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This paper concerns the large-scale separation flow control over an airfoil using a synthetic jet (SJ). The flow is simulated by solving unsteady Reynolds averaged Navier-Stokes (URANS) equations w...

This paper presents the recent developments in hierarchical genetic algorithms (HGAs) to speed up the optimization of aerodynamic shapes. It first introduces HGAs, a particular instance of parallel GAs based on the notion of interconnected sub-populations evolving independently. Previous studies have shown the advantages of introducing a multi-layered hierarchical topology in parallel GAs. Such a topology allows the use of multiple models for optimization problems, and shows that it is possible to mix fast low-fidelity models for exploration and expensive high-fidelity models for exploitation. Finally, a new class of multi-objective optimizers mixing HGAs and Nash Game Theory is defined. These methods are tested for solving design optimization problems in aerodynamics. A parallel version of this approach running a cluster of PCs demonstrate the convergence speed up on an inverse nozzle problem and a high-lift problem for a multiple element airfoil.

This article is concerned with the numerical solution of multiobjective control problems associated with nonlinear partial differential equations and more precisely the Burgers equation. For this kind of problems, we look for the Nash equilibrium, which is the solution to a noncooperative game. To compute the solution of the problem, we use a combination of finite-difference methods for the time discretization, finite-element methods for the space discretization, and a quasi-Newton BFGS algorithm for the iterative solution of the discrete control problem. Finally, we apply the above methodology to the solution of several tests problems. To be able to compare our results with existing results in the literature, we discuss first a single-objective control problem, already investigated by other authors. Finally, we discuss the multiobjective case.

This article is concerned with the numerical solution of multiobjective control problems associated with linear partial differential equations. More precisely, for such problems, we look for the Nash equilibrium, which is the solution to a noncooperative game. First, we study the continuous case. Then, to compute the solution of the problem, we combine finite-difference methods for the time discretization, finite-element methods for the space discretization, and conjugate-gradient algorithms for the iterative solution of the discrete control problems. Finally, we apply the above methodology to the solution of several tests problems.

In this article we investigate computational methods for the control and stabilization of systems modeled by parabolic equations of the advection-reaction-difTusion type and by the Navier-Stokes equations for incompressible viscous fluids. For the first class of control problems wc shall discuss open loop control methods and closed loop methods a la Riccati. Concerning the second class of problems we shall consider the Dirichlet boundary control of low around cylinders and attempt to reduce the viscous drag. The results of numerical experiments will validate the computational methods described in this article.

CFD played a critical role as design tool in the 1970-80s in French laboratories and aeronautical industries with the rapid progress of computing facilities. Three short contributions by senior scientists and technologists describe how CFD developed rapidly in the French scientific and industrial community and was recognized as a mature tool in aerospace engineering for the aerodynamic design of civil and military aircraft and space vehicles like the European HERMES Space plane.

International audience; The industry requires innovative technologies to support the numeric design and simulation of manufactured products in order to reduce time to market delays and improve the performance of the products and the efficiency of the industries in the global competitive market. Innovation also requires advanced tools to support the design of new products. For example, remote teams are working collaboratively on the preliminary design of future aircraft that will be “safer, quieter, cleaner”, and environmentally friendly by 2020. The automotive industry has similar concerns. The telecom industries (e.g., mobile phones design) and nuclear power plant design face large-scale multi-physics simulation and optimization challenges. This paper suggests that distributed workflows running on computational grids are adequate to support their application needs.

In these few pages, we have attempt to describe the main trenbds of our multigrid research program. The adaptative MG method is already an efficient 2-D solver, which in several cases is twice as faster as an implicit time-stepping previously derived [12]. The agglomerating MG method is still in an experimental phase but seems very promising.

