unknown middle surface at each step of the refinement. For this, an interpolation method by edges, coupled with a triangle bisection algorithm, is applied. This strategy is illustrated on various geometries and mechanical problems

Adaptation de maillage avec approximation de la géométrie pour le calcul de coques minces

Une méthodologie relative au raffinement de maillage pour le calcul des coques minces est présentée. Nous supposons que les seules informations dont nous disposons sur la géométrie de la coque sont donnéespar un ensemble de sommets situés sur sa surface moyenne et de la normale unitaire en ces sommets. Une méthode d'interpolation par arêtes des sommets et des normales, couplée avec un algorithme de subdivision des triangles du maillage de la surface moyenne est mise en oeuvre. L'estimation d'erreur locale est basée sur la détection des défauuts de régularité des efforts de la coque. Quelques exemples numériques illustrent les bons résultats obtenus

Un algorithme pour la simulation du transport convectif et de la propagation acoustique à tout mombre de Mach

A pressure-correction algorithm is presented for compressible fluid flow regimes. It is well-suited to simulate flows at all levels of Mach number with smooth and discontinuous flow field changes, by providing a precise representation of convective transport and acoustic propagation. The co-located finite volume space discretisation is used with the AUSM flux splitting. It is demonstrated that two ingredients are essential for obtaining good quality solutions : the presence of an inertia term in the transporting velocity expression ; a velocity difference diffusive term in the face pressure expression, with a correct Mach number scaling to recover the hydrodynamic and acoustic low Mach number limits. To meet these two requirements, a new flux scheme, named MIAU, for Momentum Interpolation with Advection Upstream splitting is proposed

Pressure-velocity coupling allowing acoustic calculation in low Mach number flow

International audienceLow Mach number flow computation in co-located grid arrangement requires pressure-velocity coupling in order to prevent the checkerboard phenomenon. Two broad categories of pressure-velocity coupling methods for unsteady flows can be distinguished based on the time-step dependency of the coupling coefficient in the definition of the transporting velocity on a face of a control volume. As an example of the time-step independent category , the AUSM +-up scheme is studied. As an example of the second category, Rhie-Chow momentum interpolation methods are studied. Within the momentum interpolation techniques, again two broad categories can be distinguished based on the time-step dependency of the coupling coefficient used for unsteady flow computations, but when a steady state is reached. Variants of Rhie-Chow interpolation methods in each subcategory are studied on critical test cases. The result of the study is that for a good representation of unsteady flows containing acoustic information, the pressure-velocity coupling coefficient must explicitly depend on the time-step, but that the transporting velocity must become independent of the time-step when a steady state is reached

Efficacité du mélange chaotique pour des fluides non newtoniens thermodépendants chauffés ou refroidis

Ce travail concerne l'étude numérique du mélange et du transfert thermique au sein de fluides très visqueux au comportement rhéologique non newtonien (rhéofluidifiants ou rhéoépaississants) soumis à un régime d'advection chaotique. Les fluides considérés sont modélisés par des lois de puissance en prenant en compte la thermodépendance. Le mélangeur est constitué de deux barreaux cylindriques maintenus verticalement dans une cuve. Nous montrons ici l'impact de la variation de la viscosité avec la température et le cisaillement sur la qualité du mélange en réchauffement et en refroidissement

