The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche's method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable variational formulation. In this contribution we extend the multimesh finite element method to the Navier-Stokes equations based on the incremental pressure correction scheme. For each step in the pressure correction scheme, we derive a multimesh finite element formulation with suitable stabilization terms. The overall scheme yields expected spatial and temporal convergence rates on the Taylor-Green problem, and demonstrates good agreement for the drag and lift coefficients on the Turek-Schafer benchmark (DFG benchmark 2D-3). Finally, we illustrate the capabilities of the proposed scheme by optimizing the layout of obstacles in a channel.

中文翻译：

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基于投影法的 Navier-Stokes 方程多网格有限元方法

多网格有限元方法是一种通过使用 Nitsche 方法强制界面条件来求解多个非匹配网格上的偏微分方程的技术。由于不匹配的网格会导致任意切割单元格，因此需要额外的稳定项来获得稳定的变分公式。在这个贡献中，我们将多网格有限元方法扩展到基于增量压力校正方案的 Navier-Stokes 方程。对于压力校正方案中的每一步，我们都导出了具有合适稳定项的多网格有限元公式。总体方案在 Taylor-Green 问题上产生了预期的空间和时间收敛率，并证明了 Turek-Schafer 基准（DFG 基准 2D-3）上阻力和升力系数的良好一致性。最后，