Éditeur(s) : HAL CCSD Springer Verlag (Germany) Springer Verlag
Résumé : Direct numerical simulations of flow through two millimeter-scale rock samples of limestone and sandstone are performed using three diverse fluid dynamic simulators. The resulting steady-state velocity fields are compared in terms of the associated empirical probability density functions (PDFs) and key statistics of the velocity fields. The pore space geometry of each sample is imaged at 5.06−μm voxel size resolution using X-ray microtomography. The samples offer contrasting characteristics in terms of total connected porosity (about 0.31 for the limestone and 0.07 for the sandstone) and are typical of several applications in hydrogeology and petroleum engineering. The three-dimensional fluid velocity fields within the explicit pore spaces are simulated using ANSYS® FLUENT® ANSYS Inc. (2009), EULAG Prusa et al. (Comput. Fluids 37, 1193–1207 2008), and SSTOKES Sarkar et al. (2002). These computational approaches are highly disperse in terms of algorithmic complexity, differ in terms of their governing equations, the adopted numerical methodologies, the enforcement of internal no-slip boundary conditions at the fluid-solid interface, and the computational mesh structure. As metrics of comparison to probe in a statistical sense the internal similarities/differences across sample populations of velocities obtained through the computational systems, we consider (i) integral quantities, such as the Darcy flux and (ii) main statistical moments of local velocity distributions including local correlations between velocity fields. Comparison of simulation results indicates that mutually consistent estimates of the state of flow are obtained in the analyzed samples of natural pore spaces despite the considerable differences associated with the three computational approaches. We note that in the higher porosity limestone sample, the structures of the velocity fields obtained using ANSYS FLUENT and EULAG are more alike than either compared against the results obtained using SSTOKES. In the low-porosity sample, the structures of the velocity fields obtained by EULAG and SSTOKES are more similar than either is to the fields obtained using ANSYS FLUENT. With respect to macroscopic quantities, ANSYS FLUENT and SSTOKES provide similar results in terms of the average vertical velocity for both of the complex microscale geometries considered, while EULAG tends to render the largest velocity values. The influence of the pore space structure on fluid velocity field characteristics is also discussed.
ISSN: 1420-0597

hal-01174152
https://hal.archives-ouvertes.fr/hal-01174152
DOI : 10.1007/s10596-015-9486-7

Résumé : Cette thèse à pour objet l'étude théorique et numérique de solutions dans les équations aux dérivées partielles non linéaires de la physique, en particulier en dynamique des fluides. La présence de discontinuités dans les solutions de ces équations complique la compréhension mathématique des phénomènes mis enjeu et leur traitement numérique, notamment en vue de simulations informatiques . Nous étudions ces équations par une méthode de régularisation dans un espace fonctionnel approprié. Lorsque des schémas numériques construits par des méthodes différentes conduisent à des résultats identiques, ceci jusque dans leurs moindres détails, il semble alors naturel de s'interroger dans quelle mesure ces suites de solutions numériques constituent une approximation d'une solution des équations étudiées. Nous construisons des suites de solutions approchées à partir d'un schéma numérique original,stable et suffisamment simple pour démontrer que ses suites constituent une méthode asymptotique de Maslov au sens des distributions en dimension trois d'espèce. La technique de régularisation employée consiste à étendre les variables réelles du problème ne des variables complexes, ce qui nous permet de construire des familles de solutions particulières que l'on ramène au cas réel en faisant tendre un petit paramètre vers O. Les solutions physiques recherchées apparaissent alors comme valeurs au bord de fonction holomorphes. Nous illustrons les résultats obtenus par des applications en cosmologie dans les cadres Newtoniens et relativistes pour des systèmes sans pression, puis avec pression et auto-gravitation, ainsi que pour le système des gaz parfaits.
This thesis is devoted to the theoretical and numerical study of singular solutions appearing in nonlinear partial differential complicates the mathematical understanding of the phenomena under concem as well as their numerical treatment, in particular in view of computation. These equations are studied by a regularization method in an appropriate functional space. When completely different numerical methods give the same results up to the smallest details one can reasonably expect that these numerical results suggest the existence of a mathematical solution of theses equations. We construct sequences of approximate solutions from an original numerical scheme, which is stable and simple enough to prove that these sequences constitute a Maslov asymptotic method in three space dimension. The regularization technique in use consits in extending the real variables of the problem into complex ones, which perrnits to construct families of particular equations that we bring back to the real case by letting a small paramater tend to zero. The expected physical solutions appear as boundary values of holomorphie functions . Illustrations are given by applications to cosmology in the Newtorian and re1ativistic settings for pressure1ess fluid dynamics, then in presence of self-gravitation and pressure as weil as for the systemof ideal gases

http://www.theses.fr/2011AGUY0478/document

Éditeur(s) : HAL CCSD InTech
Résumé : Available from: http://www.intechopen.com/books/evaporation-condensation-and-heat-transfer/heat-transfer-in-buildings-application-to-solar-air-collector-and-trombe-wall-design
International audience
The aim of this paper is to briefly recall heat transfer modes and explain their integration within a software dedicated to building simulation (CODYRUN). Detailed elements of the validation of this software are presented and two applications are finally discussed. One concerns the modeling of a flat plate air collector and the second focuses on the modeling of Trombe solar walls. In each case, detailed modeling of heat transfer allows precise understanding of thermal and energetic behavior of the studied structures. Recent decades have seen a proliferation of tools for building thermal simulation. These applications cover a wide spectrum from very simplified steady state models to dynamic simulation ones, including computational fluid dynamics modules (Clarke, 2001). These tools are widely available in design offices and engineering firms. They are often used for the design of HVAC systems and still subject to detailed research, particularly with respect to the integration of new fields (specific insulation materials, lighting, pollutants transport, etc.). Available from: http://www.intechopen.com/books/evaporation-condensation-and-heat-transfer/heat-transfer-in-buildings-application-to-solar-air-collector-and-trombe-wall-design
Evaporation, condensation and heat transfer

