Abstract
This chapter presents topology optimization of two-phase flow with immiscible fluids, where the level set method and diffuse-interface model are combined to implement the proposed method.
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S. Zhou, Q. Li, A variational level set method for the topology optimization of steady-state Navier-Stokes flow. J. Comput. Phys. 227, 10178–10195 (2008)
X. Duan, Y. Ma, R. Zhang, Shape-topology optimization for Navier-Stokes problem using variational level set method. J. Comput. Appl. Math. 222, 487–499 (2008)
T. Borrvall, J. Petersson, Topology optimization of fluid in Stokes flow. Int. J. Numer. Meth. Fluids 41, 77–107 (2003)
J.W. Cahn, J. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28, 258–267 (1958)
J.W. Cahn, On spinodal decomposition. Acta Metall. 9, 795–801 (1961)
D. Jacqmin, Contact-line dynamics of a diffuse fluid interface. J. Fluid Mech. 402, 57–88 (2000)
J.W. Cahn, Critical-point wetting. J. Chem. Phys. 66, 3667–3672 (1977)
T. Qian, X.P. Wang, P. Sheng, Molecular hydrodynamics of the moving contact line in two-phase immiscible flows. Comm. Comput. Phys. 1, 1–52 (2006)
P. Yue, C. Zhou, J.J. Feng, C.F. Ollivier-Gooch, H.H. Hu, Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing. J. Comput. Phys. 219, 47–67 (2006)
Y. Deng, Z. Liu, Y. Wu, Topology optimization of steady and unsteady incompressible Navier-Stokes flows driven by body forces. Struct. Multidisc. Optim. 47, 555–570 (2013)
P. Yue, J.J. Feng, C. Liu, J. Shen, A diffuse-interface method for simulating two-phase flows of complex fluids. J. Fluid Mech. 515, 293–317 (2004)
S. Osher, R.P. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, New York, 2002)
J. Nocedal, S. Wright, Numerical Optimization, 2nd edn. (Springer, 2000)
L.H. Olesen, F. Okkels, H. Bruus, A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow. Int. J. Numer. Methods Eng. 65, 975–1001 (2006)
Y. Deng, Z. Liu, P. Zhang, Y. Liu, Y. Wu, Topology optimization of unsteady incompressible Navier-Stokes flow. J. Comput. Phys. 230, 6688–6708 (2011)
H.C. Elman, D.J. Silvester, A.J. Wathen, Finite Elements and Fast Iterative: Solvers With Applications in Incompressible Fluid Dynamics (Oxford University Press, 2006)
S. Osher, R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, New York, 2003)
R. Defay, I. Prigogine, Surface Tension and Adsorption, Longmans (Green & Co Ltd, London, 1966)
L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Pergamon Press, Oxford, 1987)
M.B. Giles, N.A. Pierce, An introduction to the adjoint approach to design. Flow, Turbulence and Combustion 65, 393–415 (2000)
M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich, Optimization with PDE Constraints (Springer, Berlin, 2009)
B. Mohammadi, O. Pironneau, Applied Shape Optimization for Fluids (Oxford University Press, USA, Oxford, 2010)
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Deng, Y., Wu, Y., Liu, Z. (2018). Topology Optimization for Two-Phase Flows. In: Topology Optimization Theory for Laminar Flow. Springer, Singapore. https://doi.org/10.1007/978-981-10-4687-2_4
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DOI: https://doi.org/10.1007/978-981-10-4687-2_4
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