Sequential Quadratic Programming (SQP) for optimal control in direct numerical simulation of turbulent flow

Journal of Computational Physics

Volumn 256, Issue , 2014, Pages 1-16

  Badreddine, Hassan ^a,c   Vandewalle, Stefan ^b   Meyers, Johan ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b KU Leuven   (Belgium)

^c Paul Scherrer Insitut   (Switzerland)

Author keywords

Adjoint equations; Damped limited memory BFGS; Direct Numerical Simulations; Optimal control; Sequential Quadratic Programming; Turbulent mixing layer

Indexed keywords

CONJUGATE GRADIENT METHOD; CONSTRAINED OPTIMIZATION; DIRECT NUMERICAL SIMULATION; MIXING; NUMERICAL MODELS; QUADRATIC PROGRAMMING; SHOCK TUBES; TURBULENT FLOW;

'CURRENT; ADJOINT EQUATIONS; BFGS ALGORITHM; DAMPED LIMITED-MEMORY BFGS; DIRECT-NUMERICAL-SIMULATION; LIMITED MEMORY; NON LINEAR; OPTIMAL CONTROLS; SEQUENTIAL QUADRATIC PROGRAMMING; TURBULENT MIXING LAYERS;

LARGE EDDY SIMULATION;

EID: 84884241819     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2013.08.044     Document Type: Article

References (47)

