Two dimensional shape optimization using partial control and finite element method for compressible flows
Two dimensional shape optimization using partial control and finite element method for compressible flows
复制标题
使用部分控制和有限元方法对可压缩流进行二维形状优化
DOI：
10.1016/j.cma.2010.06.009
复制
发表时间：
2010
影响因子：
7.2
通讯作者：
M. Kawahara
中科院分区：
文献类型：
--
作者：
S. Nakajima;M. Kawahara
本研究的目的是确定位于可压缩粘性流中的物体的二维形状，其中所施加的流体力最小化。获得最佳形状的配方是基于最优控制理论。最佳状态被定义为这样的状态，在该状态中，由于所施加的流体力的减小，被定义为所施加的流体力的平方和的积分的性能函数被最小化。可压缩Navier-Stokes方程被视为约束方程。换句话说，物体被认为具有在纳维尔-斯托克斯方程约束下使流体力最小化的形状。使用伴随变量计算性能函数的梯度。一个加权梯度法被用作最小化算法。假设物体的体积与初始物体的体积相同。在本研究中使用的算法的情况下，无论是创建一个结构化的网格周围的表面的身体和平滑过程的梯度的计算。在这项研究中，网格重划分技术的基础上的结构化网格周围的身体改变其配置在迭代周期。对于保持体积恒定的校正，表面坐标沿径向方向沿着移动。对于状态方程和伴随方程的离散化，采用了作者（Nakajima和Kawahara [18]）先前提出的有效泡函数插值。该算法，这是众所周知的部分控制算法，被应用到数值程序，以确定坐标的移动。在梯度法的情况下，为了避免最终形状收敛到局部最小形状，新的算法，这是所谓的部分控制算法，在这项研究中。在数值研究中，均匀流场中物体的形状确定是在2D域中进行的。假设物体的初始形状为椭圆柱体。通过最小化所施加的流体力来修改形状。最后，得到了目标形状，其性能函数被约简并收敛到一个常数值。通过执行涉及使用部分控制算法的过程，获得了其性能函数进一步降低的物体的期望形状。用该方法确定了可压缩粘性流中物体的稳定形状。结果表明，采用局部控制算法可以获得最优形状。
The objective of this study is to determine the two dimensional shape of a body located in a compressible viscous flow, where the applied fluid force is minimized. The formulation to obtain the optimal shape is based on an optimal control theory. An optimal state is defined as a state, in which the performance function defined as the integration of the square sum of the applied fluid forces is minimized due to a reduction in the applied fluid forces. Compressible Navier–Stokes equations are treated as constraint equations. In other words, the body is considered to have a shape that minimizes the fluid forces under the constraint of the Navier–Stokes equations. The gradient of the performance function is computed using the adjoint variables. A weighted gradient method is used as the minimization algorithm. The volume of the body is assumed to be the same as that of the initial body. In the case of the algorithm used in this study, both the creation of a structured mesh around the surface of the body and the smoothing procedure are employed for the computation of gradient. In this study, a remeshing technique based on the structured mesh around the body changing its configuration in the iteration cycle is employed. For the correction to keep the volume constant, the surface coordinates are moved along the radial direction. For the discretization of both the state and adjoint equations, the efficient bubble function interpolation presented previously by the authors (Nakajima and Kawahara [18]) is employed. The algorithm, which is known as the partial control algorithm, is applied to the numerical procedure to determine the movement of the coordinates. In the case of the gradient method, in order to avoid the convergence of the final shape to the local minimum shape, the new algorithm, which is called the partial control algorithm, is presented in this study. In numerical studies, the shape determination of a body in a uniform flow field is carried out in 2D domains. The initial shape of the body is assumed to be an elliptical cylinder. The shape is modified by minimizing the applied fluid forces. Finally, the desired shape of a body, whose performance function is reduced and converged to a constant value, is obtained. By carrying out a procedure that involves the use of the partial control algorithm, the desired shape of a body, whose performance function is reduced further, is obtained. Stable shape determination of a body in a compressible viscous flow is carried out by using the presented method. It is indicated that the optimal shape can be obtained by using the partial control algorithm.
DOI：
10.1002/9780470549124.ch1
发表时间：
2019-10
期刊：
Optimization for Chemical and Biochemical Engineering
影响因子：
--
作者：
Xin-She Yang;Xingshi He
通讯作者：
Xin-She Yang;Xingshi He