For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a boundary-conforming mesh becomes more difficult and time consuming. One might therefore decide to resort to an approach where individual boundary-conforming meshes are pieced together in a modular fashion to form a larger domain. This paper presents a stabilized finite element formulation for fluid and temperature equations on sliding meshes. It couples the solution fields of multiple subdomains whose boundaries slide along each other on common interfaces. Thus, the method allows to use highly tuned boundary-conforming meshes for each subdomain that are only coupled at the overlapping boundary interfaces. In contrast to standard overlapping or fictitious domain methods the coupling is broken down to few interfaces with reduced geometric dimension. The formulation consists of the following key ingredients: the coupling of the solution fields on the overlapping surfaces is imposed weakly using a stabilized version of Nitsche's method. It ensures mass and energy conservation at the common interfaces. Additionally, we allow to impose weak Dirichlet boundary conditions at the non-overlapping parts of the interfaces. We present a detailed numerical study for the resulting stabilized formulation. It shows optimal convergence behavior for both Newtonian and generalized Newtonian material models. Simulations of flow of plastic melt inside single-screw as well as twin-screw extruders demonstrate the applicability of the method to complex and relevant industrial applications.

中文翻译：

---

使用滑动网格方法在移动域上结合边界一致的有限元网格

对于大多数有限元模拟，边界一致网格在精度或效率方面具有显着优势。对于复杂的域尤其如此。然而，随着域复杂性的增加，生成符合边界的网格变得更加困难和耗时。因此，人们可能会决定采用一种方法，将符合边界的各个网格以模块化方式拼凑在一起，以形成更大的域。本文提出了滑动网格上流体和温度方程的稳定有限元公式。它耦合了多个子域的解决方案字段，这些子域的边界在公共界面上相互滑动。因此，该方法允许为仅在重叠边界界面处耦合的每个子域使用高度调谐的边界一致网格。与标准重叠或虚拟域方法相反，耦合被分解为几何尺寸减小的几个界面。该公式由以下关键成分组成：使用稳定版本的 Nitsche 方法弱强加重叠表面上的溶液场耦合。它确保公共界面处的质量和能量守恒。此外，我们允许在界面的非重叠部分施加弱狄利克雷边界条件。我们对所得的稳定配方进行了详细的数值研究。它显示了牛顿和广义牛顿材料模型的最佳收敛行为。