Droits : info:eu-repo/semantics/OpenAccess
ISBN : 978-953-307-583-9
hal-00767482
https://hal.archives-ouvertes.fr/hal-00767482
https://hal.archives-ouvertes.fr/hal-00767482/document
https://hal.archives-ouvertes.fr/hal-00767482/file/InTecSubmitted.pdf

Résumé : Ce travail de thèse est consacré à l'étude numérique de la forme instationnaire des équations de Navier--Stokes incompressibles en dimension trois d'espace. Ces équations sont étudiées dans leur formulation classique mais aussi dans leur formulation hydrostatique. Le schéma en temps est résolu à l'aide d'une méthode de projection, la méthode de projection incrémentale standard qui sert de référence à l'étude numérique des nouvelles méthodes proposées: la méthode de projection hydrostatique et la méthode de projection dynamique étendue. Ces méthodes sont combinées à la méthode de pénalisation de volume qui permet de tenir compte de la présence d'obstacles de forme quelconque dans le domaine de simulation en utilisant un maillage cartésien. Une nouvelle expression des équations de Navier--Stokes hydrostatiques issue de l'application de la méthode de pénalisation de volume est obtenue et étudiée. La discrétisation en espace s'effectue en utilisant la méthode des volumes finis sur une maillage décalé de type MAC. Un nouveau code de calcul baptisé VivAn'O a été conçu et validé durant ce travail. Il a permis l'étude numérique des différentes méthodes proposées et a également permis de réaliser des simulations dans la zone portuaire de Pointe-à-Pitre à partir de données bathymétriques réelles.
The present work is about the numerical study of the three dimensional form of the unstationnary Navier--Stokesequations. These equations are studied under their classical form but also under their hydrostatic one. Thetime--dependent problem is solved using a projection method called the standard incremental projection method which isused as the reference to the numerical study of the new projection methods we proposed : the hydrostatic projectionmethod and the extended dynamical projection method. These methods are combined with a volume penalization methodto take into account obstacles of any shape in the simulation domain using cartesian meshes. A new formulation of the hydrostatic Navier--Stokes equations is obtained from the use of the penalization method and studied. The space isdiscretized using the finite volume method on a staggered MAC mesh.A new computational fluid dynamic code nammed VivAn'O have been developped during this work. It had permitted thenumerical study of the proposed methods. It was also used to carry out simulations in the harbour area of Pointe--à--Pitre usine real bathvmetric data.

http://www.theses.fr/2013AGUY0631

Éditeur(s) : HAL CCSD Wiley
Résumé : International audience
We study if the multilevel algorithm introduced by Debussche, T. Dubois and R. Temam [Theoret. Comput. Fluid Dynam. 7 (1995), no. 4, 279-315; Zbl 838.76060] and Dubois, F. Jauberteau and Temam [J. Sci. Comput. 8 (1993), no. 2, 167-194; MR1242960 (94f:65098)] for the 2D Navier-Stokes equations with periodic boundary conditions and spectral discretization can be generalized to more general boundary conditions and to finite elements. We first show that a direct generalization, as in [C. Calgaro, J. Laminie and R. Temam, Appl. Numer. Math. 23 (1997), no. 4, 403-442; MR1453424 (98d:76124)], for the Burgers equation, would not be very efficient. We then propose a new approach where the domain of integration is decomposed into subdomains. This enables us to define localized small-scale components and we show that, in this context, there is a good separation of scales. We conclude that all the ingredients necessary for the implementation of the multilevel algorithm are present.
ISSN: 0271-2091

hal-00730709
https://hal.archives-ouvertes.fr/hal-00730709

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Crystal growth driven by a flowing solution is modeled for a flow with low Reynolds number using a computational dynamic software. Considering equivalent crystallographic faces, the chemical flux is calculated along upstream and downstream faces. Upstream flux is higher compared to downstream and leads to a symmetry breakdown of the crystal shape and develops mirror symmetry parallel to the flow velocity. Moreover the ratio of these two fluxes (upstream / downstream) gives a quantitative relation between the relative crystal growth rate and the flow velocity. Thus, using an inverse method, the flow direction and velocity can be deduced by the study of the variation of the growth band thicknesses of equivalent crystallographic faces. This new method was applied to the formation of metasomatic tourmalinite associated with a leucogranite sill. The approach is complemented by a study of the chemistry of the tourmaline. In the studied case, the application of the new method gives the high fluid velocities in pores (10-3 - 10-4 m/s) during metasomatism. Equivalent Darcy velocities are estimated and discussed accounting for the major role played by the regional deformation. Finally, a two-stage tectono-hydrodynamic model is proposed for the metsomatism. The first stage is genetically linked to the sill injection, and the second is characterized by a wider event with hydrothermal flow passing along the leucogranite sills.
ISSN: 0012-821X

Droits : info:eu-repo/semantics/OpenAccess
insu-00352307
https://hal-insu.archives-ouvertes.fr/insu-00352307
https://hal-insu.archives-ouvertes.fr/insu-00352307/document
https://hal-insu.archives-ouvertes.fr/insu-00352307/file/Sizaret_et_al_final.pdf
DOI : 10.1016/j.epsl.2009.01.013