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32
Scalable Parallel Approach for HighFidelity SteadyState Aeroelastic Analysis and Derivative
 Computations,” AIAA Journal
, 2014
"... In this paper we present several significant improvements to both coupled solution methods and sensitivity analysis techniques for highfidelity aerostructural systems. We consider the analysis of full aircraft configurations using Euler CFD models with more than 80 million state variables and stru ..."
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Cited by 23 (19 self)
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In this paper we present several significant improvements to both coupled solution methods and sensitivity analysis techniques for highfidelity aerostructural systems. We consider the analysis of full aircraft configurations using Euler CFD models with more than 80 million state variables and structural finiteelement models with more than 1 million degrees of freedom. A coupled Newton–Krylov solution method for the aerostructural system is presented that accelerates the convergence rate for highly flexible structures. A coupled adjoint technique is presented that can compute gradients with respect to thousands of design variables accurately and efficiently. The efficiency of the presented methods is assessed on a high performance parallel computing cluster for up to 544 processors. To demonstrate the effectiveness of the proposed approach and the developed framework, an aerostructural model based on the Common Research Model is optimized with respect to hundreds of variables representing the wing outer mold line and the structural sizing. Two separate problems are solved: one where fuel burn is minimized, and another where the maximum takeoff weight is minimized. Multipoint optimizations with 5 cruise conditions and 2 maneuver conditions are performed with a 2 million cell CFD mesh and 300 000 DOF structural mesh. The optima for problems with 476 design variables are obtained within 36 hours of wall time on 435 processors. The resulting optimal aircraft are discussed and analyze the aerostructural tradeoffs for each objective. Convergence tolerance for aerostructural solution Convergence tolerance for aerostructural adjoint solution Nomenclature α Angle of attack AS Convergence tolerance for aerostructural solution A Convergence tolerance for aerodynamic solution S Convergence tolerance for structural solution A Aerodynamic residuals R All residuals
Automatic Differentiation Adjoint of the ReynoldsAveraged Navier–Stokes Equations with a Turbulence Model
 43rd AIAA Fluid Dynamics Conference and Exhibit
, 2013
"... This paper presents an approach for the rapid implementation of an adjoint solver for the ReynoldsAveraged Navier–Stokes equations with a Spalart–Allmaras turbulence model. Automatic differentiation is used to construct the partial derivatives required in the adjoint formulation. The resulting adj ..."
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Cited by 10 (10 self)
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This paper presents an approach for the rapid implementation of an adjoint solver for the ReynoldsAveraged Navier–Stokes equations with a Spalart–Allmaras turbulence model. Automatic differentiation is used to construct the partial derivatives required in the adjoint formulation. The resulting adjoint implementation is computationally efficient and highly accurate. The assembly of each partial derivative in the adjoint formulation is discussed. In addition, a coloring acceleration technique is presented to improve the adjoint efficiency. The RANS adjoint is verified with complexstep method using a flow over a bump case. The RANSbased aerodynamic shape optimization of an ONERA M6 wing is also presented to demonstrate the aerodynamic shape optimization capability. The drag coefficient is reduced by 19 % when subject to a lift coefficient constraint. The results are compared with Eulerbased aerodynamic shape optimization and previous work. Finally, the effects of the frozenturbulence assumption on the accuracy and computational cost are assessed. I.
MultiObjective Design Exploration for Aerodynamic Configurations
, 2007
"... A new approach, MultiObjective Design Exploration (MODE), is presented to address Multidisciplinary Design Optimization problems. MODE reveals the structure of the design space from the tradeoff information and visualizes it as a panorama for Decision Maker. The present form of MODE consists of Kr ..."
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Cited by 10 (2 self)
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A new approach, MultiObjective Design Exploration (MODE), is presented to address Multidisciplinary Design Optimization problems. MODE reveals the structure of the design space from the tradeoff information and visualizes it as a panorama for Decision Maker. The present form of MODE consists of Kriging Model, Adaptive Range Multi Objective Genetic Algorithms, Analysis of Variance and SelfOrganizing Map. The main emphasis of this approach is visual data mining. Two data mining examples using high fidelity simulation codes are presented: fourobjective aerodynamic optimization for the flyback booster and Multidisciplinary Design Optimization problem for a regionaljet wing. The first example confirms that two different data mining techniques produce consistent results. The second example illustrates the importance of the present approach because design knowledge can produce a better design even from the brief exploration of the design space. I.
