We introduce a new regularization model for incompressible fluid flow, which is a regularization of the EMAC (energy, momentum, and angular momentum conserving) formulation of the Navier–Stokes equations (NSE) that we call EMAC-Reg. The EMAC formulation has proved to be a useful formulation because it conserves energy, momentum, and angular momentum even when the divergence constraint is only weakly enforced. However, it is still a NSE formulation and so cannot resolve higher Reynolds number flows without very fine meshes. By carefully introducing regularization into the EMAC formulation, we create a model more suitable for coarser mesh computations but that still conserves the same quantities as EMAC, i.e., energy, momentum, and angular momentum. We show that EMAC-Reg, when semi-discretized with a finite element spatial discretization is well-posed and optimally accurate. Numerical results are provided that show EMAC-Reg is a robust coarse mesh model.

中文翻译：

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不可压缩流正则化模型的能量、动量和角动量守恒方案

我们为不可压缩流体流动引入了一种新的正则化模型，它是我们称之为 EMAC-Reg 的 Navier-Stokes 方程 (NSE) 的 EMAC（能量、动量和角动量守恒）公式的正则化。EMAC 公式已被证明是一个有用的公式，因为即使在散度约束只是很弱的情况下，它也能保持能量、动量和角动量。但是，它仍然是 NSE 公式，因此如果没有非常精细的网格，则无法解析更高的雷诺数流。通过仔细地将正则化引入 EMAC 公式，我们创建了一个更适合粗网格计算的模型，但仍保留与 EMAC 相同的量，即能量、动量和角动量。我们展示了 EMAC-Reg，当使用有限元空间离散化进行半离散化时，空间离散化是适定的并且是最优准确的。提供的数值结果表明 EMAC-Reg 是一种稳健的粗网格模型。