Reduced order models for the incompressible Navier-Stokes equations on collocated grids using a ‘discretize-then-project’ approach,International Journal for Numerical Methods in Fluids

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Reduced order models for the incompressible Navier-Stokes equations on collocated grids using a ‘discretize-then-project’ approach
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-04-28 , DOI: 10.1002/fld.4994
S. Kelbij Star _{1,

2} , Benjamin Sanderse ₃ , Giovanni Stabile ₄ , Gianluigi Rozza ₄ , Joris Degroote ₂

Affiliation

A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This ‘discretize-then-project’ approach requires no pressure stabilization technique (even though the pressure term is present in the ROM) nor a boundary control technique (to impose the boundary conditions at the ROM level). These are two main advantages compared to existing approaches. The fully discrete FOM is obtained by a finite volume discretization of the incompressible Navier-Stokes equations on a collocated grid, with a forward Euler time discretization. Two variants of the time discretization method, the inconsistent and consistent flux method, have been investigated. The latter leads to divergence-free velocity fields, also on the ROM level, whereas the velocity fields are only approximately divergence-free in the former method. For both methods, accurate results have been obtained for test cases with different types of boundary conditions: a lid-driven cavity and an open-cavity (with an inlet and outlet). The ROM obtained with the consistent flux method, having divergence-free velocity fields, is slightly more accurate but also slightly more expensive to solve compared to the inconsistent flux method. The speedup ratio of the ROM and FOM computation times is the highest for the open cavity test case with the inconsistent flux method.

中文翻译：

使用“离散然后投影”方法的并置网格上不可压缩 Navier-Stokes 方程的降阶模型

通过基于完全（空间和时间）离散全阶模型 (FOM) 公式执行 Galerkin 投影，开发了一种用于不可压缩流的新型降阶模型 (ROM)。这种“离散然后项目”的方法不需要压力稳定技术（即使压力项存在于 ROM 中），也不需要边界控制技术（在 ROM 级别施加边界条件）。与现有方法相比，这是两个主要优点。完全离散 FOM 是通过不可压缩 Navier-Stokes 方程在并置网格上的有限体积离散化获得的，使用前向欧拉时间离散化。已经研究了时间离散化方法的两种变体，即不一致和一致通量方法。后者导致无发散速度场，也在 ROM 级别，而在前一种方法中，速度场只是近似无发散。对于这两种方法，已针对具有不同类型边界条件的测试用例获得了准确的结果：盖子驱动的空腔和开放的空腔（带有入口和出口）。使用一致通量方法获得的 ROM 具有无发散速度场，与不一致通量方法相比，精度稍高，但求解成本也稍高。对于使用不一致通量方法的开腔测试用例，ROM 和 FOM 计算时间的加速比最高。一个盖子驱动的空腔和一个开放的空腔（带有入口和出口）。与不一致通量方法相比，使用一致通量方法获得的 ROM 具有无发散速度场，精度稍高，但求解成本也稍高。对于使用不一致通量方法的开腔测试用例，ROM 和 FOM 计算时间的加速比最高。一个盖子驱动的空腔和一个开放的空腔（带有入口和出口）。使用一致通量方法获得的 ROM 具有无发散速度场，与不一致通量方法相比，精度稍高，但求解成本也稍高。对于使用不一致通量方法的开腔测试用例，ROM 和 FOM 计算时间的加速比最高。

更新日期：2021-07-01

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