In this work, we study the performance of some local projection-based solvers in the Large Eddy Simulation (LES) of laminar and turbulent flows governed by the incompressible Navier–Stokes Equations (NSE). On one side, we focus on a high-order term-by-term stabilization Finite Element (FE) method that has one level, in the sense that it is defined on a single mesh, and in which the projection-stabilized structure of standard Local Projection Stabilization (LPS) methods is replaced by an interpolation-stabilized structure. The interest of LPS methods is that they ensure a self-adapting high accuracy in laminar regions of turbulent flows, which turns to be of overall optimal high accuracy if the flow is fully laminar. On the other side, we propose a new Reduced Basis (RB) Variational Multi-Scale (VMS)-Smargorinsky turbulence model, based upon an empirical interpolation of the sub-grid eddy viscosity term. This method yields dramatical improvements of the computing time for benchmark flows. An overview about known results from the numerical analysis of the proposed methods is given, by highlighting the used mathematical tools. In the numerical study, we have considered two well known problems with applications in industry: the (3D) turbulent flow in a channel and the (2D/3D) recirculating flow in a lid-driven cavity.

中文翻译：

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评估基于局部投影的自适应解决方案，用于层流和湍流工业流

在这项工作中，我们研究了由不可压缩的Navier–Stokes方程（NSE）控制的层流和湍流的大涡模拟（LES）中一些基于局部投影的求解器的性能。一方面，我们专注于具有一个级别的高阶逐项稳定有限元（FE）方法，即它是在单个网格上定义的，并且其中标准的投影稳定结构局部投影稳定（LPS）方法由插值稳定的结构代替。LPS方法的兴趣在于，它们可确保在湍流的层流区域中实现自适应的高精度，如果流为完全层流，则这将成为总体上最佳的高精度。另一方面，我们提出了一个新的简化基（RB）变分多尺度（VMS）-Smargorinsky湍流模型，基于子网格涡流粘度项的经验插值。这种方法极大地提高了基准流的计算时间。通过突出显示所使用的数学工具，对所提出方法进行数值分析得出的已知结果进行了概述。在数值研究中，我们考虑了工业应用中的两个众所周知的问题：通道中的（3D）湍流和盖驱动腔中的（2D / 3D）再循环流。