A stabilized pseudo-shell approach for surface parametrization in CFD design problems

Soto, Orlando; Löhner, Rainlad; Yang, Chuanghuang

doi:10.1002/cnm.490.abs

Cited by 3 publications

(7 citation statements)

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“…Proposed methods for the latter usually involve mesh morphing, e.g. via a pseudo-shell approach or free-form deformation [26][27][28]. From the industrial point of view, the most promising method of shape update probably relies on a mapping of the sensitivities onto a CAD parametrization of the geometry, as proposed in [29].…”

Section: Discussionmentioning

confidence: 99%

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A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows

Othmer

2008

Numerical Methods in Fluids

291

224

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SUMMARYTopology optimization of fluid dynamic systems is a comparatively young optimal design technique. Its central ingredient is the computation of topological sensitivity maps. Whereas, for finite element solvers, implementations of such sensitivity maps have been accomplished in the past, this study focuses on providing this functionality within a professional finite volume computational fluid dynamics solver. On the basis of a continuous adjoint formulation, we derive the adjoint equations and the boundary conditions for typical cost functions of ducted flows and present first results for two-and three-dimensional geometries. Emphasis is placed on the versatility of our approach with respect to changes in the objective function. We further demonstrate that surface sensitivity maps can also be computed with the implemented functionality and establish their connection with topological sensitivities.

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Section: Discussionmentioning

confidence: 99%

“…The second integral of Equation (27) therefore cancels, and with p = 0 Equation (28) is identically fulfilled. The only remaining term is thus the first integral of Equation (27), which can be made to cancel by enforcing the integrand to vanish:…”

Section: Wall and Inletmentioning

confidence: 99%

A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows

Othmer

2008

Numerical Methods in Fluids

291

224

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“…In order to overcome such problems, additional smoothing approaches can be used, e.g., use of regularization methods [33][34][35]. The airfoil shape in this work is defined via a set of Catmull-Rom splines [36], which are connected to each other leading to a smooth airfoil representation.…”

Section: Projection Of the Gradients Of The Objective Functionmentioning

confidence: 99%

Optimization of Airfoils Using the Adjoint Approach and the Influence of Adjoint Turbulent Viscosity

2018

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Abstract:The adjoint approach in gradient-based optimization combined with computational fluid dynamics is commonly applied in various engineering fields. In this work, the gradients are used for the design of a two-dimensional airfoil shape, where the aim is a change in lift and drag coefficient, respectively, to a given target value. The optimizations use the unconstrained quasi-Newton method with an approximation of the Hessian. The flow field is computed with a finite-volume solver where the continuous adjoint approach is implemented. A common assumption in this approach is the use of the same turbulent viscosity in the adjoint diffusion term as for the primal flow field. The effect of this so-called "frozen turbulence" assumption is compared to the results using adjoints to the Spalart-Allmaras turbulence model. The comparison is done at a Reynolds number of Re = 2 × 10 6 for two different airfoils at different angles of attack.

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“…The main steps required for the evaluation of gradients based on adjoint variables are well known (Elliott and Peraire, 1998; Jameson, 1988, 1995; Mohammadi and Pironneau, 2001; Soto and Löhner, 2001a, b, 2002; Soto et al , 2002), and therefore only a summary is given here. A variation in the objective function I and the PDE constraint R result in: Equation 8 Equation 9 We can now introduce a Lagrange multiplier Ψ to merge these two expressions: Equation 10 After rearrangement of terms this results in: Equation 11 This implies that if we can solve: Equation 12 the variation of I is given by: Equation 13 The consequences of this rearrangement are profound:the variation of I exhibits only derivatives with respect to β , i.e.…”

Section: Gradients Via Adjoint Variablesmentioning

confidence: 99%

“…While the experiment (or stand alone CFD run) only measures the performance of the product “as is”, numerical methods can also predict the effect of changes in the shape of the product. This has led, over the last decade, to a large body of literature on optimal shape design (Anderson and Venkatakrishnan, 1997; Drela, 1998; Dreyer and Matinelli, 2001; Elliott and Peraire, 1997, 1998; Gumbert et al , 2001; Jameson, 1988, 1995; Korte et al , 1997; Kuruvila et al , 1995; Li et al , 2001; Medic et al , 1998; Mohammadi, 1997; Mohammadi and Pironneau, 2001; Nielsen and Anderson, 1998; Reuther et al , 1999; Soto and Löhner, 2001a, b, 2002; Soto et al , 2002). In order to compare the merit of different designs, a function I is defined.…”

Section: Introductionmentioning

confidence: 99%

An adjoint‐based design methodology for CFD problems

Soto

Löhner

Yang

2004

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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A complete CFD design methodology is presented. The main components of this methodology are a general edge‐based compressible/incompressible flow solver; a continuous adjoint formulation for the gradient computations; a steepest descent technique for the change of design variables; evaluation of the gradient of the discretized flow equations with respect to mesh by finite differences; a CAD‐free pseudo‐shell surface parametrization, allowing every point on the surface to be optimized to be used as a design parameter; and a level type scheme for the movement of the interior points. Several examples are included to demonstrate the methodology developed.

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A stabilized pseudo-shell approach for surface parametrization in CFD design problems

Cited by 3 publications

References 0 publications

A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows

A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows

Optimization of Airfoils Using the Adjoint Approach and the Influence of Adjoint Turbulent Viscosity

An adjoint‐based design methodology for CFD problems

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