×

Adjoint-based optimization of particle trajectories in laminar flows. (English) Zbl 1338.76027

Summary: We present a performant numerical algorithm for the optimal control of particle controls in low Reynolds number flows. In particular, circular particles with mass are considered. An optimal control problem for the particle trajectories is presented, which is solved by means of a steepest descent algorithm. Here, the derivative information is obtained using adjoint calculus. Finally, numerical results are presented underlining the feasibility of our approach.

MSC:

76D55 Flow control and optimization for incompressible viscous fluids
49M20 Numerical methods of relaxation type
76D05 Navier-Stokes equations for incompressible viscous fluids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Huynh, W. H.; Diettmer, J. J.; Libby, W. C.; Whiting, G. L.; Alivisatos, A. P., Controlling the morphology of nanocrystal-polymer composites for solar cells, Adv. Funct. Mater., 13, 73-79 (2003)
[4] Hou, L.; Ravindran, S.; Yan, Y., Numerical solution of optimal distributed control problems for incompressible flows, IJCFD, 8, 99-114 (1997) · Zbl 0892.76044
[5] Hou, L.; Yan, Y., Dynamics for controlled Navier-Stokes systems with piecewise distributed controls, SIAM J. Control Optim., 35, 2, 654-677 (1997) · Zbl 0871.49008
[6] Hinze, M.; Volkwein, K., Instantaneous control for the Burgers equation: convergence analysis and numerical implementation, Nonlinear Anal., 50, 1-26 (2002) · Zbl 1022.49001
[7] Hinze, M., Optimal and Instantaneous Control of the Instationary Navier-Stokes Equations (2002), University Dresden: University Dresden Habilitationsschrift
[8] Cox, R., The motion of long slender bodies in a viscous fluid. Part 1. General theory, J. Fluid Mech., 44, 4, 791-810 (1970) · Zbl 0267.76015
[9] Doi, M.; Chen, D., Simulation of aggregating colloids in shear flow, J. Chem. Phys., 90, 10, 5271-5279 (1989)
[10] Fan, F.; Ahmadi, G., Wall deposition of small ellipsoids from turbulent air flows - a Brownian dynamics simulation, J. Aerosol Sci., 31, 10, 1205-1229 (2000)
[11] Glowinski, R.; Pan, T.; Hesla, T.; Joseph, D. D., A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flows, 25, 755-794 (1999) · Zbl 1137.76592
[12] Glowinski, R.; Pan, T.; Hesla, T.; Joseph, D. D.; Périaux, J., A distributed Lagrange multiplier/fictitious domain method for the simulation of flow around moving rigid bodies: application to particulate flow, Comput. Methods Appl. Mech. Eng., 184, 241-267 (2000) · Zbl 0970.76057
[13] Hu, H.; Joseph, D.; Chrochet, M., Direct simulation of fluid particle motions, Theor. Comput. Fluid Dyn., 3, 285-306 (1992) · Zbl 0754.76054
[14] Jeffery, G., The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Soc. Lond. A, 161, 161-179 (1922) · JFM 49.0748.02
[15] Pittman, J.; Kasiri, N., The motion of rigid rod-like particles suspended in non-homogeneous flow fields, Int. J. Multiphase Flow, 18, 1077-1091 (1992) · Zbl 1144.76442
[16] Lázaro, B.; Lasheras, J., Particle dispersion in a turbulent, plane, free shear layer, Phys. Fluids A, 1, 6, 1035-1044 (1989)
[17] Lee, S.; Durst, F., On the motion of particles in turbulent duct flow, Int. J. Multiphase Flow, 8, 125-146 (1982)
[18] Liron, N.; Barta, E., Motion of a rigid particle in Stokes flow: a new second-kind boundary-integral equation formulation, J. Fluid Mech., 238, 579-598 (1992) · Zbl 0756.76020
