Efficient stabilization and acceleration of numerical simulation of fluid flows by residual recombination

Citro, Vincenzo; Luchini, Paolo; Giannetti, Filippo; Auteri, Franco

doi:10.1016/j.jcp.2017.04.081

Cited by 42 publications

(44 citation statements)

References 33 publications

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“…Unstable limit cycles are not easy to track, since they require stabilisation techniques, such as BoostConv (Citro et al 2017) or edge-state tracking (Bengana et al 2019), or the use of continuation techniques, such as harmonic balance (Fabre et al 2019). Alternatively, we have performed a multiple-scale analysis up to fifth order (see appendix C).…”

Section: Weakly Nonlinear Analysismentioning

confidence: 99%

Bifurcation scenario in the two-dimensional laminar flow past a rotating cylinder

et al. 2020

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Section: Weakly Nonlinear Analysismentioning

confidence: 99%

Bifurcation scenario in the two-dimensional laminar flow past a rotating cylinder

et al. 2020

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“…LetQ be aT -periodic solution of (133), such thatQ(t +T ) =Q(t). Robust numerical procedures to compute limit cycles in high dimensional systems can be found in [307][308][309], among others. The objective is to investigate the stability of the periodic solution,Q(t), by calculating the evolution of small perturbations on the periodic attractor.…”

Section: Floquet Analysismentioning

confidence: 99%

Adjoint Methods as Design Tools in Thermoacoustics

Magri

2019

Applied Mechanics Reviews

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In a thermoacoustic system, such as a flame in a combustor, heat release oscillations couple with acoustic pressure oscillations. If the heat release is sufficiently in phase with the pressure, these oscillations can grow, sometimes with catastrophic consequences. Thermoacoustic instabilities are still one of the most challenging problems faced by gas turbine and rocket motor manufacturers. Thermoacoustic systems are characterized by many parameters to which the stability may be extremely sensitive. However, often only few oscillation modes are unstable. Existing techniques examine how a change in one parameter affects all (calculated) oscillation modes, whether unstable or not. Adjoint techniques turn this around: They accurately and cheaply compute how each oscillation mode is affected by changes in all parameters. In a system with a million parameters, they calculate gradients a million times faster than finite difference methods. This review paper provides: (i) the methodology and theory of stability and adjoint analysis in thermoacoustics, which is characterized by degenerate and nondegenerate nonlinear eigenvalue problems; (ii) physical insight in the thermoacoustic spectrum, and its exceptional points; (iii) practical applications of adjoint sensitivity analysis to passive control of existing oscillations, and prevention of oscillations with ad hoc design modifications; (iv) accurate and efficient algorithms to perform uncertainty quantification of the stability calculations; (v) adjoint-based methods for optimization to suppress instabilities by placing acoustic dampers, and prevent instabilities by design modifications in the combustor's geometry; (vi) a methodology to gain physical insight in the stability mechanisms of thermoacoustic instability (intrinsic sensitivity); and (vii) in nonlinear periodic oscillations, the prediction of the amplitude of limit cycles with weakly nonlinear analysis, and the theoretical framework to calculate the sensitivity to design parameters of limit cycles with adjoint Floquet analysis. To show the robustness and versatility of adjoint methods, examples of applications are provided for different acoustic and flame models, both in longitudinal and annular combustors, with deterministic and probabilistic approaches. The successful application of adjoint sensitivity analysis to thermoacoustics opens up new possibilities for physical understanding, control and optimization to design safer, quieter, and cleaner aero-engines. The versatile methods proposed can be applied to other multiphysical and multiscale problems, such as fluid–structure interaction, with virtually no conceptual modification.

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“…Nevertheless, implementing RPM is not straightforward as it requires the Jacobian matrix (or a good approximation) of the discrete-time system considered. Recently, [18] have introduced BoostConv, a new fixed point computation technique somehow related to the recursive projection method. Let us rewrite Eq.…”

Section: Boostconvmentioning

confidence: 99%

“…It can moreover be implemented as a black box around an existing solver since it only requires the residual r k as input and returns the corrected one ξ ξ ξ k as output. Also, BoostConv can be easily adapted to stabilize periodic orbits [18].…”

Section: Boostconvmentioning

confidence: 99%

Time-Stepping and Krylov Methods for Large-Scale Instability Problems

Loiseau

Bucci

Cherubini

et al. 2018

Computational Methods in Applied Sciences

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With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has been become reachable. It must be noted however that the memory capabilities of computers increase at a slower rate than their computational capabilities. Consequently, the traditional matrix-forming approaches wherein the Jacobian matrix of the system considered is explicitly assembled become rapidly intractable. Over the past two decades, so-called matrixfree approaches have emerged as an efficient alternative. The aim of this chapter is thus to provide an overview of well-grounded matrix-free methods for fixed points computations and linear stability analyses of very large-scale nonlinear dynamical systems.

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Efficient stabilization and acceleration of numerical simulation of fluid flows by residual recombination

Cited by 42 publications

References 33 publications

Bifurcation scenario in the two-dimensional laminar flow past a rotating cylinder

Bifurcation scenario in the two-dimensional laminar flow past a rotating cylinder

Adjoint Methods as Design Tools in Thermoacoustics

Time-Stepping and Krylov Methods for Large-Scale Instability Problems

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