Goal oriented mesh adaptation using total derivative of aerodynamic functions with respect to mesh coordinates – With applications to Euler flows

Peter, Jacques; Nguyen-Dinh, Maxime; Trontin, Pierre

doi:10.1016/j.compfluid.2012.06.016

Cited by 16 publications

(19 citation statements)

References 50 publications

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“…The adjoint capability of the elsA software [5] [6] has been used to compute the gradient of aerodynamic coefficients with respect to all design variables. It is capable to solve the discrete adjoint equations of either the Euler or RANS equation, with frozen eddy viscosity assumption (more robust) or with the complete linearisation of the Spalart-Allmaras turbulence model.…”

Section: Adjoint Solvermentioning

confidence: 99%

Gradient-Based Aerodynamic Optimization with the elsA Software

Carrier¹,

Destarac²,

Dumont³

et al. 2014

52nd Aerospace Sciences Meeting

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This paper describes the work performed by ONERA and Airbus to solve several aerodynamic optimization problems proposed in 2013 by the AIAA Optimization Discussion Group (ADODG). Three of the four test cases defined by this group have been addressed, respectively a 2D invicid, non-lifting, transonic airfoil optimization problem, a 2D RANS transonic airfoil optimization problem and a 3D RANS transonic wing optimization problem. All three problems have been investigated using local, gradient-based, optimization techniques and the elsA[1][2] CFD software and its adjoint capability. Through these three optimization exercises, several generic issues introduced by aerodynamic gradient-based optimization have been investigated. Among the investigated aspects are the impact of the geometry parameterization (nature and dimension), of the accuracy of the gradient calculation method, optimization algorithm and presence of constraints in the optimization problem. NomenclatureC p = pressure coefficient CD = total drag coefficient CDp = pressure drag coefficient CDf = friction drag coefficient CDw = wave drag coefficient CDvp = viscous pressure drag coefficient CL = lift coefficient CM = pitching moment coefficient c ref = chord reference d.c. = drag counts (0.0001) Ma = Mach number Re = Reynolds number AoA = Angle of attack f = objective function g = inequality constraint 1

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Section: Adjoint Solvermentioning

confidence: 99%

Gradient-Based Aerodynamic Optimization with the elsA Software

Carrier¹,

Destarac²,

Dumont³

et al. 2014

52nd Aerospace Sciences Meeting

Self Cite

View full text Add to dashboard Cite

show abstract

“…mesh nodes is detailed. The derivation follows the papers of Peter et al and Nguyen‐Dinh et al . The refinement indicator is presented as well.…”

Section: Projected Total Derivative Of the Functional Output With Resmentioning

confidence: 99%

“…Namely, ( d J / d X ) = d J / d X − ( d J / d X · n )· n if the node is on the support of J , walls, farfield (or mesh block) borders; ( d J / d X ) = 0 if the node is on a corner of the support of J or on a corner of farfield (or mesh block) domain, while ( d J / d X ) = d J / d X elsewhere. In this paper, the θ ‐criterion introduced by Peter et al and Nguyen‐Dinh et al will be exploited. This indicator follows directly from the second term of the right‐hand side of relation (), and it reads as follows:

θ (i, j) = (∥∥, sans-serif P ((), \frac{d J}{d bold-italicX})) \frac{h_{i, j}}{2} .

The presence of h i , j in the refinement indicator is important in situations where large vector of ( d J / d X ) is encountered in a mesh that is already fine.…”

Section: Projected Total Derivative Of the Functional Output With Resmentioning

confidence: 99%

“…Concerning finite volume, the major reference is the Venditti and Darmofal method . A list of main applications involving the latter method can be found in .…”

Section: Introductionmentioning

confidence: 99%

“…mesh nodal coordinates in a finite‐volume‐structured grid framework for RANS flow. The method principles have been already introduced by Peter et al and Nguyen‐Dinh et al with applications to Euler flows. In contrast to the Venditti and Darmofal method that requires two levels of meshes, the proposed method is based on a scalar indicator for one mesh level only.…”

Section: Introductionmentioning

confidence: 99%

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Mono‐block and non‐matching multi‐block structured mesh adaptation based on aerodynamic functional total derivatives for RANS flow

Resmini

Peter

Lucor

2016

Numerical Methods in Fluids

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Summary An enhanced goal‐oriented mesh adaptation method is presented based on aerodynamic functional total derivatives with respect to mesh nodes in a Reynolds‐Averaged Navier‐Stokes (RANS) finite‐volume mono‐block and non‐matching multi‐block‐structured grid framework. This method falls under the category of methods involving the adjoint vector of the function of interest. The contribution of a Spalart–Allmaras turbulence model is taken into account through its linearization. Meshes are adapted accordingly to the proposed indicator. Applications to 2D RANS flow about a RAE2822 airfoil in transonic, and detached subsonic conditions are presented for the drag coefficient estimation. The asset of the proposed method is patent. The obtained 2D anisotropic mono‐block mesh well captures flow features as well as global aerodynamic functionals. Interestingly, the constraints imposed by structured grids may be relaxed by the use of non‐matching multi‐block approach that limits the outward propagation of local mesh refinement through all of the computational domain. The proposed method also leads to accurate results for these multi‐block meshes but at a fraction of the cost. Finally, the method is also successfully applied to a more complex geometry, namely, a mono‐block mesh in a 3D RANS transonic flow about an M6 wing. Copyright © 2016 John Wiley & Sons, Ltd.

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Sequential feature‐based mesh movement and adjoint error‐based mesh refinement

Vivarelli

Qin

Shahpar

et al. 2020

Numerical Methods in Fluids

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Nowadays, aerodynamic computational modeling is carried out on a daily basis in an industrial setting. This is done with the aim of predicting the performance and flow characteristics of new components. However, limited resources in terms of time and hardware force the engineer to employ relatively coarse computational grids, thus achieving results with variable degree of inaccuracy. In this article, a novel combination of feature and adjoint-based mesh adaptation methods is investigated and applied to typical three-dimensional turbomachinery cases, such as compressor and fan blades. The proposed process starts by employing feature-based mesh movement to improve the global flow solution and then adjoint refinement to tune the mesh for each quantity of interest. Comparison of this process with one utilizing only the adjoint refinement procedure shows significant benefits in terms of accuracy of the performance quantity.

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Goal oriented mesh adaptation using total derivative of aerodynamic functions with respect to mesh coordinates – With applications to Euler flows

Cited by 16 publications

References 50 publications

Gradient-Based Aerodynamic Optimization with the elsA Software

Gradient-Based Aerodynamic Optimization with the elsA Software

Mono‐block and non‐matching multi‐block structured mesh adaptation based on aerodynamic functional total derivatives for RANS flow

Sequential feature‐based mesh movement and adjoint error‐based mesh refinement

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