ABSTRACT

In this study, we present a novel method for the topology optimization of the irregular flow domain using a parametric level set method (PLSM). Some improvement was applied on the CS-RBFs (radial basis functions with compact support)-based PLSM to make it suitable for nonuniform mesh, expanding the range field of engineering application of the PLSM. The optimization problem is solved by a gradient-based algorithm with Stokes equations as state constraints, and the objective is set to minimize the power dissipation subject to the volume constraint of flow channels. A PLSM is introduced to avoid the direct solving of the Hamilton–Jacobi partial differential equation, which can have the potential to break through the restriction of relying on structured meshes because no finite difference scheme is required. Then, a self-adaption support radius approach is presented to allow the parametric level set to be evolved on the nonuniformed mesh, which can expand the application of the PLSM to more complicated engineering problems with irregular geometric shapes. A volume integration scheme is applied during the design sensitivity analysis to calculate the shape derivatives, allowing the nucleation of new holes. Numerical examples in two and three dimensions are provided to demonstrate the effectiveness of the proposed method.

中文翻译：

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非结构化网格中参数水平集方法不规则流域拓扑优化

摘要

在这项研究中，我们提出了一种使用参数水平集方法 (PLSM) 对不规则流域进行拓扑优化的新方法。对基于CS-RBFs（具有紧支撑的径向基函数）的PLSM进行了一些改进，使其适用于非均匀网格，扩大了PLSM的工程应用范围。优化问题采用基于梯度的算法求解，以斯托克斯方程为状态约束，目标为在流道体积约束下最小化功耗。引入PLSM以避免直接求解Hamilton-Jacobi偏微分方程，由于不需要有限差分格式，因此有可能突破依赖结构化网格的限制。然后，提出了一种自适应支撑半径方法，允许在非均匀网格上演化参数水平集，这可以将PLSM的应用扩展到更复杂的几何形状不规则的工程问题。在设计敏感性分析期间应用体积积分方案来计算形状导数，从而允许新孔的成核。提供了二维和三维的数值例子来证明所提出方法的有效性。允许新空穴的成核。提供了二维和三维的数值例子来证明所提出方法的有效性。允许新空穴的成核。提供了二维和三维的数值例子来证明所提出方法的有效性。