TY - JOUR

T1 - Topology optimization for incompressible viscous fluid flow using the lattice kinetic scheme

AU - Xie, Suqiong

AU - Yaji, Kentaro

AU - Takahashi, Toru

AU - Isakari, Hiroshi

AU - Yoshino, Masato

AU - Matsumoto, Toshiro

N1 - Funding Information:
The authors are grateful to Dr. Kosuke Suzuki, Associate Professor of Shinshu University, for his valuable advice and assistance in the part of testing the new LKS.
Publisher Copyright:
© 2021 Elsevier Ltd

PY - 2021/9/1

Y1 - 2021/9/1

N2 - This paper presents a topology optimization method for flow channel design using the lattice kinetic scheme (LKS). LKS is a numerical scheme merging the lattice Boltzmann method with the kinetic scheme for solving the incompressible Navier-Stokes equations. In the lattice Boltzmann method, the discrete distribution functions for every grid in the analysis domain need to be stored to compute the flow field, while in the LKS, only the flow velocities and the densities are stored, and thus requiring less storage. Moreover, in the LKS, the macroscopic boundary conditions in terms of the velocity and the pressure can be imposed directly rather than considering the bounce-back boundary condition against the distribution function. In this study, the optimization is performed based on the gradient of the objective functional with respect to the design variables and the design sensitivity is computed by the adjoint variable method. Both the forward and the adjoint problems are solved using the LKS. The validity of the design sensitivity is verified by comparing it with the finite difference approximation of objective functional. Numerical examples of solving two-dimensional flow channel design problems are presented to demonstrate the proposed method.

AB - This paper presents a topology optimization method for flow channel design using the lattice kinetic scheme (LKS). LKS is a numerical scheme merging the lattice Boltzmann method with the kinetic scheme for solving the incompressible Navier-Stokes equations. In the lattice Boltzmann method, the discrete distribution functions for every grid in the analysis domain need to be stored to compute the flow field, while in the LKS, only the flow velocities and the densities are stored, and thus requiring less storage. Moreover, in the LKS, the macroscopic boundary conditions in terms of the velocity and the pressure can be imposed directly rather than considering the bounce-back boundary condition against the distribution function. In this study, the optimization is performed based on the gradient of the objective functional with respect to the design variables and the design sensitivity is computed by the adjoint variable method. Both the forward and the adjoint problems are solved using the LKS. The validity of the design sensitivity is verified by comparing it with the finite difference approximation of objective functional. Numerical examples of solving two-dimensional flow channel design problems are presented to demonstrate the proposed method.

KW - Adjoint lattice Boltzmann method

KW - Lattice kinetic scheme

KW - Topology optimization

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U2 - 10.1016/j.camwa.2021.05.032

DO - 10.1016/j.camwa.2021.05.032

M3 - Article

AN - SCOPUS:85108080330

SN - 0898-1221

VL - 97

SP - 251

EP - 266

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

ER -