New parallel hierarchical multi -objective optimization approaches based on Genetic Algorithms (GAs) with Nash scenarios of Game Theory are i nvestigated for solving high lift multi -element airfoil design problems in Aerodynamics on distributed parallel enviro nments. High lift devices from a multi -element airfoil system evolving in a complex viscous flow at low Mach number conditions are still critical challenges for modern aircraft design. A multi -objective optimization methodology presented here relies on b inary coded Genetic Algorithms (GAs) and coupled with Game Strategies (GS). The design variables of such optimization problems are split between se veral players, the global multi -criterion optimization pro blem being replaced by several sub optimizations o perating in the decomposed search space. The viscous flow around the multi -element system is sim ulated with a non-expensive but non-differentiable CFD solver coupling a panel approach with the vi scous effects modeled by laminar or turbulent boun dary layers and wakes. Two problems solved in this paper, for shape/position optimization, are: a) Inverse problem which consist in retrieving a target pressure distrib ution, b) Lift optimization prob lem which consist in maximizing the lift of a multi -element airfoil. N umerical results show that hierarchical GAs combined with Nash strategy are more efficient and robust than simple GAs, not only for reconstruction pro blems, but also for multidisciplinar y optimiz ation problems in aerodynamic design

This paper presents the discussion and comparison of the different optimization strategies and their associated evolutionary tools for the multi-point design optimization of a multi-element airfoil system during landing and taking off operations of an aircraft. New optimization algorithms based on binary coded genetic algorithms (GAs) coupling with game theory, such as Nash GAs (N-GAs) and Stackelberg GAs (S-GAs), are introduced and implemented to optimize the position of slat and flap of a high lift system operating simultaneous at taking off and landing conditions. A cheap nondifferentiable CFD solver coupling an inviscid panel approach with laminar or turbulent boundary layers and wake is used to solve the flow field around this system. Numerical results are compared with different strategies which demonstrates the flexible capability and robustness of such algorithms for multi-objective and multidisciplinary optimization problems in aerodynamics.

This paper presents a multi-objective evolutionary optimization method combining Genetic Algorithms (GAs) and Game Theory (GT) for high lift multi-airfoil systems in Aerospace Engineering. GAs are IT based evolutionary methods introduced by J.H. Holland for mimicking natural adaptation systems in the computer. Due to large dimension global optimization problems and the increasing importance of low cost distributed parallel environments it is a natural idea to replace a global optimization by decentralized local sub-optimizations using GT which introduces the notion of games associated to an optimization problem. This GT/GAs combined optimization method is developed in this paper and used for reconstruction and optimization problems applied to high lift multi-airfoil design. Numerical results obtained with this new approach are compared favorably with single global GAs’ ones and illustrate the promising robustness and efficient parallel properties of coupled GAs with different game scenarios for future advanced multidisciplinary aerospace technologies.

Over the last three decades, Prof. Satofuka made many important contributions to Computational Fluid Dynamics (CFD). In this article, after a brief introduction, some of his work will be discussed, and a complete list of his publications (through December 1999) is included for the record.

The problem of finding an optimal, smooth, convex, blunt body shape having minimum integral convective heat flux for 2D laminar supersonic viscous gas flow for large Reynolds number under condition, that the equilibrium temperature of the body surface does not exceed the preassigned limit value, is considered. This heat-flux optimal-shape-design problem is solved by means of the asynchrone parallel floating-point genetic algorithms via calculation of the heat-flux distribution along the body surface in the framework of 2D boundary layer theory. As a test task, the inverse problem that consists in finding the body shape that realizes target heat-flux distribution for given flow condition was considered. The influence of the number of processors on the algorithm properties was investigated.

