Aircraft conceptual optimization using simulated evolution

Crispin, Yechiel

doi:10.2514/6.1994-92

Cited by 21 publications

(8 citation statements)

References 2 publications

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“…However, to describe the low order discrete adjoint approach used in this work, it is neccesary to brie y expose the speci c numerical method used to obtain the solution of the turbulent equations (1). This is a stabilized Finite-Element OSS-type implicit method (see 38] for details), which can be written as: Given u n , nd (u n+1 p n+1 n+1 n+1 ) i n V Q Ṽ Ṽ such that 1 t (u n+1 i ; u n v) + ( u n+ i;1 r u n+ i v) +(2 "(u n+ i ) rv) + ( rp n+1 i;1 v) + ( u n+ i;1 r u n+ i ; n+ i;1 u n+ i;1 r v) = 0 (8) t(rp n+1 i ; r p n+1 i;1 rq)+ ( (rp n+1 i ; n+1 i;1 ) rq) = ;(r u n+1 i q ) (9) ( n+ i ṽ) = ( u n+ i r u n+ i ṽ) (10) is the trapezoidal rule parameter for time discretization which was taken equal to one (only the steady state solution is interesting for the objectives of this work).The superscripts n and i refer to the time step and to the iteration counter into a given time step, respectively. is the intrinsic time or elemental stabilizing parameter, which is the same critical local time step (see 38] for details).…”

Section: Flow Solutionmentioning

confidence: 99%

A mixed adjoint formulation for incompressible turbulent problems

Soto

Loehner²

2002

40th AIAA Aerospace Sciences Meeting &Amp; Exhibit

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A design methodology based on a mixed adjoint a p p r o a c h for ow problems governed by the Incompressible Turbulent N a vier Stokes equations is deduced and tested. The main feature of the algorithm is that instead of solving an exact discrete adjoint equation, it solves a fastconverging low-order adjoint formulation, saving an important amount of CPU time, and giving a smoothed approximation to the real gradient. It has been shown that this type of smoothed gradients is very convenient to avoid possible diverging cycles in the whole design process, and to reduce the total optimization cost. The boundary conditions for the discrete adjoint f o r m ulation are inferred at the continuous level. In this way, the formulation is mixed. Furthermore, the methodology is general in the sense that it does not depend on the geometry representation, and all the gridpoints on the surface to be optimized can be chosen as design parameters. The partial derivatives of the ow equations with respect to the mesh movements are computed by nite di erences. Hence, this computation is independent of the numerical scheme employed to obtain the ow solution and of the mesh type. Once the sensitivities and the direction of movement h a ve been computed, the new solid surface is obtained with an improved pseudo-shell approach i n s u c h a way that local singularities, which can degrade or inhibit the convergence to the optimal solution, are avoided. Moreover, this surface parametrization allows to impose geometrical restrictions in a very easy manner. The volume mesh is updated to x the new boundary using an innovative l e v el approach for the highly stretched elements close to the solid boundary (boundary layer mesh), and a quasi-incompressible elastic movement scheme for the rest of them. Such t ype of combined mesh movement a lgorithm allows to compute the sensitivity c o n tribution of the interior mesh points by using nite di erences in a very fast manner, and avoids expensive remeshing procedures during the whole design process. The method-ologies can deal with multi-objective function problems. Some numerical examples are presented to demonstrate the methodology behaviour.

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Section: Flow Solutionmentioning

confidence: 99%

A mixed adjoint formulation for incompressible turbulent problems

Soto

Loehner²

2002

40th AIAA Aerospace Sciences Meeting &Amp; Exhibit

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“…The classical GA can handle bounds (boundary constraints) on the design variables, but it is not inherently capable of handling equality or inequality constraint functions 21 . Previous implementations of the GA have involved problems posed in such a way as to eliminate constraint functions, or to penalize the cost function when a constraint is violated.…”

Section: Genetic Algorithms and Constraintsmentioning

confidence: 99%

Three-dimensional aerodynamic shape optimization using genetic evolution and gradient search algorithms

Foster

Dulikravich

Bowles

1996

34th Aerospace Sciences Meeting and Exhibit

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“…On the other hand, GAs are able to generate Pareto fronts in a single optimization run by improving the objective functions simultaneously and independently [15]. Firstly, GAs was studied by Gage and Kroo [16] and Crispin [17] for aerodynamic shape optimization problems. Quagliarella and Cioppa [18] applied GAs to find shockless airfoils while Crossley and Laananen [19] used them for helicopter design.…”

Section: Introductionmentioning

confidence: 99%