A multiscale procedure to couple a mesoscale discrete particle model and a macroscale continuum model of incompressible fluid flow is proposed in this study. We call this procedure the mesoscopic bridging scale (MBS) method since it is developed on the basis of the bridging scale method for coupling molecular dynamics and finite element models [G.J. Wagner, W.K. Liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys. 190 (2003) 249-274]. We derive the governing equations of the MBS method and show that the differential equations of motion of the mesoscale discrete particle model and finite element (FE) model are only coupled through the force terms. Based on this coupling, we express the finite element equations which rely on the Navier-Stokes and continuity equations, in a way that the internal nodal FE forces are evaluated using viscous stresses from the mesoscale model. The dissipative particle dynamics (DPD) method for the discrete particle mesoscale model is employed. The entire fluid domain is divided into a local domain and a global domain. Fluid flow in the local domain is modeled with both DPD and FE method, while fluid flow in the global domain is modeled by the FE method only. The MBS method is suitable for modeling complex (colloidal) fluid flows, where continuum methods are sufficiently accurate only in the large fluid domain, while small, local regions of particular interest require detailed modeling by mesoscopic discrete particles. Solved examples - simple Poiseuille and driven cavity flows illustrate the applicability of the proposed MBS method.

中文翻译：

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流体的细观桥接尺度法与连续介质有限元法耦合耗散粒子动力学

本研究提出了一种将中尺度离散粒子模型和不可压缩流体流动的宏观连续介质模型耦合的多尺度程序。我们将此过程称为细观桥接尺度 (MBS) 方法，因为它是在用于耦合分子动力学和有限元模型的桥接尺度方法的基础上开发的 [GJ Wagner，WK Liu，使用桥接尺度分解进行原子和连续模拟的耦合, J. 计算。物理。190 (2003) 249-274]。我们推导出 MBS 方法的控制方程，并表明中尺度离散粒子模型和有限元 (FE) 模型的运动微分方程仅通过力项耦合。基于这种耦合，我们表达了依赖于 Navier-Stokes 和连续性方程的有限元方程，以使用来自中尺度模型的粘性应力评估内部节点有限元力的方式。离散粒子中尺度模型采用耗散粒子动力学 (DPD) 方法。整个流体域分为局部域和全局域。局部域中的流体流动采用 DPD 和有限元方法建模，而全局域中的流体流动仅采用有限元方法建模。MBS 方法适用于对复杂（胶体）流体流动进行建模，其中连续介质方法仅在大流体域中足够准确，而特别感兴趣的小局部区域需要通过细观离散粒子进行详细建模。解决的例子 - 简单的泊肃叶流和驱动腔流说明了所提出的 MBS 方法的适用性。