This thesis concerns the numerical simulation and the remote sensing of aircraft wake vortex flows. Due to its lift force, an aircraft releases large scale swirling flows (vortices) in its wake. As these vortices can impact significantly the trajectory of a following aircraft, their study is of great importance for practical applications concerning safety of air traffic management. The investigation carried here is twofold: it concerns, on one hand, the physics and the numerical simulation of aircraft wake vortices and, on the other hand, the technique to detect those vortices and measure their properties.The numerical simulation of aircraft wake vortices requires high order and energy conserving codes. Moreover, as aircraft wake vortex flows are turbulent, subgrid scale (SGS) models are required to perform Large Eddy Simulation (LES) of these flows. In the first part of this work, the numerical codes used (here spectral and high order finite differences) are presented and validated. Several SGS models are presented and their ability to perform LES of vortical flows, also in presence of a ground is assessed. In particular a new “multiscale” model with a natural wall damping behaviour has been developed and investigated: its performance is very good. In the second part, two flows relevant to the wake vortex problem are analyzed. The LES of a wake vortex system in a weakly turbulent atmosphere allowed highlighting the turbulent equilibrium state of such a flow. LES of wake vortices in ground effect, with and without wind, were also carried out. These simulations help to better understand the physics of wake vortices. In the last part, we simulate the remote sensing of aircraft wake vortices using a ground based LIDAR (Light Detection And Ranging) system. The aim of this LIDAR is to sense aircraft wake vortices and turbulent winds. As the LIDAR signals are simulated using realistic parameters and realistic turbulent flows, this work serves as support in the design of an airport based LIDAR system.

We study approximation techniques for incompressible flows with heterogeneous properties. Speci cally, we study two types of phenomena. The first is the flow of a viscous incompressible fluid through a rigid porous medium, where the permeability of the medium depends on the pressure. The second is the ow of a viscous incompressible fluid with variable density. The heterogeneity is the permeability and the density, respectively. For the first problem, we propose a finite element discretization and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence is exponential, we propose a splitting scheme which involves solving only two linear systems. For the second problem, we introduce a fractional time-stepping scheme which, as opposed to other existing techniques, requires only the solution of a Poisson equation for the determination of the pressure. This simpli cation greatly reduces the computational cost. We prove the stability of first and second order schemes, and provide error estimates for first order schemes. For all the introduced discretization schemes we present numerical experiments, which illustrate their performance on model problems, as well as on realistic ones.

A study of the use of solution adaptive grid (SAG) method for simulations of incompressible flows is carried out in this work. Both laminar and turbulent types of flows are chosen. Investigation on laminar flow simulation starts with mesh adaptation criteria that are based on strong changes of some selected flow parameters; pressure and velocity components. Three most common laminar types of flows are studied; flow in a circular pipe, flow in a channel with sudden expansion and flow in a cavity with a moving lid. It is found that with the use of SAG, a reduction in both computational grid nodes and CPU time can be obtained when compared to those of fixed grid while satisfactory solutions are also achievable. Nevertheless, the refinement criteria setup procedure reveals inconveniences and requirement for several judgments that have to be defined ‘ad hoc’. This hence, makes the refinement criteria dubious for real engineering applications. For the study of turbulent flows with large eddy simulation (LES) and implicit filtering, examination of literature reveals that the lack of connections between the filter width and a physical scale has made LES somewhat unclosed, i.e. in a physical sense. In addition, it is known that numerical and modelling errors are always combined and it is difficult to study each of them separately making the total error magnitude difficult to control. Since both error types are characterised by the grid size, LES users very often find cases where a finer mesh no longer provides better accuracy. An attempt to address this ‘physical’ enclosure property of LES and its complication to implement/setup in FLUENT begins with the construction of a new refinement variable as a function of the Taylor scale. Then a new SAG algorithm is formed. The requirement to satisfy a condition of the selected subgrid scale (SAG) model, the Smagorinsky model, is taken into consideration to minimize the modeling error. The construction of a new refinement algorithm is also aimed to be the key to studying the interaction between the two types of error and could lead to the means of controlling their total magnitude. The validation in terms of its effectiveness, efficiency and reliability of the algorithm are made based on several criteria corresponding to suitability for practical applications. This includes the simplicity to setup/employ, computational affordability, and the accuracy level. For this, two different turbulent flow types that represent different commonly found turbulent phenomena are chosen; plane free jet and the flow over a circular cylinder. The simulations of the two cases were carried out in two dimensions. It is found that there are two key factors that strongly determine the success of the algorithm. The first factor is the Taylor scale definition, with literature only available for the turbulent plane jet study, for which good level of accuracy is expected. Unfortunately, this is not true for the flow over a circular cylinder, indicating a need for further analytical work. The second encountered difficulty results from limited access to software codes, which makes it impossible to implement the proposed scheme. As a result, the algorithm formulation needs be modified with carful judgment. Nevertheless, overall results are in reasonably good agreement with their corresponding experimental data.

