In this work, we present a multiscale model to characterize the constitutive behavior of a macroscale fluid accounting for microscale convective, transient, and obstacle effects. Thus, at the macroscale, a generalized continuum flow is considered, and the unsteady incompressible Navier-Stokes equation models the fine scale. From the concept of Representative Volume Element (RVE), we establish a connection between the macroscale and the RVE to perform computational homogenization of several scenarios accentuating the capabilities of the proposed two-scale model. The presented theory does not require classical homogenization constraints like periodicity of RVEs and separation of scales. Therefore, to analyze the constitutive relation provided by this approach, numerical simulations are performed, including several rigid obstacles with different geometries at the RVE level and the responses are compared with the classical principles.

中文翻译：

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流体流动核算惯性效应中刚性障碍本构关系的两种尺度分析方法

在这项工作中，我们提出了一个多尺度模型来描述宏观尺度对流，瞬态和障碍物效应的宏观尺度流体的本构行为。因此，在宏观尺度上，要考虑广义的连续流，并且不稳定的不可压缩的Navier-Stokes方程对精细尺度进行建模。从具有代表性的体积元素（RVE）的概念出发，我们在宏量表和RVE之间建立了连接，以执行几种方案的计算均质化，从而增强了所提出的两尺度模型的功能。提出的理论不需要经典的均质化约束，如RVE的周期性和标度分离。因此，为了分析这种方法提供的本构关系，进行了数值模拟，