Communication takes a significant amount of elapsed execution time in parallel CFD. Recent studies showed that the high communication rates in most parallel CFD algorithms is necessary only for maintaining the stability of numerical integration but not for solving the CFD problem. Once the stability can be achieved by using filtering techniques, a reduction of communication rate can significantly reduce the elapsed execution time. This study is to determine the optimal communication rates for all interfaces between parallel processes during the execution of parallel CFD. The objective is to minimize the overall elapsed program execution time. How communication rates affect the elapsed execution time for parallel CFD applications was first investigated. Experiments demonstrated that the selection of communication rates based on human intuition is very difficult and unreliable. Since the search of optimal communication rate in parallel CFD is an NP-hard problem, genetic algorithms were adopted for finding the sub-optimal solutions. An automatic on-line optimization process for the selection of the optimal communication rate was developed.

The following sections contain the different contributions from the ECARP consortium to the resolution of the workshop test cases defined in section II. Each contribution contains a theoretical description of the optimization technique used by each partner and the results obtained by using this techniques for the resolution of some test cases.

The laminar flow past ellipsoidal shapes, see figure 1, was chosen most often as test case, and more than 20 groups have presented results for such flows at the Antibes workshop. The present attempt to evaluate the different computational contributions for cold hypersonic flows is based on the contributions to the proceedings, and, in particular, on those numerical data which were provided in discrete form by contributors to the first author. Seventeen contributions have been received associated with test case 6.1: eight of these contributions deal with two-dimensional flows only (6.1-1 to 6.1-4) and four are only for three-dimensional simulations (6.1-5 to 6.1-8), see table 1. The request for field data was not followed, in general, so that wall values are used for comparison purpose.

In this paper we address the problem of solving the compressible Navier Stokes equations. The development of space programs in Europe and the U.S. has generated renewed interest in aerodynamic ~ aerothermal design. Significant progress has been made recently in the Finite Element solutions of the Euler equations or their coupling with species convection equations for reactive flows and the difficulties associated mainly accurate and stable shock capturing capabilities are well known. When solving the Navier Stokes equations, additionnal features have to he computed: a precise representation of the houndary layer yielding pressure, skin friction and heat transfer coefficients is required along with recirculation, vortex, wake and shock interaction structures. This is critical for a number of aerospace applications dealing with strongly separated flows, including the simulation of flight at high angle of attack or the evaluation of the efficiency of body flaps. We will outline two Finite Element methodologies coupled with mesh adaptation that are being developed to accurately capture those features. One is based on a Galerkin Least-square formulation which brings good stability properties and makes this approach especially attractive for high Mach number calculations (space applications). The other one relies on accurate centered space discretbation and makes use of compatible finite element approximation and is advocated for aerodynamic shape design at subsonic and transonic regimes(aircraft application). For both methods, the grid quality control is still a major open problem even in the context of triangular Finite Element unstructured meshes; in order to capture the essential features of the flow, the mesh has to take into account not only the geometry hut also he fine enough in those regions where the solution needs accuracy. The mesh adaption used in this paper relies on refinement and node movement procedures provided by physical or geometrical criteria. Numerical flow simulation around reference simplified 2D geometries and 3D industrial computations originating from aircraft aerospace applications are presented for the development and validation of the above methodologies.

Solutions of elliptic boundary value problems are obtained with variational formulations by minimization of functionals. Conventional tools of the finite element strategy are emphasized; linear or quadratic approximations on triangular elements, curved iso-parametric elements, Ni shape funtions, Li homogeneous co-ordinates. High speed of computation of the final assembled matrices require the use of the Formal–FORMAC calculus. Illusrations of the finite element method are chosen in the class of the 2d–3d compressible subsonic irrotational flows in a nozzle and around one or several lifting bodies of arbitary shape.

One of the simplest deterministic mathematical model for the spread of an epidemic disease is the so-called SI system made of two Ordinary Differential Equations. It exhibits simple dynamics: a bifurcation parameter \(\mathscr {T}_0\) yielding persistence of the disease when \(\mathscr {T}_0 > 1\), else extinction occurs. A natural question is whether this gentle dynamic can be disturbed by spatial diffusion. It is straightforward to check it is not feasible for linear/nonlinear diffusions. When cross diffusion is introduced for suitable choices of the parameter data set this persistent state of the ODE model system becomes linearly unstable for the resulting initial and no-flux boundary value problem. On the other hand “natural” weak solutions can be defined for this initial and no-flux boundary value problem and proved to exist provided nonlinear and cross diffusivities satisfy some constraints. These constraints are not fully met for the parameter data set yielding instability. A remaining open question is: to which solutions does this apply? Periodic behaviors are observed for a suitable range of cross diffusivities.

