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We consider the gradient method applied to the optimal control of a system for which each simulation is expensive. A method for increasing the number of unknowns, and relying on multilevel ideas is tested for the academic problem of shape optimization of a nozzle in a subsonic or transonic Euler flow.

To propose an integrated algorithm for aerodynamic shape optimization of aircraft wings under the effect of aeroelastic deformations at supersonic regime.

A methodology is proposed in which a high‐fidelity aeroelastic analyser and an aerodynamic optimizer are loosely coupled. The shape optimizer is based on a “CAD‐free” approach and an exact gradient method with a single adjoint state. The global iterative process yields optimal shapes in the at‐rest condition (i.e. with the aeroelastic deformations substracted).

The methodology was tested under different conditions, taking into account a combined optimization goal: to reduce the sonic boom production, while preserving the aerodynamic performances of flexible wings. The objective function model contains both aerodynamic parameters and an acoustic term based on the sonic boom downwards emission.

This paper proposes a shape optimization methodology developed by researchers but aiming at the final strategic goal of creating tools that can be really integrated in design processes.

The paper presents an original loosely coupled method for the shape optimization of flexible wings in which recent and modern techniques are used at different levels of the global algorithm: the aerodynamic optimizer, the aeroelastic analyser, the shape parametrization and the objective function model.

Two numerical methods, based on high order finite volume formulations and upwind schemes, are used to compute the two‐ and three‐dimensional flow field in a transonic nozzle. The influence of numerical diffusivity, boundary treatment and mesh structure is explored for inviscid and turbulent configurations. First order computations provide significantly different inviscid results. However, high order methods lead to similar solutions. An explanation of the error generated through the shockwave is proposed in this case. The two‐dimensional interaction of the shock with the thin turbulent boundary layer developing on the bump wall is also presented. Good agreement between both approaches is obtained considering the rapid thickening of the boundary layer due to the shock. Furthermore, the downstream velocity recovery is almost identical. Only slight discrepancies occur in the main flow, near the outer edge of the boundary layer. These seem to be related to the way the turbulence model deals with the free stream turbulence. Finally, preliminary three‐dimensional unstructured turbulent results are presented and discussed.

The purpose of this paper is to compare the efficiency of four different algorithmic parallelization methods for inverse shape design flow problems.

The included algorithms are: a parallelized differential evolution algorithm; island‐model differential evolution with multiple subpopulations; Nash differential evolution with geometry decomposition using competitive Nash games; and the new Global Nash Game Coalition Algorithm (GNGCA) which combines domain and geometry decomposition into a “distributed one‐shot” method. The methods are compared using selected academic reconstruction problems using a different number of simultaneous processes.

The results demonstrate that the geometry decomposition approach can be used to improve algorithmic convergence. Additional improvements were achieved using the novel distributed one‐shot method.

This paper is a part of series of articles involving the GNGCA method. Further tests implemented for more complex problems are needed to study the efficiency of the approaches in more realistic cases.

We investigate the application of a least squares finite element method for the solution of fluid flow problems. The least squares finite element method is based on the minimization of the L2 norm of the equation residuals. Upon discretization, the formulation results in a symmetric, positive definite matrix system which enables efficient iterative solvers to be used. The other motivations behind the development of least squares finite element methods are the applicability of higher order elements and the possibility of using the norm associated to the least squares functional for error estimation. For steady incompressible flows, we develop a method employing linear and quadratic triangular elements and compare their respective accuracy. For steady compressible flows, an implicit conservative least squares scheme which can capture shocks without the addition of artificial viscosity is proposed. A refinement strategy based upon the use of the least squares residuals is developed and several numerical examples are used to illustrate the capabilities of the method when implemented on unstructured triangular meshes.

An optimized multigrid method (NSFLEX‐MG) for the NSFLEX‐code (Navier‐Stokes solver using characteristic flux extrapolation) of MBB (Messerschmitt Bolkow Blohm GmbH) is described. The method is based on a correction scheme and implicit relaxation procedures and is applied to two‐dimensional test cases. The principal feature of the flow solver is a Godunov‐type averaging procedure based on the eigenvalues analysis of the Euler equations by means of which the inviscid fluxes are evaluated at the finite volume faces. Viscous fluxes are centrally differenced at each cell face. The performance of NSFLEX‐MG is demonstrated for a large range of Mach numbers for compressible inviscid and viscous (laminar and turbulent) flows over a RAE‐2822 airfoil and over a NACA‐0012 airfoil.

