Suboptimal feedback control of flow separation by POD model reduction. (English) Zbl 1228.49041
Biegler, Lorenz T. (ed.) et al., Real-time PDE-constrained optimization. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-0-898716-21-4/pbk; 978-0-89871-893-5/ebook). Computational Science & Engineering, 233-250 (2007).
Summary: Optimal design for fluid dynamical systems, which is a useful computational tool in aerodynamic drag reduction, turbulence delay, and combustion control, etc., has been an interesting research area for many years.
Generally speaking it is infeasible to carry out feedback design on infinite-dimensional fluid dynamical systems by numerically solving the Dynamic Programming Equation (DPE) or the Hamilton-Jacobi-Bellman (HJB) equation. The development of Proper Orthogonal Decomposition (POD) techniques in recent years provides a promising approach to perform suboptimal feedback design on reduced-order models. In this technique, a set of basis functions is constructed from preselected snapshots. Subsequently, the fluid dynamic system is projected onto the space spanned by the basis functions, and the infinite-dimensional nonlinear Partial Differential Equations (PDEs) of the fluid system are reduced to finite-dimensional Ordinary Differential Equations (ODEs). Then the optimal design is performed on this reduced system at reasonable computational cost. This suboptimal approach has been applied for open-loop design on the one-dimensional Burgers equation and on the two-dimensional Navier-Stokes (NS) equations with different geometrical shapes.
The prohibitive computational cost of feedback design for nonlinear systems strongly suggests the use of parallel computations. In this work several computers are exploited concurrently; furthermore, on different computers, a different number of MATLAB sessions is invoked, depending on the overall performance and the available computational power of each computer. The message passing interface based on MATLAB software is utilized to exchange data between MATLAB sessions on different computers. This parallel implementation reduces the computing time to an acceptable level.
For the entire collection see [Zbl 1117.49004].
Generally speaking it is infeasible to carry out feedback design on infinite-dimensional fluid dynamical systems by numerically solving the Dynamic Programming Equation (DPE) or the Hamilton-Jacobi-Bellman (HJB) equation. The development of Proper Orthogonal Decomposition (POD) techniques in recent years provides a promising approach to perform suboptimal feedback design on reduced-order models. In this technique, a set of basis functions is constructed from preselected snapshots. Subsequently, the fluid dynamic system is projected onto the space spanned by the basis functions, and the infinite-dimensional nonlinear Partial Differential Equations (PDEs) of the fluid system are reduced to finite-dimensional Ordinary Differential Equations (ODEs). Then the optimal design is performed on this reduced system at reasonable computational cost. This suboptimal approach has been applied for open-loop design on the one-dimensional Burgers equation and on the two-dimensional Navier-Stokes (NS) equations with different geometrical shapes.
The prohibitive computational cost of feedback design for nonlinear systems strongly suggests the use of parallel computations. In this work several computers are exploited concurrently; furthermore, on different computers, a different number of MATLAB sessions is invoked, depending on the overall performance and the available computational power of each computer. The message passing interface based on MATLAB software is utilized to exchange data between MATLAB sessions on different computers. This parallel implementation reduces the computing time to an acceptable level.
For the entire collection see [Zbl 1117.49004].
