Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers

Reuther, James; Rimlinger, Mark J.; Alonso, Juan J.; Jameson, Antony

doi:10.2514/6.1996-4045

Cited by 31 publications

(15 citation statements)

References 11 publications

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“…"Time ratio (coarse/fine)" refer to the percentage of the total time spent on solving the coarse-level problem. 'Linear' and 'Nonlinear' refer to the coarse linear problem (20) and the coarse nonlinear problem (10), respectively. 'Fine' and 'Coarse' refer to the fine-level problem and coarse-level problem, respectively.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…From Table III, we see that the fine grid linear stopping criteria has a significant impact on the performance of the algorithm, and we need to carefully choose the stopping criteria 959 in order to obtain a good performance. We mention here that the coarse preconditioner in the twolevel Schwarz preconditioner, that is, M 1 c in (20) is solved by GMRES with a one-level additive Schwarz preconditioner. For tests to be presented in the next subsection, we will solve the coarse problem by a parallel direct method SuperLU_DIST [56].…”

Section: Cannula Optimizationmentioning

confidence: 99%

“…Such computations often require large-scale parallel computers for their memory capacity and processing speed. There are some publications studying parallel algorithms for shape optimization problems; see, for example, [19][20][21]. It is clear by now that the increase of computing power is no longer from faster processors but from the increase of the number of processors.…”

Section: Introductionmentioning

confidence: 99%

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A parallel two‐level domain decomposition based one‐shot method for shape optimization problems

Chen

Cai

2014

Numerical Meth Engineering

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A two-level domain decomposition method is introduced for general shape optimization problems constrained by the incompressible Navier-Stokes equations. The optimization problem is first discretized with a finite element method on an unstructured moving mesh that is implicitly defined without assuming that the computational domain is known and then solved by some one-shot Lagrange-Newton-Krylov-Schwarz algorithms. In this approach, the shape of the domain, its corresponding finite element mesh, the flow fields and their corresponding Lagrange multipliers are all obtained computationally in a single solve of a nonlinear system of equations. Highly scalable parallel algorithms are absolutely necessary to solve such an expensive system. The one-level domain decomposition method works reasonably well when the number of processors is not large. Aiming for machines with a large number of processors and robust nonlinear convergence, we introduce a two-level inexact Newton method with a hybrid two-level overlapping Schwarz preconditioner. As applications, we consider the shape optimization of a cannula problem and an artery bypass problem in 2D. Numerical experiments show that our algorithm performs well on a supercomputer with over 1000 processors for problems with millions of unknowns. that is, Here,ˇD 10, Re D 500, N h D 1:1 10 6 , and N H D 7:0 10 4 . In algorithm One-One: ı D 8; in algorithm Two-One: ı h D 8, and ı H D 4; in algorithm Two-Two: ı h D 0 and ı H D 2.

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Section: Numerical Experimentsmentioning

confidence: 99%

Section: Cannula Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A parallel two‐level domain decomposition based one‐shot method for shape optimization problems

Chen

Cai

2014

Numerical Meth Engineering

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“…Supersonic aircraft is significant for not only military value but also civil value. It is one of the most important aspects in aerospace field (Bolender & Doman, 2007;Gao et al, 2007;Hedrick & Bryson, 1971;Jedidi et al, 2005;Marrison & Stengel, 1998;Reuther et al, 1999). In addition, supersonic flight is inevitable during a reentry process (Anderson, 2006).…”

Section: Introductionmentioning

confidence: 99%

Neglected Radio Blackout Induced by the Nonionized Airflow Sheath Around a Supersonic Aircraft

et al. 2018

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The characteristics of the flow field around a supersonic aircraft are discussed. It is analyzed that there are interfaces between two adjacent regions with jump change of refractive index in the supersonic flow. The physical mechanism of the Fresnel reflection of an electromagnetic wave at the interfaces mentioned above is analyzed according to the Fresnel reflection phenomenon in the Earth atmosphere. The conditions for the Fresnel reflection in the supersonic flow field are discussed, and the formulae for calculating the Fresnel reflection coefficient are given. According to the process of a radio wave propagating across the interfaces in the supersonic flow field, the other radio blackout phenomenon is proposed for the first time, which is induced by the nonionized atmospheric sheath around a supersonic aircraft, and may be well neglected or mistaken for the plasma‐sheath‐caused radio blackout. The conditions of the nonionized‐atmospheric‐sheath‐induced radio blackout are investigated. The calculation results show that the neglected radio blackout is confined to a rather specific case, a very small range of grazing angles. However, it is significant for identifying the mechanism of radio blackout.

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“…Optimization problems constrained by Partial Differential Equations (PDEs) commonly arise in engineering practice, particularly in the context of design or control of physics-based systems. A majority of the research in PDE-constrained optimization has been focused on steady or static PDEs, with a large body of literature detailing many aspects of the subject, including continuous and discrete adjoint methods [1,2,3,4,5], parallel implementations [6,7], one-shot or infeasible path methods [6,8], and generalized reduced gradient or feasible path methods [1,9]. This emphasis on steady problems is largely due to the fact that (a) static analysis is sufficient for a large class of problems of interest and (b) unsteady analysis is expensive to perform in a many-query setting, such as optimization [10].…”

Section: Introductionmentioning

confidence: 99%

An adjoint method for a high-order discretization of deforming domain conservation laws for optimization of flow problems

Zahr

Persson

2016

Journal of Computational Physics

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The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally highorder accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain is transformed into one on a fixed reference domain by the introduction of a time-dependent mapping that encapsulates the domain deformation and parametrization, resulting in an Arbitrary Lagrangian-Eulerian form of the governing equations. A high-order discontinuous Galerkin method is used to discretize the transformed equation in space and a high-order diagonally implicit Runge-Kutta scheme is used for the temporal discretization. Quantities of interest that take the form of space-time integrals are discretized in a solver-consistent manner. The corresponding fully discrete adjoint method is used to compute exact gradients of quantities of interest along the manifold of solutions of the fully discrete conservation law. These quantities of interest and their gradients are used in the context of gradient-based PDE-constrained optimization.The adjoint method is used to solve two optimal shape and control problems governed by the isentropic, compressible Navier-Stokes equations. The first optimization problem seeks the energetically optimal trajectory of a 2D airfoil given a required initial and final spatial position. The optimization solver, driven by gradients computed via the adjoint method, reduced the total energy required to complete the specified mission nearly an order of magnitude. The second optimization problem seeks the energetically optimal flapping motion and time-morphed geometry of a 2D airfoil given an equality constraint on the x-directed impulse generated on the airfoil. The optimization solver satisfied the impulse constraint to greater than 8 digits of accuracy and reduced the required energy between a factor of 2 and 10, depending on the value of the impulse constraint, as compared to the nominal configuration.

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Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers

Cited by 31 publications

References 11 publications

A parallel two‐level domain decomposition based one‐shot method for shape optimization problems

A parallel two‐level domain decomposition based one‐shot method for shape optimization problems

Neglected Radio Blackout Induced by the Nonionized Airflow Sheath Around a Supersonic Aircraft

An adjoint method for a high-order discretization of deforming domain conservation laws for optimization of flow problems

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