This work is concerned with the shape optimal design of an obstacle immersed in the Stokes–Brinkman fluid, which is also coupled with a thermal model in the bounded domain. The shape optimal problem is formulated and analyzed based on the framework of the continuous adjoint method, with the advantage that the computing cost of the gradients and sensitivities is independent of the number of design variables. Then, the velocity method is utilized to describe the domain deformation, and the Eulerian derivative for the cost functional is established by applying the differentiability of a minimax problem based on the function space parametrization technique. Moreover, an iterative algorithm is proposed to optimize the boundary of the obstacle in order to reduce the total dissipation energy. Finally, numerical examples are presented to illustrate the feasibility and effectiveness of our method.

中文翻译：

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传热模型的Stokes-Brinkman方程形状优化设计的迭代方法

这项工作与浸入Stokes-Brinkman流体中的障碍物的形状优化设计有关，该障碍物还与有限域中的热模型耦合。基于连续伴随方法的框架，对形状最优问题进行了表述和分析，其优点是梯度和灵敏度的计算成本与设计变量的数量无关。然后，利用速度方法描述区域变形，并基于函数空间参数化技术，通过应用极小极大问题的可微性，建立了成本函数的欧拉导数。此外，提出了一种迭代算法来优化障碍物的边界，以减少总耗散能量。最后，