Lattice Boltzmann Method has been quite successful for incompressible flows. Its extension for compressible (especially supersonic and hypersonic) flows has attracted lot of attention in recent time. There have been some successful attempts but nearly all of them have either resulted in complex or expensive equilibrium function distributions or in extra energy levels. Thus, an efficient Lattice Boltzmann Method for compressible fluid flows is still a research idea worth pursuing for. In this thesis, a new Lattice Boltzmann Method has been developed for compressible flows, by using the concept of a relaxation system, which is traditionally used as semilinear alternative for non-linear hypebolic systems in CFD. In the relaxation system originally introduced by Jin and Xin (1995), the non-linear flux in a hyperbolic conservation law is replaced by a new variable, together with a relaxation equation for this new variable augmented by a relaxation term in which it relaxes to the original nonlinear flux, in the limit of a vanishing relaxation parameter. The advantage is that instead of one non-linear hyperbolic equation, two linear hyperbolic equations need to be solved, together with a non-linear relaxation term. Based on the interpretation of Natalini (1998) of a relaxation system as a discrete velocity Boltzmann equation, with a new isotropic relaxation system as the basic building block, a Lattice Boltzmann Method is introduced for solving the equations of inviscid compressible flows. Since the associated equilibrium distribution functions of the relaxation system are not based on a low Mach number expansion, this method is not restricted to the incompressible limit. Free slip boundary condition is introduced with this new relaxation system based Lattice Boltzmann method framework. The same scheme is then extended for curved boundaries using the ghost cell method. This new Lattice Boltzmann Relaxation Scheme is successfully tested on various bench-mark test cases for solving the equations of compressible flows such as shock tube problem in 1-D and in 2-D the test cases involving supersonic flow over a forward-facing step, supersonic oblique shock reflection from a flat plate, supersonic and hypersonic flows past half-cylinder.

