基于格子-波尔兹曼法的流体拓扑优化

	基于格子-波尔兹曼法的流体拓扑优化
	刘耕
学位类型	硕士
导师	陈涛,刘震宇
	2014-07
学位授予单位	中国科学院大学
学位专业	机械电子工程
摘要	格子-波尔兹曼法（LBM）是近年来新兴的一种流体问题数值仿真方法。这种方法本身具有介观特征，使得其适用性较其他方法有所扩展。随着计算机技术的不断发展，尤其是最近一段时间并行计算设备的问世，LBM凭借其自身良好的并行性，被广泛应用于并行快速求解大型复杂流体问题。这种方法目前主要被应用于流体仿真领域。流体的优化也是近年来的学术研究热点，并被广泛应用于微流控芯片设计，汽车，船舶和航空器外形设计等领域。然而对于用LBM解决优化等复杂问题，以前并没有进行过多探讨。本课题致力于使用LBM方法求解流体拓扑优化问题。以特定函数（通常为流体能耗）为目标，以变材料密度法所确定的离散材料密度为设计变量，以格子-波尔兹曼方程（LBE）为约束条件，求解目标极小条件下的流道拓扑结构。优化过程中使用LBM求解正问题，并通过离散伴随分析，得到伴随格子-波尔兹曼方程（Adjoint-LBE或ALBE），进而求解该方程，得到目标对设计变量的敏度。将解得的目标函数值和敏度代入移动渐近线法（MMA）等数值优化方法，通过循环迭代求解，最终得到优化后的拓扑结构。本课题通过分析得到了LBE的伴随方程及伴随格子-波尔兹曼法（ALBM）求解敏度方法，基于这一方法，成功编写了基于CUDA并行计算和LBM的流体拓扑优化程序，并通过大量数值测试得到适用的优化参数。本课题还对新方法进行数值验证，在和其他方法所得结果对比中得到一致结果。在本文的最后，新方法还被用来对一些流体器件进行优化设计。本课题基于LBM拓展了现有的优化理论。新的理论和现有其他优化理论保持数值一致性的同时，具有适用性广，并行性高，求解稳定等诸多特点，是现代计算条件下的有效理论。为高效求解优化过程中的正问题和伴随问题，本课题在实施中还使用了图形处理器（GPU）并行加速计算技术。
其他摘要	The lattice Boltzmann method (LBM) is a newly developed numerical method for fluid simulation. The method, which is more general and flexible than other traditional methods, is a mesoscopic-quantity-driven simulation approach. Owing to the development of computer techniques, especially the invention of parallel computation in recent years, the LBM has been widely applied in fast computations of large-scale fluid problems considering that it is naturally parallel. The optimization of fluid is another hot research field, and is used in the design of micro-fluidic devices, vehicles, ships and aircrafts. However, hardly have any efforts been made for the LBM based fluid optimization problems in the past.This research focuses on the fluid optimization problems solved by the LBM. The objective functionals (usually the energy dissipation), the design variables (which are defined by the density type optimization method), the control equation (i.e. the lattice Boltzmann equations (LBE)) and the other constraints like the volume limitation are selected to finally determine what the topology structures of the fluid channels would be like when the objectives go to the optima. In the optimization process, the original LBM is used to solve the forward problem (i.e. simulation), the adjoint sensitivity analysis is applied to LBM to get the adjoint lattice Boltzmann equations (ALBE), which is used to calculate the objective sensitivity with respect to the design variables. Through bringing the calculated objective and sensitivity into optimizing strategies, like the method of moving asymptotes (MMA), the topology of the channel structure can be optimized after iterative computations.In this research, the ALBE and the adjoint lattice Boltzmann method (ALBM), which are used to calculate the sensitivity, are derived through the adjoint sensitivity analysis. Based on this approach, a parallel computing program for solving the fluid topology optimization problems is developed on the Compute Unified Device Architecture (CUDA). The appropriate optimization parameters are chosen according to a large amount of numerical tests. The new approach and the code are validated by numerical benchmarks, and the results are very similar to results achieved by traditional approaches. The new approach is then used to design bifurcating channels, a simple fluidic device.This research based on LBM is an extension to the current optimization theory. The new theory is proved to be highly numerically similar with the other optimization theories, meanwhile it is more general, more parallel and more stable, and is an effective theory to solve the fluid optimization problems based on the highly developed modern computing facilities. In this research, the acceleration technique is used to pursue high performances where both forward and adjoint problems are implemented on the Graphic Processing Unit (GPU).
语种	中文
文献类型	学位论文
条目标识符	http://ir.ciomp.ac.cn/handle/181722/41436
专题	中科院长春光机所知识产出
推荐引用方式 GB/T 7714	刘耕. 基于格子-波尔兹曼法的流体拓扑优化[D]. 中国科学院大学,2014.

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