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Topology optimization of unsteady flow problems using the lattice Boltzmann method

Published: 15 February 2016 Publication History

Abstract

This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems. The optimization problem is solved with a gradient based method, and the design sensitivities are computed by solving the discrete adjoint problem. For moderate Reynolds number flows, it is demonstrated that topology optimization can successfully account for unsteady effects such as vortex shedding and time-varying boundary conditions. Such effects are relevant in several engineering applications, i.e. fluid pumps and control valves.

References

[1]
M.P. Bendsøe, O. Sigmund, Topology Optimization: Theory, Methods and Applications, Springer, 2004.
[2]
M.P. Bendsøe, N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Comput. Methods Appl. Mech. Eng., 71 (1988) 197-224.
[3]
T. Borrvall, J. Petersson, Topology optimization of fluids in Stokes flow, Int. J. Numer. Methods Fluids, 41 (2003) 77-107.
[4]
A. Gersborg-Hansen, O. Sigmund, R.B. Haber, Topology optimization of channel flow problems, Struct. Multidiscip. Optim., 30 (2005) 181-192.
[5]
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 (2006) 975-1001.
[6]
N. Aage, A. Gersborg-Hansen, O. Sigmund, Topology optimization of large scale Stokes flow problems, Struct. Multidiscip. Optim., 35 (2008) 175-180.
[7]
C.S. Andreasen, A.R. Gersborg, O. Sigmund, Topology optimization of microfluidic mixers, Int. J. Numer. Methods Fluids, 61 (2009) 498-513.
[8]
D. Makhija, G. Pingen, R. Yang, K. Maute, Topology optimization of multi-component flows using a multi-relaxation time lattice Boltzmann method, Comput. Fluids, 67 (2012) 104-114.
[9]
M.C. Sukop, D.T. Thorne, Lattice Boltzmann Modelling, Springer, 2007.
[10]
D.A. Wolf-Gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models - An Introduction, Springer, 2005.
[11]
M.A.A. Spaid, F. Phelan, Lattice Boltzmann methods for modeling microscale flow in fibrous porous media, Phys. Fluids, 9 (1997) 2468-2474.
[12]
S.D.C. Walsh, H. Burwinkle, M.O. Saar, A new partial-bounceback lattice-Boltzmann method for fluid flow through heterogeneous media, Comput. Geosci., 35 (2009) 1186-1193.
[13]
J. Zhu, J. Ma, An improved gray lattice Boltzmann model for simulating fluid flow in multi-scale porous media, Adv. Water Resour., 56 (2013) 61.
[14]
T. Inamuro, T. Ogata, S. Tajima, N. Konishi, A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comput. Phys., 198 (2004) 628-644.
[15]
P. Asinari, Semi-implicit-linearized multiple-relaxation-time formulation of lattice Boltzmann schemes for mixture modeling, Phys. Rev. E, 73 (2006).
[16]
G. Pingen, A. Evgrafov, K. Maute, Topology optimization of flow domains using the lattice Boltzmann method, Struct. Multidiscip. Optim., 34 (2007) 507-524.
[17]
G. Pingen, M. Waidmann, A. Evgrafov, K. Maute, A parametric level-set approach for topology optimization of flow domains, Struct. Multidiscip. Optim., 41 (2010) 117-131.
[18]
S. Kreissl, G. Pingen, K. Maute, An explicit level set approach for generalized shape optimization of fluids with the lattice Boltzmann method, Int. J. Numer. Methods Fluids, 65 (2011) 496-519.
[19]
K. Yaji, T. Yamada, M. Yoshino, Topology optimization using the lattice Boltzmann method incorporating level set boundary expressions, J. Comput. Phys., 274 (2014) 158.
[20]
M.M. Tekitek, M. Bouzidi, F. Dubois, P. Lallemand, Adjoint lattice Boltzmann equation for parameter identification, Comput. Fluids, 35 (2006) 805-813.
[21]
M.J. Krause, G. Thaeter, V. Heuveline, Adjoint-based fluid flow control and optimisation with lattice Boltzmann methods, Comput. Math. Appl., 65 (2013) 945-960.
[22]