1. Bewley T.R., Moin P., Temam R. DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms. J. Fluid Mech. 2001, 447:179-225.
2. Wei M.J., Freund J.B. A noise-controlled free shear flow. J. Fluid Mech. 2006, 546:123-152.
3. Delport S., Baelmans M., Meyers J. Constrained optimization of turbulent mixing-layer evolution. J. Turbul. 2009, 10(18):26.
4. Delport S., Baelmans M., Meyers J. Maximizing dissipation in a turbulent shear flow by optimal control of its initial state. Phys. Fluids 2011, 23:045105.
5. Freund J.B. Adjoint-based optimization for understanding and suppressing jet noise. J. Sound Vib. 2011, 330:4114-4122.
6. Hilgers A., Boersma B.J. Optimization of turbulent jet mixing. Fluid Dyn. Res. 2001, 29(6):345-368.
7. Kern S., Koumoutsakos P. Simulations of optimized anguilliform swimming. J. Exp. Biol. 2006, 209:4841-4857.
8. Verstraete T., Alsalihi Z., Van den Braembussche R.A. Multidisciplinary optimization of a radial compressor for microgas turbine applications. Trans. ASME, J. Turbomach. 2010, 132:031004.
9. Gunzburger M.D. Perspectives in Flow Control and Optimization 2003, SIAM, Philadelphia.
10. Abergel F., Temam R. On some control problems in fluid mechanics. Theor. Comput. Fluid Dyn. 1990, 1:303-325.
11. Optimal Control of Viscous Flow 1998, SIAM, Philadelphia. S.S. Sritharan (Ed.).
12. Giles M.B., Pierce N.A. Adjoint equations in CFD - Duality, boundary conditions and solution behavior. 13th AIAA Computational Fluid Dynamics Conference, AIAA-1997-1850 1997.
13. Jameson A., Martinelli L., Pierce N.A. Optimum aerodynamic design using the Navier-Stokes equations. Theor. Comput. Fluid Dyn. 1998, 10(1-4):213-237.
14. Choi H., Hinze M., Kunisch K. Instantaneous control of backward-facing step flows. Appl. Numer. Math. 1999, 31:133-158.
15. Giles M.B., Pierce N.A. An introduction to the adjoint approach to design. Flow Turbul. Combust. 2000, 65(3-4):393-415.
16. Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Numerical Recipes in FORTRAN 77: The Art of Scientific Computing 1996, Cambridge University Press. 2nd edn.
17. Luenberger D.G. Linear and Nonlinear Programming 2005, Springer, New York. 2nd edn.
18. Nocedal J., Wright S. Numerical Optimization 2006, Springer, New York. 2nd edn.
19. Brent R. Algorithms for Minimization Without Derivatives. Series in Automatic Computation 1973, Prentice-Hall, Inc., Englewood Cliffs, NJ.
20. Nicoud F., Baggett J.S., Moin P., Cabot W. Large eddy simulation wall-modeling based on suboptimal control theory and linear stochastic estimation. Phys. Fluids 2001, 13(10):2968-2984.
21. Templeton J.A., Wang M., Moin P. An efficient wall model for large-eddy simulation based on optimal control theory. Phys. Fluids 2013, 18(2).
22. Hinze M., Pinnau R., Ulbrich M., Ulbrich S. Optimization with PDE Constraints. Mathematical Modelling: Theory and Applications 2009, vol. 23. Springer.
23. Ghattas O., Bark J.-H. Optimal control of two- and three-dimensional incompressible Navier-Stokes flows. J. Comput. Phys. 1997, 136:231-244.
24. Heinkenschloss M. Formulation and analysis of a sequential quadratic programming method for the optimal Dirichlet boundary control of Navier-Stokes flow. Applied Optimization 1998, vol. 15:178-203. Springer, Dordrecht. W.H. Hager, P.M. Pardalos (Eds.).
25. Hinze M., Kunisch K. Second order methods for optimal control of time-dependent fluid flow. SIAM J. Control Optim. 2001, 40:925-946.
26. Hintermüller M., Hinze M. Globalization of SQP-methods in control of the instationary Navier-Stokes equations. ESAIM. Math. Model. Numer. Anal. 2002, 36:725-746.
27. Ravindran S.S. Numerical approximation of optimal control of unsteady flows using SQP and time decomposition. Int. J. Numer. Methods Fluids 2004, 45:21-42.
28. Ulbrich M. Constrained optimal control of Navier-Stokes flow by semismooth Newton methods. Syst. Control. Lett. 2003, 48:297-311.
29. Rogers M.M., Moser R.D. The 3-dimensional evolution of a plane mixing layer - the Kelvin-Helmholtz rollup. J. Fluid Mech. 1992, 243:183-226.
30. Moser R.D., Rogers M.M. The 3-dimensional evolution of a plane mixing layer - pairing and transition to turbulence. J. Fluid Mech. 1993, 247:275-320.
31. Rogers M.M., Moser R.D. Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids 1994, 6(2):903.
32. Vreman B., Geurts B., Kuerten H. Large-eddy simulation of the turbulent mixing layer. J. Fluid Mech. 1997, 339:357-390.
33. Pierrehumbert R.T., Widnall S.E. The two-dimensional and 3-dimensional instabilities of a spatially periodic shear-layer. J. Fluid Mech. 1982, 114(Jan.):59-82.
34. Pironneau O. On optimum design in fluid mechanics. J. Fluid Mech. 1974, 64(1):97-110.
35. Canuto C., Hussaini M., Quarteroni A., Zang T. Spectral Methods, Fundamentals in Single Domains. Scientific Computation 2006, Springer.
36. Verstappen R., Veldman A.E.P. Symmetry-preserving discretization of turbulent flow. J. Comput. Phys. 2003, 187(1):343-368.
37. Fletcher R. Practical Methods of Optimization 1987, John Wiley, Chichester.
38. Gill P.E., Murray W., Wright M. Practical Optimization 1982, Academic Press, London.
39. Boggs P.T., Tolle J.W. Sequential quadratic programming. Acta Numer. 1982, 4:1-51.
40. Powell M.J. A fast algorithm for nonlinearly constrained optimization calculations. Lecture Notes in Mathematics 1978, 630. Springer Verlag. G.A. Watson (Ed.).
41. Griewank A. The local convergence of Broyden-like methods in Lipschitzian problems in Hilbert spaces. SIAM J. Numer. Anal. 1987, 24:684-705.
42. Han S.P. A globally convergent method for nonlinear programming. J. Optim. Theory Appl. 1977, 22:297.
43. Armijo L. Minimization of functions having Lipschitz continuous first partial derivatives. Pac. J. Math. 1966, 16:1-3.
44. Byrd R.H., Tapia R.A., Zhang Y. An SQP augmented Lagrangian BFGS algorithm for constrained optimization. SIAM J. Optim. 1992, 2:210-241.
45. Shang Y.-W., Qiu Y.-H. A note on the extended Rosenbrock function. Evol. Comput. 2006, 14:119-126.
46. Rosenbrock H.H. An automatic method for finding the greatest or least value of a function. Comput. J. 1960, 3:175-184.
47. Borzi A., Schulz V. Computational Optimization of Systems Governed by Partial Differential Equations 2012, SIAM, Philadelphia.