论文标题
纤维束拓扑优化表面流
Fiber bundle topology optimization for surface flows
论文作者
论文摘要
本文为可变设计域上的表面流提供了一种拓扑优化方法。通过这种方法，可以优化表面流的模式与用于定义模式的2个manifold之间的匹配，其中2个manifold被隐式定义在另一个固定的2个词法上，称为基本歧管。纤维束拓扑优化方法是基于使用纤维束的差异几何概念来开发表面流的拓扑结构的描述。材料分布方法用于实现表面流的模式的演变。隐式2个manifold的演变是通过同质图实现的。表面流的模式的设计变量和隐式2个manifold的设计变量由两个顺序实现的表面PDE过滤器正规化。两个表面PDE滤波器是耦合的，因为它们分别在隐式2个manifold和碱基歧管上定义。在隐式2个manifold上定义的表面Navier-Stokes方程用于描述表面流。使用一阶Sobolev空间上实现的连续伴随方法分析光纤束拓扑优化问题。提供了几个数值示例来证明这种方法，其中将粘性耗散和压降的组合用作设计目标。
This paper presents a topology optimization approach for the surface flows on variable design domains. Via this approach, the matching between the pattern of a surface flow and the 2-manifold used to define the pattern can be optimized, where the 2-manifold is implicitly defined on another fixed 2-manifold named as the base manifold. The fiber bundle topology optimization approach is developed based on the description of the topological structure of the surface flow by using the differential geometry concept of the fiber bundle. The material distribution method is used to achieve the evolution of the pattern of the surface flow. The evolution of the implicit 2-manifold is realized via a homeomorphous map. The design variable of the pattern of the surface flow and that of the implicit 2-manifold are regularized by two sequentially implemented surface-PDE filters. The two surface-PDE filters are coupled, because they are defined on the implicit 2-manifold and base manifold, respectively. The surface Navier-Stokes equations, defined on the implicit 2-manifold, are used to describe the surface flow. The fiber bundle topology optimization problem is analyzed using the continuous adjoint method implemented on the first-order Sobolev space. Several numerical examples have been provided to demonstrate this approach, where the combination of the viscous dissipation and pressure drop is used as the design objective.