Cette thèse a pour objet le développement d'un modèle numérique de simulation des fluides fondé sur la méthode Smoothed Particle Hydrodynamics (SPH). SPH est une méthode de simulation numérique sans maillage présentant un certain nombre d'avantages par rapport aux méthodes Eulériennes. Elle permet notamment de modéliser des écoulements à surface libre ou interfaces fortement déformées. Ce travail s'adresse principalement à quatre problématiques liées aux fondements de la méthode SPH : l'imposition des conditions aux limites, la prédiction précise des champs de pression, l'implémentation d'un modèle thermique et la réduction des temps de calcul. L'objectif est de modéliser des écoulements industriels complexes par la méthode SPH, en complément de ce qui peut se faire avec des méthodes à maillage. Typiquement, les problèmes visés sont des écoulements 3-D à surface libre ou confinés, pouvant interagir avec des structures mobiles et/ou transporter des scalaires, notamment des scalaires actifs (e.g. température). Dans ce but, on propose ici un modèle SPH incompressible (ISPH) basé sur une représentation semi-analytique des conditions aux limites. La technique des conditions aux limites semi-analytiques permet d'imposer des conditions sur la pression de manière précise et physique, contrairement à ce qui se fait avec des conditions aux limites classiques en SPH. Un modèle k-epsilon a été incorporé à ce nouveau modèle ISPH, à partir des travaux de Ferrand et al. (2013). Un modèle de flottabilité a également été ajouté, reposant sur l'approximation de Boussinesq. Les interactions entre flottabilité et turbulence sont prises en compte. Enfin, une formulation pour les frontières ouvertes dans le nouveau modèle est établie. La validation du modèle en 2-D a été réalisée sur un ensemble de cas-tests permettant d'estimer les capacités de prédiction du nouveau modèle en ce qui concerne les écoulements isothermes et non-isothermes, laminaires ou turbulents. Des cas confinés sont présentés, ainsi que des écoulements à surface libre (l'un d'eux incluant un corps solide mobile dans l'écoulement). La formulation pour les frontières ouvertes a été testée sur un canal de Poiseuille plan laminaire et sur deux cas de propagation d'une onde solitaire. Des comparaisons sont présentées avec des méthodes à maillage, ainsi qu'avec un modèle SPH quasi-incompressible (WCSPH) avec le même type de conditions aux limites. Les résultats montrent que le modèle permet de représenter des écoulements dans des domaines à géométrie complexe, tout en améliorant la prédiction des champs de pression par rapport à la méthode WCSPH. L'extension du modèle en trois dimensions a été réalisée dans un code massivement parallèle fonctionnant sur carte graphique (GPU). Deux cas de validation en 3-D sont proposés, ainsi que des résultats sur un cas simple d'application en 3-D / In this work a numerical model for fluid flow simulation was developed, based on the Smoothed Particle Hydrodynamics (SPH) method. SPH is a meshless Lagrangian Computational Fluid Dynamics (CFD) method that offers some advantages compared to mesh-based Eulerian methods. In particular, it is able to model flows presenting highly distorted free-surfaces or interfaces. This work tackles four issues concerning the SPH method : the imposition of boundary conditions, the accuracy of the pressure prediction, the modelling of buoyancy effects and the reduction of computational time. The aim is to model complex industrial flows with the SPH method, as a complement of what can be done with mesh-based methods. Typically, the targetted problems are 3-D free-surface or confined flows that may interact with moving solids and/or transport scalars, in particular active scalars (e.g. the temperature). To achieve this goal, a new incompressible SPH (ISPH) model is proposed, based on semi-analytical boundary conditions. This technique for the representation of boundary conditions in SPH makes it possible to accurately prescribe consistent pressure boundary conditions, contrary to what is done with classical boundary conditions in SPH. A k-epsilon turbulence closure is included in the new ISPH model. A buoyancy model was also added, based on the Boussinesq approximation. The interactions between buoyancy and turbulence are modelled. Finally, a formulation for open boundary conditions is proposed in this framework. The 2-D validation was performed on a set of test-cases that made it possible to assess the prediction capabilities of the new model regarding isothermal and non-isothermal flows, in laminar or turbulent regime. Confined cases are presented, as well as free-surface flows (one of them including a moving body in the flow). The open boundary formulation was tested on a laminar plane Poiseuille flow and on two cases of propagation of a solitary wave. Comparisons with mesh-based methods are provided with, as well as comparisons with a weakly-compressible SPH (WCSPH) model using the same kind of boundary conditions. The results show that the model is able to represent flows in complex boundary geometries, while improving the pressure prediction compared to the WCSPH method. The extension of the model to 3-D was done in a massively parallel code running on a Graphic Processing Unit (GPU). Two validation cases in 3-D are presented, as well as preliminary results on a simple 3-D application case

