Minimal gain marching schemes: searching for unstable steady-states with unsteady solvers

Teixeira, Renan de S.; Alves, Leonardo Santos de Brito

doi:10.1007/s00162-017-0426-0

Cited by 9 publications

(7 citation statements)

References 33 publications

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“…2006) and, more recently, a residual recombination procedure (Citro et al. 2017) and minimal gain marching (Teixeira & Alves 2017). Here the SFD method, as implemented in nektar++ and nek5000 , has been used to compute artificially stationary, unstable base states that were used for the subsequent modal analyses.…”

Section: Numerical Workmentioning

confidence: 99%

Linear modal instabilities around post-stall swept finite wings at low Reynolds numbers

Burtsev

Zhang

et al. 2022

J. Fluid Mech.

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Linear modal instabilities of flow over untapered wings with aspect ratios $AR=4$ and 8, based on the NACA 0015 profile, have been investigated numerically over a range of angles of attack, $\alpha$ , and angles of sweep, $\varLambda$ , at chord Reynolds numbers $100\le Re\le 400$ . Laminar base flows have been generated using direct numerical simulation and selective frequency damping, as appropriate. Several families of unstable three-dimensional linear global (TriGlobal) eigenmodes have been identified and their dependence on geometric parameters has been examined in detail at $Re=400$ . The leading global mode A is associated with the peak recirculation in the three-dimensional laminar separation bubble formed on the wing and becomes unstable when recirculation reaches $\textit {O}(10\,\%)$ . On unswept wings, this mode peaks in the midspan region of the wake and moves towards the wing tip with increasing $\varLambda$ , following the displacement of peak recirculation; its linear amplification leads to wake unsteadiness. Additional amplified modes exist at nearly the same and higher frequencies compared to mode A. The critical $Re$ has been identified and it is shown that amplification increases with increasing sweep, up to $\varLambda \approx 10^\circ$ . At higher $\varLambda$ , all global modes become less amplified and are ultimately stable at $\varLambda =30^\circ$ . An increase in amplification of the leading mode with sweep was not observed over the $AR=4$ wing, where tip vortex effects were shown to dominate.

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Section: Numerical Workmentioning

confidence: 99%

Linear modal instabilities around post-stall swept finite wings at low Reynolds numbers

Burtsev

Zhang

et al. 2022

J. Fluid Mech.

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“…( 15) instead is much more efficient, despite the additional pseudo-time iterations per physicaltime step. These additional iterations can be minimized by using special marching schemes designed for the calculation of steady-states [5] when performing each pseudo-time integration.…”

Section: Recovering Time Accuracymentioning

confidence: 99%

Low Mach preconditioned density-based methods with implicit Runge–Kutta schemes in physical-time

Alves

Santos

Falcão³

2021

J Braz. Soc. Mech. Sci. Eng.

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As far as the authors are aware, low Mach preconditioned density-based methods found in the peer-reviewed literature only employ multi-step schemes for physical-time integration. This essentially limits the maximum achievable temporal accuracyorder of these methods to two, since the multi-step schemes of order higher than two are conditionally stable. However, the present paper shows how these methods can employ multi-stage schemes in physical-time using the same low Mach preconditioning techniques developed over the past few decades. In doing so, it opens up the rich field of Runge-Kutta time integration schemes to low Mach preconditioned density-based methods. One and two-dimensional test cases are used to demonstrate the capabilities of this novel approach. The former simulates the propagation of marginally stable entropy perturbations superposed on a uniform flow whereas the latter simulates the temporal growth of vorticity perturbations superposed on an absolutely unstable planar mixing-layer. A novel procedure is employed to generate highly accurate initial conditions for the two-dimensional test case, it minimizes receptivity regions as well as deleterious interactions with artificial boundary conditions due to the numerical error introduced by approximate initial conditions. These test cases show that second, third and fourth order multi-stage schemes with strong linear numerical stability can be successfully utilized for the physical-time integration of low Mach preconditioned density-based methods.

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“…The differentially heated cavity was used as a prototype application to demonstrate adjoint optimization of natural convection problems [25]. Finally, contributions to numerical aspects of flow instability and control analysis presented in this volume include a criterion for optimal grid adaptation associated with error sensitivity to grid refinement [16], as well as a novel framework for the computation of unstable steady basic flows [8], alternative to the well-established selective frequency damping method [2]. A boundary condition for the collocated solution of the two-and three-dimensional eigenvalue problems on collocated grids was presented [32] and a framework for the stability analysis of flows obtained by Lattice Boltzman methods [24] was also discussed.…”

Section: Contributions To the Present Volumementioning

confidence: 99%

Special issue on global flow instability and control

Theofilis

Colonius

2017

Theor. Comput. Fluid Dyn.

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This special issue is the second on the topic of "Global Flow Instability and Control," following the first in 2011. As with the previous special issue, the participants of the last two symposia on Global Flow Instability and Control, held in Crete, Greece, were invited to submit publications. These papers were peer reviewed according to the standards of the journal, and this issue represents a snapshot of the progress since 2011. In this preface, a sampling of important developments in the field since the first issue is discussed. A synopsis of the papers in this issue is given in that context.

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Minimal gain marching schemes: searching for unstable steady-states with unsteady solvers

Cited by 9 publications

References 33 publications

Linear modal instabilities around post-stall swept finite wings at low Reynolds numbers

Linear modal instabilities around post-stall swept finite wings at low Reynolds numbers

Low Mach preconditioned density-based methods with implicit Runge–Kutta schemes in physical-time

Special issue on global flow instability and control

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