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	KTH Computational Science and Engineering Centre

Title	Speaker
Linear and non-linear optimisation of shear flows	Antonios Monokrousos

Location	Time and Date
PDC seminar room, Teknikringen 14, level 3	14.30-15.30, 2011-03-09 (Wed)

Abstract
Adjoint-based iterative methods are employed in order to compute optimal disturbances in the case of both linear and non-linear perturbations in shear flows. The Lagrangian approach is used where an objective function is chosen and constraints are assigned. We are looking for stationary points of the Lagrange function with respect to the different design variables where optimality is fulfilled. To this purpose power iterations within a matrix-free framework are used, where the state is marched forward in time with a normal DNS solver and backward with the adjoint solver until a chosen convergence criterion is fulfilled. In the linear framework the global linear stability of the flat-plate boundary-layer flow to three-dimensional disturbances is studied. We consider both the optimal initial condition leading to the largest departure from the laminar flow at finite times and the optimal time-periodic forcing leading to the largest asymptotic response. The objective function of the optimization is the kinetic energy of the flow perturbations and the constraints involve the linearised Navier--Stokes equations. In the non-linear framework, we determine the initial condition on the laminar/turbulent boundary closest to the laminar state for plane Couette flow. Resorting to the general evolution criterion of non-equilibrium systems we optimize the route to the statistically steady turbulent state, i.e. the state characterized by the largest entropy production. This is the first time information from the fully turbulent state is included in the optimisation procedure. We demonstrate that the optimal initial condition is localized in space for realistic flow domains, larger than those previously used. We investigate the transition path and show how localized perturbations evolve into bent streaks that later break down to turbulence.

Abstract

Adjoint-based iterative methods are employed in order to compute optimal disturbances in the case of both linear and non-linear perturbations in shear flows. The Lagrangian approach is used where an objective function is chosen and constraints are assigned. We are looking for stationary points of the Lagrange function with respect to the different design variables where optimality is fulfilled. To this purpose power iterations within a matrix-free framework are used, where the state is marched forward in time with a normal DNS solver and backward with the adjoint solver until a chosen convergence criterion is fulfilled.
In the linear framework the global linear stability of the flat-plate boundary-layer flow to three-dimensional disturbances is studied. We consider both the optimal initial condition leading to the largest departure from the laminar flow at finite times and the optimal time-periodic forcing leading to the largest asymptotic response. The objective function of the optimization is the kinetic energy of the flow perturbations and the constraints involve the linearised Navier--Stokes equations.
In the non-linear framework, we determine the initial condition on the laminar/turbulent boundary closest to the laminar state for plane Couette flow. Resorting to the general evolution criterion of non-equilibrium systems we optimize the route to the statistically steady turbulent state, i.e. the state characterized by the largest entropy production. This is the first time information from the fully turbulent state is included in the optimisation procedure. We demonstrate that the optimal initial condition is localized in space for realistic flow domains, larger than those previously used. We investigate the transition path and show how localized perturbations evolve into bent streaks that later break down to turbulence.

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Uppdaterad: 2007-01-06