Stabilisation of discrete steady adjoint solvers

Xu, Shugen; Radford, David; Meyer, Marcus; Müller, Jens-Dominik

doi:10.1016/j.jcp.2015.06.036

Cited by 59 publications

(46 citation statements)

References 38 publications

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“…The JT-KIRK method presented in [4] uses m Runge-Kutta stages to proceed from an intermediate solution Un to an improved solution Un+1 as follows:…”

Section: The Jt-kirk Methodsmentioning

confidence: 99%

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Time-averaged steady vs. unsteady adjoint: a comparison for cases with mild unsteadiness

Hueckelheim

Gugala

et al. 2015

53rd AIAA Aerospace Sciences Meeting

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“…The JT-KIRK method presented in [4] uses m Runge-Kutta stages to proceed from an intermediate solution Un to an improved solution Un+1 as follows:…”

Section: The Jt-kirk Methodsmentioning

confidence: 99%

“…JT-KIRK, a method that has been presented recently [4] for problems with mild unsteadiness, uses a different approach to stabilise the adjoint solver. Instead of using an arbitrary snapshot with shedding, an implicit solver with strong temporal damping properties is used for the primal solution.…”

Section: Introductionmentioning

confidence: 99%

Time-averaged steady vs. unsteady adjoint: a comparison for cases with mild unsteadiness

Hueckelheim

Gugala

et al. 2015

53rd AIAA Aerospace Sciences Meeting

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“…The Reynolds-Averaged Navier-Stokes equations are solved on multiblock structured grids with a cell-centered finite volume formulation, based on an adaptation of the JT-KIRK scheme of Xu et al [22]. Convective fluxes are computed using Roe's approximate Riemann solver [23] with a MUSCL-type reconstruction [24] of primitive variables for second-order accuracy.…”

Section: Cfd Solvermentioning

confidence: 99%

Adjoint-Based Design Optimisation of an Internal Cooling Channel U-Bend for Minimised Pressure Losses

Verstraete

Müller

2017

IJTPP

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Abstract:The success of shape optimisation depends significantly on the parametrisation of the shape. Ideally, it defines a very rich variation in shape, allows for rapid grid generation of high quality, and expresses the shape in a standard Computer Aided Design (CAD) representation. While most existing parametrisation methods fail at least one of these criteria, this work introduces a novel parametrisation method, which satisfies all three. A tri-variate B-spline volume is used to define the volume to be optimised. The position of the external control points are used as design parameters, while the internal control points are repositioned to ensure regularity of the transformation. The grid generation process transforms a Cartesian grid (defined in parametric space) to the physical space using the tri-variate net of control points. This process guarantees a high grid quality even for large deformations, and has extremely low computational cost as it only involves a transformation from parameter space to physical space. This allows the computation of the grid sensitivities with respect to the design variables at a fraction of the cost of a Computational Fluid Dynamics (CFD) iteration, therefore allowing the use of one-shot methods. This novel parametrisation is applied to the shape optimisation of a U-bend passage of a turbine-blade serpentine-cooling channel with the objective to minimise pressure losses. A steady state, Reynolds-Averaged, density-based Navier-Stokes solver is used to predict the pressure losses at a Reynolds number of 40,000. The sensitivities of the objective function with respect to the control points are computed using a hand-derived adjoint solver and geometry generation system. A one-shot approach is used to simultaneously converge flow, gradient and design, resulting in a rapid design approach with a design time equivalent to approximately 10 normal CFD runs, while still maintaining a CAD representation of the geometry. A large reduction in pressure loss is obtained, and the flow in the optimal geometry is analysed in detail.

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“…Furthermore, to reduce the computational cost, periodic boundary conditions are applied in circumferential direction. Time integration is realized with an adaption of the JT-KIRK scheme [50] that combines Runge-Kutta time-stepping and Krylov methods inside a geometric multigrid cycle. As illustrated in [50], the proposed algorithm enables fully converged flow solutions for some cases where conventional algorithms would fail, and therefore extends the applicability of adjoint-based optimization for marginally stable applications.…”

Section: Flow Solvermentioning

confidence: 99%

“…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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Stabilisation of discrete steady adjoint solvers

Cited by 59 publications

References 38 publications

Time-averaged steady vs. unsteady adjoint: a comparison for cases with mild unsteadiness

Time-averaged steady vs. unsteady adjoint: a comparison for cases with mild unsteadiness

Adjoint-Based Design Optimisation of an Internal Cooling Channel U-Bend for Minimised Pressure Losses

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

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