Aerodynamic Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry
"... We present a new approach for the computation of shape sensitivities using the discrete adjoint and flowsensitivity methods on Cartesian meshes with general polyhedral cells (cutcells) at the wall boundaries. By directly linearizing the cutcell geometric constructors of the mesh generator, an effi ..."
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Cited by 8 (3 self)
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We present a new approach for the computation of shape sensitivities using the discrete adjoint and flowsensitivity methods on Cartesian meshes with general polyhedral cells (cutcells) at the wall boundaries. By directly linearizing the cutcell geometric constructors of the mesh generator, an efficient and robust computation of shape sensitivities is achieved. We show that the error convergence rate of the flow solution and its sensitivity, as well as the objective function and its gradient is consistent with the secondorder spatial discretization of the threedimensional Euler equations. The performance of the approach is demonstrated for an airfoil optimization problem in transonic flow, and a CADbased shape optimization of a reentry capsule in hypersonic flow. The approach is wellsuited for conceptual design studies where fast turnaround time is required. I.
Toward practical aerodynamic design through numerical optimization,” AIAA paper 20073950
, 2007
"... A NewtonKrylov algorithm for aerodynamic optimization is applied to the multipoint design of an airfoil for eighteen different operating conditions. The operating conditions include four cruise conditions and four longrange cruise conditions at maximum and minimum cruise weights and altitudes. In ..."
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Cited by 5 (4 self)
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A NewtonKrylov algorithm for aerodynamic optimization is applied to the multipoint design of an airfoil for eighteen different operating conditions. The operating conditions include four cruise conditions and four longrange cruise conditions at maximum and minimum cruise weights and altitudes. In addition, eight operating points are included in order to provide adequate maneuvering capabilities under dive conditions at the same maximum and minimum weights and altitudes with two different load factors. Finally, two lowspeed operating conditions are included at the maximum and minimum weights. The problem is posed as a multipoint optimization problem with a composite objective function that is formed by a weighted sum of the individual objective functions. The NewtonKrylov algorithm, which employs the discreteadjoint method, has been extended to include the lift constraint among the governing equations, leading to an improved liftconstrained drag minimization capability. The optimized airfoil performs well throughout the flight envelope. This example demonstrates how numerical optimization can be applied to practical aerodynamic design. Beginning with the work of Hicks et al. 1 I.
A NewtonKrylov Algorithm for the Euler Equations Using Unstructured Grids,” AIAA Paper
, 2003
"... A NewtonKrylov flow solver is presented for the Euler equations on unstructured grids. The algorithm uses a preconditioned matrixfree GMRES method to solve the linear system that arises at each Newton iteration. The preconditioner is an incomplete lowerupper factorization of an approximation to t ..."
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Cited by 5 (2 self)
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A NewtonKrylov flow solver is presented for the Euler equations on unstructured grids. The algorithm uses a preconditioned matrixfree GMRES method to solve the linear system that arises at each Newton iteration. The preconditioner is an incomplete lowerupper factorization of an approximation to the Jacobian matrix after applying the reverse CuthillMcKee reordering. The algorithm successfully converges for a wide range of steady two and threedimensional aerodynamic flows. A tenorder reduction of the density residual is obtained in a computing time equivalent to fewer than 520 and 1, 800 residual evaluations for the twodimensional and threedimensional cases, respectively.
A CADFree and a CADBased Geometry Control System for Aerodynamic Shape Optimization,” AIAA Paper 2005–0451
, 2005
"... The performance of an aerodynamic shape optimization routine is greatly dependent on its geometry control system. This system must accurately parameterize the initial geometry and generate a flexible set of design variables for the optimization cycle. It must also generate new instances of the geome ..."
