High-Speed MHD Flow Control Using Adjoint-Based Sensitivities

Marta, André C.; Alonso, Juan J.

doi:10.2514/6.2006-8009

Cited by 5 publications

(8 citation statements)

References 21 publications

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“…For our final calculations, we used the hypersonic vehicle configuration from Marta and Alonso [25]. This is representative of a typical mesh used in the external aerodynamic analysis of aerospace vehicles.…”

Section: Performance On Real Meshesmentioning

confidence: 99%

Large calculation of the flow over a hypersonic vehicle using a GPU

Elsen

LeGresley

Darve

2008

Journal of Computational Physics

211

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Section: Performance On Real Meshesmentioning

confidence: 99%

Large calculation of the flow over a hypersonic vehicle using a GPU

Elsen

LeGresley

Darve

2008

Journal of Computational Physics

211

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“…The control theory approach has been used extensively in recent years for both aerodynamic shape optimization and aero-structural design 5 and has recently also been proved successful in MHD design 12,21 by the authors. This approach is well known for its capability to effectively handle design problems involving a large number of design variables and a small number of objective functions.…”

Section: Discrete Adjoint Formulationmentioning

confidence: 99%

“…The theory of the implementation of the discrete adjoint solver for this work follows that of the authors previous work. [10][11][12] The discrete adjoint system of equations (9) was constructed by differentiating all the numerical fluxes that comprised the residual R ijk in the discretized governing equations (6). This differentiation has been automated using an AD tool, namely Tapenade, [23][24][25][26] which is a non-commercial tool that supports Fortran 90.…”

Section: A Discrete Adjoint Solvermentioning

confidence: 99%

Towards Aircraft Design Using an Automatic Discrete Adjoint Solver

Mader

Martins

Marta

2007

18th AIAA Computational Fluid Dynamics Conference

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The ADjoint method is applied to a three-dimensional Computational Fluid Dynamics (CFD) solver to generate the sensitivities required for aerodynamic shape optimization. The ADjoint approach selectively uses Automatic Differentiation (AD) to generate the partial derivative terms in the discrete adjoint equations. By selectively applying AD techniques, the computational cost and memory overhead incurred by using AD are significantly reduced, while still allowing for the the accurate treatment of arbitrarily complex governing equations and boundary conditions. Once formulated, the discrete adjoint equations are solved using the Portable, Extensible Toolkit for Scientific computation (PETSc). With this approach, the computed adjoint vector can be used to calculate the total sensitivities required for aerodynamic shape optimization of a complete aircraft configuration. The resulting sensitivities are compared with complex-step derivatives to establish their accuracy. The tools developed are applied to an infinite wing test case to demonstrate the accuracy and efficiency of the method.

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“…The adjoint method has been extended to 3D problems, leading to applications such as the aerodynamic shape optimization of complete aircraft configurations (Reuther et al 1999a,b), as well as aerostructural design (Martins et al 2004). The adjoint theory has since been generalized for multidisciplinary systems (Martins et al 2005) and for magneto-hydrodynamic (MHD) problems, using both the ideal model (Marta and Alonso 2006a) and the low magnetic Reynolds number approximation (Marta and Alonso 2006b).…”

Section: Introductionmentioning

confidence: 98%

A methodology for the development of discrete adjoint solvers using automatic differentiation tools

Marta

Mader

Martins

et al. 2007

International Journal of Computational Fluid Dynamics

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A methodology for the rapid development of adjoint solvers for computational fluid dynamics (CFD) models is presented. The approach relies on the use of automatic differentiation (AD) tools to almost completely automate the process of development of discrete adjoint solvers. This methodology is used to produce the adjoint code for two distinct 3D CFD solvers: a cell-centred Euler solver running in single-block, single-processor mode and a multi-block, multi-processor, vertex-centred, magnetohydrodynamics (MHD) solver. Instead of differentiating the entire source code of the CFD solvers using AD, we have applied it selectively to produce code that computes the transpose of the flux Jacobian matrix and the other partial derivatives that are necessary to compute sensitivities using an adjoint method. The discrete adjoint equations are then solved using the Portable, Extensible Toolkit for Scientific Computation (PETSc) library. The selective application of AD is the principal idea of this new methodology, which we call the AD adjoint (ADjoint). The ADjoint approach has the advantages that it is applicable to any set of governing equations and objective functions and that it is completely consistent with the gradients that would be computed by exact numerical differentiation of the original discrete solver. Furthermore, the approach does not require hand differentiation, thus avoiding the long development times typically required to develop discrete adjoint solvers for partial differential equations, as well as the errors that result from the necessary approximations used during the differentiation of complex systems of conservation laws. These advantages come at the cost of increased memory requirements for the discrete adjoint solver. However, given the amount of memory that is typically available in parallel computers and the trends toward larger numbers of multi-core processors, this disadvantage is rather small when compared with the very significant advantages that are demonstrated. The sensitivities of drag and lift coefficients with respect to different parameters obtained using the discrete adjoint solvers show excellent agreement with the benchmark results produced by the complex-step and finite-difference methods. Furthermore, the overall performance of the method is shown to be better than most conventional adjoint approaches for both CFD solvers used.

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High-Speed MHD Flow Control Using Adjoint-Based Sensitivities

Cited by 5 publications

References 21 publications

Large calculation of the flow over a hypersonic vehicle using a GPU

Large calculation of the flow over a hypersonic vehicle using a GPU

Towards Aircraft Design Using an Automatic Discrete Adjoint Solver

A methodology for the development of discrete adjoint solvers using automatic differentiation tools

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