A flow topology optimization method for steady state flow using transient information of flow field solved by lattice Boltzmann method

A topology optimization method for fluid flow using transient information is proposed. In many conventional methods, the design domain is updated using steady state information which is obtained after solving the flow field equations completely. Hence we must solve the flow field at each iterative which leads to high computational cost. In contrast, the proposed method updates the design domain using transient information of flow field. Hence the flow field is solved only once. The flow field is solved by lattice Boltzmann method (LBM). It is found that, by using LBM, the flow field is stably computed even though the design domain drastically changes during the computation. The design domain is updated according to sensitivity analysis. In many conventional methods, the sensitivity of objective functionals under lattice Boltzmann equations is obtained using additional adjoint equations. However, in the proposed method, the sensitivity is explicitly formulated and computed without using adjoint variables. In this paper, we show some numerical examples for low Reynolds number flows. The results demonstrate good convergence property in small computation time.

[1]  Kurt Maute,et al.  Adjoint parameter sensitivity analysis for the hydrodynamic lattice Boltzmann method with applications to design optimization , 2009 .

[2]  Qing Li,et al.  A variational level set method for the topology optimization of steady-state Navier-Stokes flow , 2008, J. Comput. Phys..

[3]  Ole Sigmund,et al.  Topology optimization of large scale stokes flow problems , 2008 .

[4]  K. Maute,et al.  A parametric level-set approach for topology optimization of flow domains , 2010 .

[5]  G. Allaire,et al.  Structural optimization using sensitivity analysis and a level-set method , 2004 .

[6]  Limin Wang,et al.  Heuristic optimality criterion algorithm for shape design of fluid flow , 2010, J. Comput. Phys..

[7]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[8]  Suresh V. Garimella,et al.  Topological design of channels for squeeze flow optimization of thermal interface materials , 2012 .

[9]  Stefan Ulbrich,et al.  A Continuous Adjoint Approach to Shape Optimization for Navier Stokes Flow , 2009 .

[10]  K. Maute,et al.  Conceptual design of aeroelastic structures by topology optimization , 2004 .

[11]  R. Haftka.  Simultaneous analysis and design , 1985 .

[12]  O. Pironneau.  On optimum profiles in Stokes flow , 1973, Journal of Fluid Mechanics.

[13]  J. Petersson,et al.  Topology optimization of fluids in Stokes flow , 2003 .

[14]  O. Sigmund,et al.  Topology optimization of channel flow problems , 2005 .

[15]  K. Maute,et al.  Topology optimization of flexible micro-fluidic devices , 2010 .

[16]  Pierre Lallemand,et al.  Lattice Gas Hydrodynamics in Two and Three Dimensions , 1987, Complex Syst..

[17]  Zhaoli Guo,et al.  Lattice Boltzmann model for incompressible flows through porous media. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Ping Zhang,et al.  Topology optimization of unsteady incompressible Navier-Stokes flows , 2011, J. Comput. Phys..

[19]  K. Maute,et al.  Topology optimization for unsteady flow , 2011 .

[20]  J. Boon.  The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , 2003 .

[21]  Tuomo Rossi,et al.  Comparison of implementations of the lattice-Boltzmann method , 2008, Comput. Math. Appl..

[22]  K. Maute,et al.  Topology optimization of flow domains using the lattice Boltzmann method , 2007 .

[23]  Kurt Maute,et al.  Lattice Boltzmann Topology Optimization for Transient Flow , 2011 .

[24]  Qing Li,et al.  Evolutionary topology and shape design for general physical field problems , 2000 .

[25]  Gudrun Thäter,et al.  Adjoint-based fluid flow control and optimisation with lattice Boltzmann methods , 2013, Comput. Math. Appl..

[26]  Kurt Maute,et al.  Optimal design for non-Newtonian flows using a topology optimization approach , 2010, Comput. Math. Appl..

[27]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[28]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[29]  Oliver Moos,et al.  Bionic Optimization of Air-Guiding Systems , 2004 .

[30]  James K. Guest,et al.  Topology optimization of creeping fluid flows using a Darcy–Stokes finite element , 2006 .