The local convergence of Broyden-like methods on Lipschitzian problems in Hilbert spaces
SIAM Journal on Numerical Analysis
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Optimal control of two- and three-dimensional incompressible Navier-Stokes flows
Journal of Computational Physics
Instantaneous control of backward-facing step flows
Applied Numerical Mathematics
Second Order Methods for Optimal Control of Time-Dependent Fluid Flow
SIAM Journal on Control and Optimization
Perspectives in Flow Control and Optimization
Perspectives in Flow Control and Optimization
Symmetry-preserving discretization of turbulent flow
Journal of Computational Physics
A Note on the Extended Rosenbrock Function
Evolutionary Computation
Computational Optimization of Systems Governed by Partial Differential Equations
Computational Optimization of Systems Governed by Partial Differential Equations
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The current work focuses on the development and application of an efficient algorithm for optimization of three-dimensional turbulent flows, simulated using Direct Numerical Simulation (DNS) or Large-Eddy Simulations, and further characterized by large-dimensional optimization-parameter spaces. The optimization algorithm is based on Sequential Quadratic Programming (SQP) in combination with a damped formulation of the limited-memory BFGS method. The latter is suitable for solving large-scale constrained optimization problems whose Hessian matrices cannot be computed and stored at a reasonable cost. We combine the algorithm with a line-search merit function based on an L"1-norm to enforce the convergence from any remote point. It is first shown that the proposed form of the damped L-BFGS algorithm is suitable for solving equality constrained Rosenbrock type functions. Then, we apply the algorithm to an optimal-control test problem that consists of finding the optimal initial perturbations to a turbulent temporal mixing layer such that mixing is improved at the end of a simulation time horizon T. The controls are further subject to a non-linear equality constraint on the total control energy. DNSs are used to resolve all turbulent scales of motion, and a continuous adjoint formulation is employed to calculate the gradient of the cost functionals. We compare the convergence speed of the SQP L-BFGS algorithm to a conventional non-linear conjugate-gradient method (i.e. the current standard in DNS-based optimal control), and find that the SQP algorithm is more than an order of magnitude faster than the conjugate-gradient method.