水平集与灵敏度分析相结合的流体形状识别与优化方法

Fluid Shape Recognition and Optimization by Combining Level Set Method with Sensitivity Analysis

针对流体拓扑优化很难得到较为精确结果的问题,将水平集方法与灵敏度分析方法相结合,发展了一种可用于流动形状识别的改进水平集优化方法。为实现水平集法向速度由界面到整个水平集函数求解区域的准确扩展,首先借助快速行进法,将法向速度由流体区向固体区扩展,然后经求解偏微分方程向整个设计区域扩展。通过求解二元二次方程组提取界面,采用无需样条参数化网格重构方法实现了流体区域内网格的重新划分,从而有效提高了物理场控制方程的求解精度。对Navier-Stokes和Stokes流动形状识别问题的研究表明:所发展的方法可以直接、较准确地求出边界上的法向速度,且将界面附近的法向速度准确地沿界面的法线方向扩展到整个水平集函数求解区域;最终,通过有效处理拓扑和形状优化过程中的拓扑变化识别出目标形状。

An improved level set optimization method for shape recognition of fluid was developed by combining the improved level set method with the sensitivity analysis since the fluid topology optimization was difficult to obtain accurate results.To achieve the accurate extension of level set normal velocity from the fluid/solid interface to the entire level set solving domain,the normal velocity was extended firstly from fluid domain to solid domain by the fast marching method,and then it was extended to the whole design domain by solving the partial differential equation.In the optimization process,to improve the solving accuracy of the physical field equations,the interface was obtained by solving the system of binary quadratic equations,and the meshes in the fluid domain were remeshed by using a spline-free parameterization remeshing method.Through investigating an example on the shape recognition of Navier-Stokes and Stokes flows,the results show that the developed method can directly obtain an accurate normal velocity on the fluid/solid interface and precisely extend the normal velocity to the whole level set solving domain along the normal direction of the interface,and the method can also effectively handle the topology change in the shape-topology optimization procedure and achieve the recognition of the target shape.