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首页> 外文期刊>Computers & mathematics with applications >Discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice Boltzmann method
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Discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice Boltzmann method

机译：基于广义格子玻尔兹曼方法的离散伴随灵敏度分析

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摘要

A discrete adjoint sensitivity analysis for fluid flow topology optimization based on the lattice Boltzmann method (LBM) with multiple-relaxation-times (MRT) is developed. The lattice Boltzmann fluid solver is supplemented by a porosity model using a Darcy force. The continuous transition from fluid to solid facilitates a gradient based optimization process of the design topology of fluidic channels. The adjoint LBM equation, which is used to compute the gradient of the optimization objective with respect to the design variables, is derived in moment space and found to be as simple as the original LBM. The moment based spatial momentum derivatives used to express the discrete objective functional (cost function) have the advantage that the local stress tensor is a local quantity avoiding the numerical computation of gradients of the discrete velocity field. This is particularly useful if dissipation is a design criterion as demonstrated in this paper. The method is validated by a detailed comparison with results obtained by Borrvall et al. for Stokes flow. While their approach is only valid for Stokes flow (i.e. very low Reynolds numbers) our approach in its present form can in principle be applied for flows of different Reynolds numbers just like the Navier-Stokes equation based approaches. This point is demonstrated with a bending pipe example for various Reynolds numbers.
机译：提出了基于具有多重弛豫时间（MRT）的格子玻尔兹曼方法（LBM）的离散伴随灵敏度分析，用于流体流动拓扑优化。格子Boltzmann流体求解器通过使用达西力的孔隙度模型进行了补充。从流体到固体的连续过渡促进了流体通道设计拓扑的基于梯度的优化过程。在矩空间中导出了用于计算优化目标相对于设计变量的梯度的伴随LBM方程，发现它与原始LBM一样简单。用于表示离散目标函数（成本函数）的基于矩的空间动量导数具有以下优点：局部应力张量是局部量，从而避免了对离散速度场的梯度进行数值计算。如果耗散是本文所述的设计标准，则这特别有用。通过与Borrvall等人获得的结果进行详细比较，验证了该方法的有效性。斯托克斯流。尽管它们的方法仅适用于斯托克斯流（即非常低的雷诺数），但我们目前形式的方法原则上可以应用于不同雷诺数的流，就像基于Navier-Stokes方程的方法一样。通过各种雷诺数的弯管示例说明了这一点。

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  • 来源
    《Computers & mathematics with applications》 |2014年第10期|1374-1392|共19页
  • 作者

    Geng Liu; Martin Geier; Zhenyu Liu; Manfred Krafczyk; Tao Chen;

  • 作者单位

    Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 130033 Changchun, Jilin, PR China,University of Chinese Academy of Sciences, 100049 Beijing, PR China;

    Institute for Computational Modelling in Civil Engineering, Technische Universitaet Braunschweig, Pockelsstr. 3, 38106 Braunschweig, Germany;

    Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 130033 Changchun, Jilin, PR China;

    Institute for Computational Modelling in Civil Engineering, Technische Universitaet Braunschweig, Pockelsstr. 3, 38106 Braunschweig, Germany;

    Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 130033 Changchun, Jilin, PR China;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Discrete adjoint analysis; Lattice Boltzmann method; Topology optimization;

    机译：离散伴随分析;格子波尔兹曼法拓扑优化;

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