Sensitivity analysis on chaotic dynamical systems by Finite Difference Non-Intrusive Least Squares Shadowing (FD-NILSS)

Ni, Angxiu; Wang, Qiqi; Fernández, Pablo; Talnikar, Chaitanya

doi:10.1016/j.jcp.2019.06.004

Cited by 20 publications

(26 citation statements)

References 48 publications

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“…In other words, we can perform, at each time step, one matrix-matrix product, where the second matrix is composed of several tangent solutions, rather than performing several matrixvector products, where we need to reload the matrix for each product. † Additionally, as discussed in (Ni & Wang 2017;Ni et al 2019), FD-NILSS and NILSS have smaller marginal cost for new parameters; for cases with more parameters than objectives or cases when we have only adjoint solvers, the non-intrusive least-squares adjoint shadowing (NILSAS) method (Ni & Talnikar 2019a) can compute the gradient of one objective with respect to many parameters in one run.…”

Section: Results Of Sensitivitiesmentioning

confidence: 99%

“…Our physical problem of the 3D flow past a cylinder is the same as in (Ni et al 2019). The front view of the geometry of the entire flow field is shown in figure 1.…”

Section: Problem Set-up and Verification Of Simulationmentioning

confidence: 99%

“…For quantities defined only at interfaces between segments, such as Q i , R i , and b i , we use the same subscripts as the time points they are defined at. Again, we use finite difference results to approximate tangent solutions: such a variant is called the finite difference non-intrusive least-squares shadowing (FD-NILSS) algorithm, whose details are given in (Ni et al 2019).…”

Section: The Nilss Algorithm For Computing Shadowing Directionsmentioning

confidence: 99%

See 2 more Smart Citations

Hyperbolicity, shadowing directions and sensitivity analysis of a turbulent three-dimensional flow

2019

J. Fluid Mech.

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This paper uses compressible flow simulation to analyze the hyperbolicity, shadowing directions, and sensitivities of a weakly turbulent three dimensional cylinder flow at Reynolds number 525 and Mach number 0.1.By computing the first 40 Covariant Lyapunov Vectors (CLVs), we find that unstable CLVs are active in the near-wake region, whereas stable CLVs are active in the far-wake region. This phenomenon is related to hyperbolicity since it shows that CLVs point to different directions; it also suggests that for open flows there is a large fraction of CLVs that are stable. However, due to the extra neutral CLV and the occasional tangencies between CLVs, our system is not uniform hyperbolic.By the Non-intrusive least-squares shadowing (NILSS) algorithm, we compute shadowing directions and sensitivities of long-time-averaged objectives. Our results suggest that shadowing methods may be valid for general chaotic fluid problems.

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Section: Results Of Sensitivitiesmentioning

confidence: 99%

“…Our physical problem of the 3D flow past a cylinder is the same as in (Ni et al 2019). The front view of the geometry of the entire flow field is shown in figure 1.…”

Section: Problem Set-up and Verification Of Simulationmentioning

confidence: 99%

Section: The Nilss Algorithm For Computing Shadowing Directionsmentioning

confidence: 99%

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Hyperbolicity, shadowing directions and sensitivity analysis of a turbulent three-dimensional flow

2019

J. Fluid Mech.

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“…There are currently several variants of NILSS [25], such as the Finite-Difference NILSS (FD-NILSS) [26] and discrete adjoint NILSS [28]. NILSAS, as well as these NILSS variants, bears part of the merit of 'non-intrusive' formulation, that is, in comparison to LSS, the minimization problems in these algorithms are constrained to the unstable subspaces.…”

Section: Comparison With Other Shadowing Algorithmsmentioning

confidence: 99%

Adjoint sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Adjoint Shadowing (NILSAS)

Talnikar

2019

Journal of Computational Physics

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We develop the NILSAS algorithm, which performs adjoint sensitivity analysis of chaotic systems via computing the adjoint shadowing direction. NILSAS constrains its minimization to the adjoint unstable subspace, and can be implemented with little modification to existing adjoint solvers. The computational cost of NILSAS is independent of the number of parameters. We demonstrate NILSAS on the Lorenz 63 system and a weakly turbulent three-dimensional flow over a cylinder.

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“…The application of the adjoint method to LES introduces certain complications. The magnitude of the adjoint solution field diverges to infinity as the LES is performed for a longer time [20,21,22,23,24,25]. This divergence introduces a significant error in the gradient computed from the adjoint solution, especially when the design objective function is a long time-averaged quantity.…”

Section: Introductionmentioning

confidence: 99%

Adjoint-based trailing edge shape optimization of a transonic turbine vane using large eddy simulations

Talnikar¹,

Wang²

2020

Preprint

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The shape of the trailing edge of a gas turbine nozzle guide vane has a significant effect on the downstream stagnation pressure loss and heat transfer over the surface of the vane. Traditionally, adjoint-based design optimization methods for turbomachinery components have used low-fidelity simulations like Reynolds averaged Navier-Stokes. To reliably capture the complex flow phenomena involved in turbulent flow over a turbine vane, high-fidelity simulations like large eddy simulation (LES) are required. In this paper, an adjoint-based trailing edge shape optimization using LES is performed to reduce pressure loss and heat transfer over the surface of the vane. The chaotic dynamics of turbulence limits the effectiveness of the adjoint method for long-time averaged objective functions computed from LES. A viscosity stabilized unsteady adjoint method is used to obtain gradients of the design objective function with reasonable accuracy. A gradient utilizing Bayesian optimization is used to robustly handle noise in the objective function and gradient evaluations. The trailing edge shape is parameterized using a linear combination of 5 convex designs. Results from the optimization, performed on the supercomputer Mira, are compared with optimal designs generated using derivative-free design optimization of the same problem.

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Sensitivity analysis on chaotic dynamical systems by Finite Difference Non-Intrusive Least Squares Shadowing (FD-NILSS)

Cited by 20 publications

References 48 publications

Hyperbolicity, shadowing directions and sensitivity analysis of a turbulent three-dimensional flow

Hyperbolicity, shadowing directions and sensitivity analysis of a turbulent three-dimensional flow

Adjoint sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Adjoint Shadowing (NILSAS)

Adjoint-based trailing edge shape optimization of a transonic turbine vane using large eddy simulations

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