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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Two dimensional shape optimization using partial control and finite element method for compressible flows
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Two dimensional shape optimization using partial control and finite element method for compressible flows

机译：基于局部控制和有限元方法的可压缩流二维形状优化

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摘要

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 [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.
机译：这项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，在该形状中，施加的流体力最小。获得最佳形状的公式是基于最佳控制理论的。最佳状态被定义为这样一种状态，其中，由于所施加的流体力的减小而使被定义为所施加的流体力的平方和的积分的性能函数最小化的状态。可压缩的Navier-Stokes方程被视为约束方程。换句话说，在Navier-Stokes方程的约束下，可以认为物体具有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。加权梯度法用作最小化算法。假定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，围绕身体表面的结构化网格的创建和平滑过程都用于计算梯度。在这项研究中，采用了基于围绕身体的结构化网格在迭代周期中更改其配置的重新网格化技术。为了保持体积恒定进行校正，表面坐标沿径向方向移动。对于状态方程和伴随方程的离散化，采用了作者先前提出的有效气泡函数插值[18]。该算法（称为部分控制算法）被应用于数值过程，以确定坐标的运动。在梯度方法的情况下，为了避免最终形状收敛到局部最小形状，本研究提出了一种新的算法，称为局部控制算法。在数值研究中，在二维流域中进行均匀流场中物体的形状确定。假定物体的初始形状为椭圆圆柱。通过最小化施加的流体力来修改形状。最终，获得期望的身体形状，其功能函数降低并收敛到恒定值。通过执行涉及使用部分控制算法的过程，可以获得期望的身体形状，其功能函数进一步降低。通过使用提出的方法，可压缩粘性流中物体的稳定形状确定。结果表明，采用局部控制算法可获得最佳形状。

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