In this paper we present a noncooperative game theoretical model for the well known problem of experimental design. A virtual player decides the design variables of an experiment and all the players solve a Nash equilibrium problem by optimizing suitable payoff functions. We consider the case where the design variables are the coordinates of n points in a region of the plane and we look for the optimal configuration of the points under some constraints. Arising from a concrete situation, concerning the ARGO-YBJ experiments, the goal is to find the optimal configuration of the detector, consisting of a single layer of resistive plate counters. Theoretical and computational results are presented for this location problem.

chapitre 7; Level set methods have recently gained much popularity to capture discontinuities, including their possible propagation. In this contribution we present a finite element approach for solving the governing equations of level set methods. After a review of the governing equations, the initialisation of the level sets, the discretisation on a finite domain and the stabilisation of the resulting finite element method will be discussed. Special attention will be given to the proper treatment of the internal boundary condition, which is achieved by exploiting the partition-of-unity property of finite element shape functions.

In this work a mathematical model for mono dimensional, two-phase, bubbly flow, is presented. The mathematical model consists of the motion equations (i.e. mass, momentum and energy balance equation) for each phase, obtained applying a suitable phase-average procedure. Such motion equations determine the evolution of the homogenized hydrodynamic variables and contain both the inter phase interaction terms and the dispersive terms too. The latter terms are usually calculated by means of closure relations or even neglected. In this work, introducing a suitable description for the local perturbation induced by the bubbles on the liquid phase motion, the inter phase momentum exchange terms are analytically calculated. Numerical simulations are performed in order to simulate an experimental case of water hammer. The agreement is good, although further work is needed on both dissipative and mass exchange terms.

Interface boundary conditions are the key ingredient to design efficient domain decomposition methods. However, convergence cannot be obtained for any method in a number of iterations less than the number of subdomains minus one in the case of a one-way splitting. This optimal convergence can be obtained with generalized Robin type boundary conditions associated with an operator equal to the Schur complement of the outer domain. Since the Schur complement is too expensive to compute exactly, a new approach based on the computation of the exact Schur complement for a small patch around each interface node is presented for the two-Lagrange multiplier FETI method.

Unsteady turbulent transonic flows over oscillating airfoils are investigated by using a novel third-order accurate scheme on block-structured meshes. Two turbulence models ( algebraic and two-transport equation models) are studied in order to generate flow fields in agreement with experimental data. Numerical results are presented for 2-D problems related to helicopter rotors in forward flight, including shock-stall phenomena. The advantages of using a high-order accurate method and a suitable turbulence model for this kind of applications are demonstrated.

Publisher Summary Air quality models (AQMs) play a fundamental role in forecasting air pollution phenomena and are an important tool in the development of control strategies for reducing the damaging effects of heavy concentrations of pollutants. The space and time scales for an effective simulation of air pollution problems on urban, regional, or global domains, and the wide range of chemical–physical phenomena included in AQMs require very powerful computational resources. Therefore, the development of efficient parallel software for AQMs is an active research field. The choice of the numerical solution method for the problem is driven by several considerations. The most widely used computational approach for the solution to the problem is based on splitting techniques. Two basic splitting approaches can be identified—that is, physical and dimensional splitting. The vertical turbulent diffusion and chemical kinetics are usually coupled because they have similar time scales, especially for highly turbulent wind fields. In a parallel distributed-memory environment, the dimensional splitting does not seem to be very effective, in terms of efficiency and scalability.