Continuous adjoint approach to the Spalart–Allmaras turbulence model for incompressible flows

Zymaris, A.S.; Papadimitriou, Dimitrios; Giannakoglou, Kyriakos C.; Othmer, Carsten

doi:10.1016/j.compfluid.2008.12.006

Cited by 124 publications

(102 citation statements)

References 32 publications

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“…Although recently the full adjoint formulation of the Navier-Stokes equations with turbulent models has been proposed [92,93], the most common approach in literature is to freeze the turbulent viscosity obtained by the direct solver and use it in the laminar Navier-Stokes adjoint equations. Special care has to be taken when the direct turbulent model uses wall functions, since this is not seen "naturally" by the laminar adjoint equations and may lead to un-physical results.…”

Section: Optimizationmentioning

confidence: 99%

Numerical Simulation of Sailing Boats: Dynamics, FSI, and Shape Optimization

Lombardi

Parolini

Quarteroni

et al. 2012

Springer Optimization and Its Applications

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The numerical simulation of free-surface flows around sailing boats is a complex topic that addresses multiple mathematical tasks: the correct study of the flow field around a rigid hull, the numerical simulation of the hull dynamics, the deformation of the sails and appendages under transient external conditions like gusts of wind or wave patterns and, overall, the coupling among all these components. In this paper, we present some recent advances that have been achieved in different research topics related to yacht design and performance prediction. In particular, we describe the numerical algorithms that have been developed in the framework of open-source libraries for the simulation of free-surface hydrodynamics and boat dynamics, as well as for the analysis of the fluid-structure interaction between wind and sails. Moreover, an algorithm for shape optimization, based on the solution of the adjoint problem and combined with the Free Form Deformation (FFD) method for the shape parametrization and mesh motion, is presented and discussed. Theoretical and methodological aspects are described and the first preliminary results are reported.

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Section: Optimizationmentioning

confidence: 99%

Numerical Simulation of Sailing Boats: Dynamics, FSI, and Shape Optimization

Lombardi

Parolini

Quarteroni

et al. 2012

Springer Optimization and Its Applications

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“…Further details can be found in common literature [15,23,25,27], where the following form is often found for steady-state and incompressible flows:…”

Section: Adjoint Equations and Gradient Calculationmentioning

confidence: 99%

“…The derivation of the adjoint approach can be found in the literature [3,4,9,10,15,25,26] and for the sake of brevity only the basic principles are described here according to the notation of Soto and Löhner [27]. Let I be the objective function, which shall be optimized with respect to the design parameters β, and R be the steady-state incompressible Navier-Stokes equations.…”

Section: The General Principlementioning

confidence: 99%

“…Zymaris et al [15] derived a continuous adjoint approach to the Spalart-Allmaras turbulence model [16] in incompressible flows. They focused on the verification of the adjoint gradients for duct flows and investigated the effect of different terms in the adjoint turbulence model as well as in its boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Besides, a complete procedure for shape optimization is presented, which may inspire interested readers to develop their own frameworks. The continuous adjoints are used and the adjoints to the turbulence model are implemented following the derivation by Zymaris et al [15]. The incompressible, steady-state Reynolds-averaged Navier-Stokes equations (RANS) are closed by the Spalart-Allmaras turbulence model [16] without transition.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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