O presente trabalho tem por objetivo desenvolver uma formulação numérica baseada em Análise Isogeométrica para o estudo de escoamentos incompressíveis isotérmicos de fluidos newtonianos. Com o emprego desta metodologia, os procedimentos de pré-processamento e análise são unificados, melhorando as condições de continuidade das funções de base empregadas tanto na discretização espacial do problema como na aproximação das variáveis do sistema de equações. O sistema de equações fundamentais do escoamento é formado pelas equações de Navier-Stokes e pela equação de conservação de massa, descrita segundo a hipótese de pseudo-compressibilidade, além de uma equação constitutiva para fluidos viscosos de acordo com a hipótese de Stokes. Para problemas com escoamentos turbulentos emprega-se a Simulação de Grandes Escalas - LES (Large Eddy Simulation), na qual o modelo clássico de Smagorinsky é utilizado para a representação das escalas inferiores à resolução da malha. O esquema explícito de dois passos de Taylor-Galerkin é aplicado no contexto da Análise Isogeométrica para a discretização das equações governantes, sendo que a discretização espacial é realizada empregando-se funções NURBS (Non Uniform Rational Basis B-Splines). Essas funções base apresentam vantagens em relação às tradicionais funções utilizadas no MEF (Método dos Elementos Finitos), principalmente no que diz respeito à facilidade de obtenção de continuidade superior a C0 entre os elementos e representação precisa das geometrias. Propõe-se também o desenvolvimento de ferramentas de pré e pós-processamento baseadas na estrutura de dados da Análise Isogeométrica para a geração de malhas e visualização de resultados. Alguns problemas clássicos da Dinâmica dos Fluidos Computacional são analisados para a validação da metodologia apresentada. Os resultados apresentados demonstram boa aproximação da formulação em relação a dados de referência, além de maior versatilidade quanto à discretização espacial dos problemas em comparação com as tradicionais formulações baseadas em elementos finitos. / This work aims to develop a numerical formulation based on Isogeometric Analysis for the study of incompressible flows of Newtonian fluids under isothermal conditions. By using this methodology, pre-processing and analysis procedures are unified, improving the conditions of continuity of the basis functions utilized in the approximations of the equation variables and spatial discretization of the problem. The system of fundamental equations of the fluid flow is constituted by the Navier-Stokes equations and the mass conservation equation, which is described according to the pseudo-compressibility hypothesis. In addition, a constitutive equation for viscous fluids according to Stokes' hypothesis is also provided. Turbulent flows are analyzed using LES (Large Eddy Simulation), where the Smagorinsky’s model is adopted for sub-grid scales. The explicit two-step Taylor-Galerkin method is applied into the context of Isogeometric Analysis for the discretization of the flow equations, where spatial discretization is carried out taking into account Non Uniform Rational Basis B-Splines (NURBS) basis functions. These basis functions have advantages over traditional functions employed in the FEM (Finite Element Method). Particularly, it is easier to obtain continuity order higher than C0 between adjacent elements and geometry representation is more accurate. Pre and post-processing tools for mesh generation and results visualization are also proposed considering the data structure inherent to Isogeometric Analysis. Some classic problems of Computational Fluid Dynamics are analyzed in order to validate the proposed methodology. Results obtained here show that the present formulation has good approximation when compared with predictions obtained by reference authors. Moreover, Isogeometric Analysis is more versatile than traditional finite element formulations when spatial discretization procedures are considered.