The optimization and tradeoff of cost-time-quality-risk in one dimension and this four-dimensional problem in ambiguous mode and risk can be neither predicted nor estimated. This study aims to solve this problem and rank fuzzy numbers using an innovative algorithm “STHD” and a special technique “radius of gyration” (ROG) for fuzzy answers, respectively.

First, it is the optimization of a fully fuzzy four-dimensional problem which has never been dealt with in regard to risk in ambiguous mode and complexities. Therefore, the risk is a parameter which has been examined neither in probability and estimableness mode nor in the ambiguous mode so far. Second, it is a fully fuzzy tradeoff which, based on the principle of incompatibility “Zadeh, 1973”, proposes that when the complexity of a system surpasses the limited point, it becomes impossible to define the performance of that system accurately, precisely and meaningfully. The authors believe that this principle is the source of fuzzy logic. Third, for calculating and ranking fuzzy numbers of answers, a special technique for fuzzy numbers has been used. Fourth, For the sake of ease, precision and efficiency, an innovative algorithm called the technique of hunting dolphins “STHD” has been used. Finally, the problem is very close to reality. By applying risk in ambiguous mode, the problem has been realistically looked at.

The results showed that the algorithm was highly robust, with its performance depending very little on the regulation of the parameters. Ranking fuzzy numbers using the ROG indicated the flexibility of fuzzy logic, and it was also determined that the most appropriate regulations were to ensure low time, risk and cost but maximum quality in calculations, which were produced non-uniformly based on the levels of Pareto answers.

The ROG and Chanas Fuzzy Critical Path Method as developed by other researchers have been used. Despite the increase in limitations, parameters can develop. The originality of this study with regard to evaluating the results of tradeoff combinatorial optimization is upon decision-making which has a special and highly strategic role in the fate of the project, with the research been conducted with a special approach and different tools in a fully fuzzy environment.

An adaptive grid solution method is described for computing the time accurate solution of an unsteady flow problem. The solution method consists of three parts: a grid point redistribution method; an unsteady Euler equation solver; and a temporal coupling routine that links the dynamic grid to the flow solver. The grid movement technique is a direct curve by curve method containing grid controls that generate a smooth grid that resolves the severe solution gradients and the sharp transitions in the solution gradients. By design, the temporal coupling procedure provides a grid that does not lag the solution in time. The adaptive solution method is tested by computing the unsteady inviscid solutions for a one‐dimensional shock tube and a two‐dimensional shock vortex interaction. Quantitative comparisons are made between the adaptive solutions, theoretical solutions and numerical solutions computed on stationary grids. Test results demonstrate the good temporal tracking of the solution by the adaptive grid, and the ability of the adaptive method to capture an unsteady solution of comparable accuracy to that computed on a stationary grid containing significantly more grid points than used in the adaptive grid.

This paper aims to propose a gradient-based shape optimization framework in which traditional time-consuming conversions between computer-aided design and computer-aided engineering and the mesh update procedure are avoided/eliminated. The scheme is general so that it can be used in all cases as a black box, no matter what the objective and/or design variables are, whilst the efficiency and accuracy are guaranteed.

The authors integrated CAD and CAE by using isogeometric analysis (IGA), enabling the present methodology to be robust and accurate. To overcome the difficulty in evaluating the sensitivities of objective and/or constraint functions by analytic method in some cases, the authors adopt the finite difference method to calculate these sensitivities, thereby providing a universal approach. Moreover, to further eliminate the inefficiency caused by the finite difference method, the authors advance the exact reanalysis method, the indirect factorization updating (IFU), to exactly and efficiently calculate functions and their sensitivities, which guarantees its generality and efficiency at the same time.

The proposed isogeometric gradient-based shape optimization using our IFU approach is reliable and accurate, as well as general and efficient.

The authors proposed a gradient-based shape optimization framework in which they first integrate IGA and the proposed exact reanalysis method for applicability to structural response and sensitivity analysis.

An upwind unstructured grid cell‐centred scheme for the solution of the compressible Euler and Navier‐Stokes equations in two dimensions is presented. The algorithm employs a finite volume formulation. Calculation of the inviscid fluxes is based on the approximate Riemann solver of Roe. Viscous fluxes are obtained from solution gradients computed by a variational recovery procedure. Higher order accuracy is achieved through performing a monotonic linear reconstruction of the solution over each cell. The steady state is obtained by a point implicit time integration of the unsteady equations using local time stepping. For supersonic inviscid flow an alternative space marching algorithm is proposed. This latter approach is applicable to supersonic flow fields containing regions of local subsonic flow. Numerical results are presented to show the performance of the proposed scheme for inviscid and viscous flows.