An implicit, exact dual adjoint solution method for turbulent flows on unstructured grids

Nielsen, Eric J.; Lu, James; Park, Michael A.; Darmofal, David L.

doi:10.1016/j.compfluid.2003.09.005

Cited by 166 publications

(94 citation statements)

References 47 publications

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“…In the current implementation, adjoint solutions for multiple functions may be computed simultaneously as outlined in Ref. 31 by storing multiple right-…”

Section: Methodsmentioning

confidence: 99%

“…For computations using this method, the complex step size has been chosen to be . The second technique used to verify the linearizations relies on the handcoded implementation 29,31 of the discrete adjoint system given by Eq. 3 for the flow equations and the handcoded direct differentiation of the mesh terms 30 as formulated in Eqs.…”

Section: Consistency Of Linearizationmentioning

confidence: 99%

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Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

Nielsen

Park

2006

AIAA Journal

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An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown. Nomenclature = vector of design variables = cost function = linear elasticity coefficient matrix = Lagrangian function = Lift-to-drag ratio = vector of dependent variables = discretized residual vector = computational mesh = vector of adjoint variables

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“…In the current implementation, adjoint solutions for multiple functions may be computed simultaneously as outlined in Ref. 31 by storing multiple right-…”

Section: Methodsmentioning

confidence: 99%

Section: Consistency Of Linearizationmentioning

confidence: 99%

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

Nielsen

Park

2006

AIAA Journal

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“…For viscous flows, this scheme is augmented with a line-relaxation algorithm in boundary layer regions as described in Ref. 31.…”

Section: Methodsmentioning

confidence: 99%

Efficient Construction of Discrete Adjoint Operators on Unstructured Grids Using Complex Variables

Nielsen

Kleb

2006

AIAA Journal

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A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.

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“…This approach has two main advantages: first, the resulting memory footprint of the adjoint solver is similar to the primal flow solver, which is largely determined by the system matrix P, while the run-time of the adjoint solver is equivalent to the primal flow solver. Secondly, since the transposed system matrix P T has the same eigenspectra as P, the adjoint solver inherits the convergence rate of the flow solver [50,52,53], which is illustrated in Figure 8 for a radial turbine test case. This is a desirable property as it guarantees convergence of the adjoint problem, provided that primal flow solver converges (i.e., the system matrix at the last iteration of the flow solver is contractive with the magnitude of all eigenvalues less than unity).…”

Section: Adjoint Solver and Gradient Evaluationmentioning

confidence: 99%

CAD Integrated Multipoint Adjoint-Based Optimization of a Turbocharger Radial Turbine

Mueller

Verstraete

2017

IJTPP

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Abstract:The adjoint method is considered as the most efficient approach to compute gradients with respect to an arbitrary number of design parameters. However, one major challenge of adjoint-based shape optimization methods is the integration into a computer-aided design (CAD) workflow for practical industrial cases. This paper presents an adjoint-based framework that uses a tailored shape parameterization to satisfy geometric constraints due to mechanical and manufacturing requirements while maintaining the shape in a CAD representation. The system employs a sequential quadratic programming (SQP) algorithm and in-house developed libraries for the CAD and grid generation as well as a 3D Navier-Stokes flow and adjoint solver. The developed method is applied to a multipoint optimization of a turbocharger radial turbine aiming at maximizing the total-to-static efficiency at multiple operating points while constraining the output power and the choking mass flow of the machine. The optimization converged in a few design cycles in which the total-to-static efficiency could be significantly improved over a wide operating range. Additionally, the imposed aerodynamic constraints with strict convergence tolerances are satisfied and several geometric constraints are inherently respected due to the parameterization of the turbine. In particular, radial fibered blades are used to avoid bending stresses in the turbine blades due to centrifugal forces. The methodology is a step forward towards robustness and consistency of gradient-based optimization for practical industrial cases, as it maintains the optimal shape in CAD representation. As shown in this paper, this avoids shape approximations and allows manufacturing constraints to be included.

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An implicit, exact dual adjoint solution method for turbulent flows on unstructured grids

Cited by 166 publications

References 47 publications

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

Efficient Construction of Discrete Adjoint Operators on Unstructured Grids Using Complex Variables

CAD Integrated Multipoint Adjoint-Based Optimization of a Turbocharger Radial Turbine

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