This thesis is concerned with the numerical simulation of high Reynolds number, three-dimensional, incompressible flows in open domains. Many problems treated in Computational Fluid Dynamics (CFD) occur in free space: e.g., external aerodynamics past vehicles, bluff bodies or aircraft; shear flows such as shear layers or jets. In observing all these flows, we can remark that they are often unsteady, appear chaotic with the presence of a large range of eddies, and are mainly dominated by convection. For years, it was shown that Lagrangian Vortex Element Methods (VEM) are particularly well appropriate for simulating such flows. In VEM, two approaches are classically used for solving the Poisson equation. The first one is the Biot-Savart approach where the Poisson equation is solved using the Green's function approach. The unbounded domain is thus implicitly taken into account. In that case, Parallel Fast Multipole (PFM) solvers are usually used. The second approach is the Vortex-In-Cell (VIC) method where the Poisson equation is solved on a grid using fast grid solvers. This requires to impose boundary conditions or to assume periodicity. An important difference is that fast grid solvers are much faster than fast multipole solvers. We here combine these two approaches by taking the advantages of each one and, eventually, we obtain an efficient VIC-PFM method to solve incompressible flows in open domain. The major interest of this combination is its computational efficiency: compared to the PFM solver used alone, the VIC-PFM combination is 15 to 20 times faster. The second major advantage is the possibility to run Large Eddy Simulations (LES) at high Reynolds number. Indeed, as a part of the operations are done in an Eulerian way (i.e. on the VIC grid), all the existing subgrid scale (SGS) models used in classical Eulerian codes, including the recent "multiscale" models, can be easily implemented.

This thesis is concerned with the numerical simulation of high Reynolds number, three-dimensional, incompressible flows in open domains. Many problems treated in Computational Fluid Dynamics (CFD) occur in free space: e.g., external aerodynamics past vehicles, bluff bodies or aircraft; shear flows such as shear layers or jets. In observing all these flows, we can remark that they are often unsteady, appear chaotic with the presence of a large range of eddies, and are mainly dominated by convection. For years, it was shown that Lagrangian Vortex Element Methods (VEM) are particularly well appropriate for simulating such flows. In VEM, two approaches are classically used for solving the Poisson equation. The first one is the Biot-Savart approach where the Poisson equation is solved using the Green's function approach. The unbounded domain is thus implicitly taken into account. In that case, Parallel Fast Multipole (PFM) solvers are usually used. The second approach is the Vortex-In-Cell (VIC) method where the Poisson equation is solved on a grid using fast grid solvers. This requires to impose boundary conditions or to assume periodicity. An important difference is that fast grid solvers are much faster than fast multipole solvers. We here combine these two approaches by taking the advantages of each one and, eventually, we obtain an efficient VIC-PFM method to solve incompressible flows in open domain. The major interest of this combination is its computational efficiency: compared to the PFM solver used alone, the VIC-PFM combination is 15 to 20 times faster. The second major advantage is the possibility to run Large Eddy Simulations (LES) at high Reynolds number. Indeed, as a part of the operations are done in an Eulerian way (i.e. on the VIC grid), all the existing subgrid scale (SGS) models used in classical Eulerian codes, including the recent "multiscale" models, can be easily implemented.

A new version of the Deforming-Spatial-Domain/Stabilized Space--Time (DSD/SST) formulation of incompressible flows has been introduced recently to have additional subgrid-scale representation features. This is the space--time version of the residual-based variational multiscale (VMS) method. The new version is called DSD/SST-VMST (i.e. the version with the VMS turbulence model) and also Space--Time VMS (ST-VMS). The thesis starts with a brief overview of the ST-VMS method. It continues with a comprehensive set of test computations with 3D airfoil geometries at high Reynolds numbers and comparison with experimental data. The thesis shows that the test computations signal a promising future for the ST-VMS method.

A new version of the Deforming-Spatial-Domain/Stabilized Space--Time (DSD/SST) formulation of incompressible flows has been introduced recently to have additional subgrid-scale representation features. This is the space--time version of the residual-based variational multiscale (VMS) method. The new version is called DSD/SST-VMST (i.e. the version with the VMS turbulence model) and also Space--Time VMS (ST-VMS). The thesis starts with a brief overview of the ST-VMS method. It continues with a comprehensive set of test computations with 3D airfoil geometries at high Reynolds numbers and comparison with experimental data. The thesis shows that the test computations signal a promising future for the ST-VMS method.