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Cited by 5 (0 self)
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The performance of an aerodynamic shape optimization routine is greatly dependent on its geometry control system. This system must accurately parameterize the initial geometry and generate a flexible set of design variables for the optimization cycle. It must also generate new instances of the geometry based on the changes to the design variables dictated by the optimization routine. In response to changes in the geometry, it is also desirable to generate a new surface grid with the same topology as the original grid. This new surface grid can be used to perturb the associated volume grid. This paper presents two geometry control systems, a CADfree system, and a CATIA V5 CADbased system. The two systems provide practical tools for aerodynamic optimization. They also provide a basis for comparing CADfree and CADbased systems and understanding additional issues that need to be addressed in order to develop reliable optimization systems.
A parallel NewtonKrylov flow solver for the three dimensional Reynoldsaveraged NavierStokes equations
 In 20th Annual Conference CFD Society of
, 2012
"... This work presents a parallel NewtonKrylov flow solver employing third and fourthorder spatial discretizations to solve the threedimensional Euler equations on structured multiblock meshes. The fluxes are discretized using summationbyparts operators; boundary and interface conditions are impl ..."
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Cited by 5 (2 self)
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This work presents a parallel NewtonKrylov flow solver employing third and fourthorder spatial discretizations to solve the threedimensional Euler equations on structured multiblock meshes. The fluxes are discretized using summationbyparts operators; boundary and interface conditions are implemented using simultaneous approximation terms. Functionals, drag and lift, are calculated using Simpson’s rule. The solver is verified using the method of manufactured solutions and Ringleb flow and validated using the ONERA M6 wing. The results demonstrate that the combination of highorder finitedifference operators with a parallel NewtonKrylov solution technique is an excellent option for efficient computation of aerodynamic flows. I.
On Aerodynamic Optimization Under a Range of Operating Conditions
 AIAA Journal
"... In aerodynamic design, good performance is generally required under a range of operating conditions, including offdesign conditions. This can be achieved through multipoint optimization. The desired performance objective and operating conditions must be specified, and the resulting optimization pro ..."
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Cited by 5 (1 self)
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In aerodynamic design, good performance is generally required under a range of operating conditions, including offdesign conditions. This can be achieved through multipoint optimization. The desired performance objective and operating conditions must be specified, and the resulting optimization problem must be solved in such a manner that the desired performance is achieved. Issues involved in formulating multipoint optimization problems are discussed. A technique is proposed for automatically choosing sampling points within the operating range and their weights to obtain the desired performance over the range of operating conditions. Examples are given involving liftconstrained drag minimization over a range of Mach numbers. Tradeoffs and their implications for the formulation of multipoint problems are presented and discussed. I.
Mesh movement for a discreteadjoint NewtonKrylov algorithm for aerodynamic optimization
 AIAA Journal
"... A grid movement algorithm based on the linear elasticity method with multiple increments is presented. The method is relatively computationally expensive but is exceptionally robust, producing highquality elements even for large shape changes. It is integrated with an aerodynamic shape optimization ..."
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Cited by 4 (2 self)
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A grid movement algorithm based on the linear elasticity method with multiple increments is presented. The method is relatively computationally expensive but is exceptionally robust, producing highquality elements even for large shape changes. It is integrated with an aerodynamic shape optimization algorithm that uses an augmented adjoint approach for gradient calculation. The discreteadjoint equations are augmented to explicitly include the sensitivities of the mesh movement, resulting in an increase in efficiency and numerical accuracy. This gradient computation method requires less computational time than a function evaluation and leads to significant computational savings as dimensionality is increased. The results of the application of these techniques to several large deformation and optimization cases are presented. Nomenclature A = coordinates of the airfoil surface E = modulus of elasticity f = external forces G = coordinates of the interior grid nodes J, F = objective functions i = increment number K = stiffness matrix L = Lagrangian l = length of a side of a triangle n = number of increments P = potential energy Q = flow variables R = radius of a circumscribed circle R = flow residual r = residual of the grid movement equations s = semiperimeter of a triangle u = element displacements V = element volume X = design variables = boundary , = adjoint vector = radius of an inscribed circle = stress tensor = element shape quality = spatial domain Subscripts e = belonging to an element t = belonging to the entire system jQ = Q is held constant in the differentiation = subtriangular element inside a quadrilateral Superscripts ^ = known variable on the boundary T = transpose