S. Kreissl, G. Pingen, K. Maute, Topology optimization for unsteady flow, Int. J. Numer. Methods Eng., 87 (2011).
[23]
Y. Deng, Z. Liu, P. Zhang, Y. Liu, Y. Wu, Topology optimization of unsteady incompressible Navier-Stokes flows, J. Comput. Phys., 230 (2011) 6688-6708.
[24]
K. Yonekura, Y. Kanno, A flow topology optimization method for steady state flow using transient information of flow field solved by lattice Boltzmann method, Struct. Multidiscip. Optim., 51 (2015) 159-172.
[25]
X. He, L. Luo, A priori derivation of the lattice Boltzmann equation, Phys. Rev. E, 55 (1997) R6333-R6336.
[26]
X. He, L. Luo, Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation, Phys. Rev. E, 56 (1997) 6811-6817.
[27]
P.L. Bhatnagar, E.P. Gross, M. Krook, A model for collision processes in gases. I: small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94 (1954).
[28]
X. He, L. Luo, Lattice Boltzmann model for the incompressible Navier-Stokes equation, J. Stat. Phys., 88 (1997) 927-944.
[29]
S. Chapman, T. Cowling, The Mathematical Theory of Non-Uniform Gases, Cambridge University Press, 1970.
[30]
M. Junk, A. Klar, L.S. Luo, Asymptotic analysis of the lattice Boltzmann equation, J. Comput. Phys., 210 (2005) 676-704.
[31]
S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, 2001.
[32]
Q. Zou, X. He, On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Phys. Fluids, 9 (1997) 1591-1596.
[33]
M. Junk, Z. Yang, Outflow boundary conditions for the lattice Boltzmann method, Prog. Comput. Fluid Dyn., 8 (2008) 38-48.
[34]
O. Dardis, J. McCloskey, Lattice Boltzmann scheme with real numbered solid density for the simulation of flow in porous media, Phys. Rev. E, 54 (1998) 4834-4837.
[35]
O. Dardis, J. McCloskey, Permeability porosity relationships from numerical simulations of fluid flow, Geophys. Res. Lett., 25 (1998) 1471-1474.
[36]
G. Liu, M. Geier, Z. Liu, M. Krafczyk, T. Chen, Discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice Boltzmann method, Comput. Math. Appl., 68 (2014) 1374-1392.
[37]
A. Griewank, A. Walther, Algorithm 799: revolve: an implementation of checkpointing for the reverse or adjoint mode of computational differentiation, ACM Trans. Math. Softw., 26 (2000) 19-45.
[38]
Q. Wang, P. Moin, G. Iaccarino, Minimal repetition dynamic checkpointing algorithm for unsteady adjoint calculation, SIAM J. Sci. Comput., 31 (2009) 2549-2567.
[39]
J. Guest, J. Prevost, T. Belytschko, Achieving minimum length scale in topology optimization using nodal design variables and projection functions, Int. J. Numer. Methods Eng., 61 (2004) 238-254.
[40]
O. Sigmund, Morphology-based black and white filters for topology optimization, Struct. Multidiscip. Optim., 33 (2007) 401-424.
[41]
S. Xu, Y. Cai, G. Cheng, Volume preserving nonlinear density filter based on heaviside functions, Struct. Multidiscip. Optim., 41 (2010) 495-505.
[42]
F. Wang, B.S. Lazarov, O. Sigmund, On projection methods, convergence and robust formulations in topology optimization, Struct. Multidiscip. Optim., 43 (2011) 767-784.
[43]
M. Zhou, B.S. Lazarov, F. Wang, O. Sigmund, Minimum length scale in topology optimization by geometric constraints, Comput. Methods Appl. Mech. Eng., 293 (2015) 266-282.
[44]
K. Svanberg, The method of moving asymptotes - a new method for structural optimization, Int. J. Numer. Methods Eng., 24 (1987) 359-373.

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Published In

cover image Journal of Computational Physics
Journal of Computational Physics  Volume 307, Issue C
February 2016
730 pages

Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 15 February 2016

Author Tags

  1. Lattice Boltzmann
  2. Topology optimization
  3. Unsteady flow

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