Modélisation et simulation d'écoulements compressibles à bas nombre de Mach

Cette étude porte sur une méthodologie permettant de calculer les champs thermodynamiques et cinématiques d'un modèle d'écoulement compressible dans lequel le nombre de Mach peut être petit devant l'unité. Un problème fondamental que l'on rencontre à bas nombre de Mach est que la vitesse d'écoulement du fluide et la célérité des ondes acoustiques dont il est le support relèvent d'échelles d'observation très différentes. L'algorithme retenu, de la forme estimation/correction, s'appuie sur une prise en compte implicite des termes véhiculant de l'information acoustique au sein de l'écoulement. Un rôle privilégié est attribué à la pression, qui joue un rôle-clef dans les découplages entre équations s'effectuant à mesure que le nombre de Mach décroît, comme cela apparaît lors des approches asymptotiques présentées. Les conditions d'interaction aéroacoustique à bas nombre de Mach, ainsi que les modalités de la disparition de cette interaction lorsque le nombre de Mach tend vers zéro, sont établies au niveau de la modélisation continue. Dans le cadre d'une méthode aux volumes finis d'ordre un centrés aux cellules, les propriétés asymptotiques continues peuvent être retrouvées au niveau discret à condition d'adopter l'interpolation centrée pour les pressions, flux de masse et vitesses aux interfaces entre cellules du maillage. L'effet d'une fluctuation de pression de fréquence acoustique sur l'énergie cinétique du gaz en écoulement est illustré numériquement avec ce choix d'interpolation, ainsi que le problème de découplage en damier qui apparaît alors. L'origine de ce problème est expliquée à l'aide d'une analyse asymptotique multi-échelle semi-discrète. Le défaut de consistance, au niveau asymptotique, de l'approximation numérique résultant de l'utilisation d'une dissipation numérique est discuté.This study presents an efficient methodology of simulation of low Mach number flows aimed at overcoming the fundamental problem caused by the large disparity between acoustic and convective speeds specific to this class of flow. The proposed algorithm is based on predictor/corrector steps in which the acoustic information is treated implicitly. Because of the specific role it plays in the progressive decoupling between the equations when the Mach number goes to zero (evidenced by asymptotic expansions), the proper handling of the pressure field is at the core of the strategy followed. The aero acoustic interaction in low Mach number flows and the disappearance of this interaction as the Mach number goes to zero are investigated through the analysis of the continuous model of equations. Then, using a first-order cell centered finite-volume method, it is shown how the continuous asymptotic properties can be conserved after applying the discretization procedure, provided that the pressure, mass flux and velocity are centrally interpolated. The effect of acoustic fluctuations on the kinetic energy of the flow is numerically illustrated along with the occurence of the observed check board oscillations related to the centered schemes used. A multi-scale semi-discrete asymptotic analysis allows us to explain the origin of this latter behaviour. Finally, consistency issues that result from the explicit introduction of a given level of numerical dissipation are also discussed from an asymptotic point of view.PAU-BU Sciences (644452103) / SudocSudocFranceF

Diffusion and dissipation in acoustic propagation simulation by convection-pressure split algorithms in all Mach number form

The topic of the paper is accuracy analysis of acoustic propagation simulation in low Mach number flows, by finite volume co-located discretisation methods of the time-dependent compressible fluid Euler equations that use the concept of convection-pressure splitting (CPS). These are algorithms that split the flux vectors into a part associated to the convection by the fluid particles, and a part associated to the propagation of the pressure waves. For the convection part, the appropriate space discretisation is the upwind one. For the pressure part, there are alternatives. We discern five types of algorithms that all are adapted for use in low Mach number flows, and thus are considered as all Mach number algorithms. We study the behaviour of the different types for the propagation of small pressure perturbations, of discontinuous or smooth shape, in low Mach number flows. We demonstrate that four of the proposed algorithms of convection-pressure split type are dissipative for such applications, although they are designed for low Mach number flows. The objective of the paper is to analyse why some algorithms are appropriate for acoustic propagation simulation and why some are not appropriate

Quelques observations sur un algorithme semi-implicite pour le calcul des écoulements à tous nombres de Mach

National audienc

A combined momentum-interpolation and advection upstream splitting pressure-correction algorithm for simulation of convective and acoustic transport at all levels of Mach number

A pressure-correction algorithm is presented for compressible fluid flow regimes. It is well-suited to simulate flows at all levels of Mach number with smooth and discontinuous flow field changes, by providing a precise representation of convective transport and acoustic propagation. The co-located finite volume space discretization is used with the AUSM flux splitting. It is demonstrated that two ingredients are essential for obtaining good quality solutions: the presence of an inertia term in the face velocity expression; a velocity difference diffusive term in the face pressure expression, with a correct Mach number scaling to recover the hydrodynamic and acoustic low Mach number limits. To meet these two requirements, a new flux scheme, named MIAU, for Momentum Interpolation with Advection Upstream splitting is proposed

Solving low mach number Riemann problems by momentum interpolation

Momentum interpolation methods for unsteady low Mach number flow calculations are re-examined to allow for solution of low Mach number Riemann problems. The classic momentum interpolation is modified in order to improve its behavior for problems with rarefaction waves and shock waves in flow of an ideal gas at low Mach number