[19] Pan, T.; Joseph, D. D.; Glowinski, R., Simulating the dynamics of fluid-ellipsoid interactions, Comput. Struct., 83, 463-478 (2005)
[20] Pismen, L.; Nir, A., On the motion of suspended particles in stationary homogeneous turbulence, JFM, 84, 193-206 (1978) · Zbl 0373.76071
[21] Glowinski, T. P.R.; Périaux, J., A Lagrange multiplier/fictitious domain method for the numerical simulation of incompressible viscous flow around moving rigid bodies: (I) case where the rigid body motions are known a priori, C.R. Acad. Sci. Paris, 324, 362-369 (1997) · Zbl 0885.76073
[22] Glowinski, T. P.R.; Périaux, J., Distributed Lagrange multiplier methods for incompressible viscous flow around moving rigid bodies, Comput. Methods Appl. Mech. Eng., 151, 181-194 (1998) · Zbl 0916.76052
[23] Ross, R.; Klingenberg, D., Dynamic simulation of flexible fibers composed of linked rigid bodies, J. Chem. Phys., 106, 7, 2949-2960 (1997)
[24] Shih, T.; Lumley, J., Second-order modelling of particle dispersion in a turbulent flow, JFM, 163, 349-363 (1986) · Zbl 0595.76056
[25] Hu, H., Direct Simulation of flows of solid-liquid mixtures, Int. J. Multiphase Flow, 22, 335-352 (1996) · Zbl 1135.76442
[26] Esmaeeli, A.; Tryggvason, G., irect numerical simulations of bubbly flows. Part 1. Low Reynolds number arrays, J. Fluid. Mech., 377, 313-345 (1998) · Zbl 0934.76090
[27] Hu, H.; Patankar, N.; Zhu, M., Direct numerical simulation of fluid-solid systems using the arbitrary Lagrangian-Eularian technique, J. Comput. Phys., 169, 427-462 (2001) · Zbl 1047.76571
[28] Hyman, M., Non-iterative numerical solution of boundary-value problems, Appl. Sci. Res. Sec. B, 2, 325-351 (1952) · Zbl 0048.10201
[29] Saul’ev, V., On solving boundary-value problems on high performance computers by fictitious-domain methods, Sib. Math. J., 4, 912-925 (1963)
[30] Buzbee, B.; Dorr, F.; George, J.; Golub, G., The direct solution of the discrete Poisson equation on irregular regions, SIAM J. Numer. Anal., 8, 722-736 (1971) · Zbl 0231.65083
[31] Diaz-Goano, C.; Minev, P.; Nandakumar, K., A fictitious domain/finite element method for particulate flows, J. Comput. Phys., 192, 105-123 (2003) · Zbl 1047.76042
[32] Glowinski, R.; Pan, T.; Hesla, T.; Joseph, D.; Périaux, J., A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow, J. Comput. Phys., 169, 363-426 (2001) · Zbl 1047.76097
[33] Patankar, N.; Singh, P.; Joseph, D.; Glowinski, R.; Pan, T., A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow, 26, 1509-1524 (2000) · Zbl 1137.76712
[34] Feistauer, M., Mathematical Methods in Fluid Dynamics (1993), Longman Scientific & Technical · Zbl 0819.76001
[35] Chorin, A.; Marsden, J., A Mathematical Introduction to Fluid Mechanics (1993), Springer Verlag: Springer Verlag New York · Zbl 0774.76001
[37] Maury, B., A many-body lubrication model, C.R Acad. Sci. Paris, 325, 1053-1058 (1997) · Zbl 0898.76019
[38] Glowinski, R.; Pan, T.; Périaux, J., A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations, Comput. Methods Appl. Mech. Eng., 112, 133-148 (1994) · Zbl 0845.76069
[39] Hinze, M.; Pinnau, R.; Ulbrich, M.; Ulbrich, S., Optimization with PDE Constraints, Mathematical Modelling: Theory and Applications, vol. 23 (2009), Springer: Springer Berlin - Heidelberg - New York · Zbl 1167.49001
[40] Leunberger, D., Optimization by Vector Space Methods (1969), John Wiley and Sons: John Wiley and Sons New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.