Self-contained automated methodology for optimal flow control

Joslin, Ronald D.; Gunzburger, Max; Nicolaides, R. A.; Erlebacher, Gordon; Hussaini, M. Y.

doi:10.2514/3.13593

Cited by 29 publications

(42 citation statements)

References 9 publications

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“…This means that we derive the adjoint equations on the PDE level and then discretize our adjoint PDEs to obtain gradient information for the optimization algorithms. The gradient information obtained from this procedure is different than the one obtained by applying the adjoint equation procedure to the discretized version of the optimal control problem (3), (6). While the two outlined procedures do result in different gradient information, one expects or at least hopes that the error between the gradients computed by both approaches goes to zero if the discretization is refined.…”

Section: Adjoint Equationsmentioning

confidence: 75%

Optimal Transpiration Boundary Control for Aeroacoustics

2003

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We consider the optimal boundary control of aeroacoustic noise governed by the two-dimensional unsteady compressible Euler equations. The control is the time and space varying wall-normal velocity on a subset of an otherwise solid wall. The objective functional to be minimized is a measure of acoustic amplitude. Optimal transpiration boundary control of aeroacoustic noise introduces challenges beyond those encountered in direct aeroacoustic simulations or in many other optimization problems governed by compressible Euler equations. One nontrivial issue that arises in our optimal control problem is the formulation and implementation of transpiration boundary conditions. Since we allow suction and blowing on the boundary, portions of the boundary may change from inflow to outflow, or vice versa, and different numbers of boundary conditions must be imposed at inflow versus outflow boundaries. Another important issue is the derivation of adjoint equations which are required to compute the gradient of the objective function with respect to the control. Among other things, this is influenced by the choice of boundary conditions for the compressible Euler equations. This paper describes our approaches to meet these challenges and presents results for three model problems. These problems are designed to validate our transpiration boundary conditions and their implementation, study the accuracy of gradient computations, and assess the performance of the computed controls.

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Section: Adjoint Equationsmentioning

confidence: 75%

Optimal Transpiration Boundary Control for Aeroacoustics

2003

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“…[2][3][4][5] Although the adjoint-based methods have been successfully used for problems of optimal design within the steady-state aerodynamics, applications of the adjoint formulation to essentially time-dependent optimal control/design problems are still lacking. In, 6 the 2-D continuous time-dependent adjoint incompressible Navier-Stokes equations and optimality conditions have been derived. This continuous adjoint-based method has been successfully used for solving the problem of boundary-layer instability suppression through wave cancellation.…”

Section: Introductionmentioning

confidence: 99%

Adjoint-Based Methodology for Time-Dependent Optimization

Yamaleev

Diskin

Nielsen

2008

12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.

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“…These choices are motivated by the existing work on control of incompressible Navier-Stokes equations. In References [1,7,11] the control is only time dependent and in Reference [10] the control varies in time and only over a small portion of the boundary, i.e. it is essentially dependent only one time.…”

Section: Introductionmentioning

confidence: 99%

“…it is essentially dependent only one time. Therefore, in References [1,7,10,11] the regularization term for the control involves only t f t0 c |g| 2 + |g t | 2 . In the papers [2,3,11] the control varies over a large portion of the boundary and in time, but the regularization terms used are essentially denote the primitive ow variables, where (t; x) is the density; v i (t; x) denotes the velocity in the x i -direction, i = 1; 2; v = (v 1 ; v 2 ) T ; and T (t; x) denotes the temperature.…”

Section: Introductionmentioning

confidence: 99%

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Optimal control of unsteady compressible viscous flows

Collis

Ghayour

Heinkenschloss

et al. 2002

Numerical Methods in Fluids

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SUMMARYThe control of complex, unsteady ows is a pacing technology for advances in uid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical ow control systems. However, most of the prior work in this area has focused on incompressible ow which precludes many of the important physical ow phenomena that must be controlled in practice including the coupling of uid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two-dimensional compressible Navier-Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter-rotating viscous vortices above an inÿnite wall which, due to the self-induced velocity ÿeld, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall-normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the in uence of control regularization for each case.

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Self-contained automated methodology for optimal flow control

Cited by 29 publications

References 9 publications

Optimal Transpiration Boundary Control for Aeroacoustics

Optimal Transpiration Boundary Control for Aeroacoustics

Adjoint-Based Methodology for Time-Dependent Optimization

Optimal control of unsteady compressible viscous flows

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