We introduce a new regularization model for incompressible fluid flow, which is a regularization of the EMAC formulation of the Navier-Stokes equations (NSE) that we call EMAC-Reg. The EMAC (energy, momentum, and angular momentum conserving) 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.
翻译:我们引入了一种新的不可压缩流体的正规化模式,这是将我们称之为EMAC-Reg的纳维-斯托克方程式(NSE)的EMAC公式正规化。EMAC(能源、动力和角动力保护)的配方已证明是一种有用的配方,因为它保护了能源、动力和角动力,即使差异限制只是执行不力。然而,它仍然是一个NSE的配方,因此无法在没有非常精细的模件的情况下解决更高的Reynolds数量流。通过在 EMAC的配方中仔细引入正规化,我们创建了一种更适合粗略中位计算的模式,但仍然保存着与EMAC(即能源、动力和角动力保护)相同的数量。我们表明,当半分解与有限元素的空间离散状态的半分解时,EMAC-Reg是精准的。我们提供了数字结果,显示EMAC-Reg是一种坚固的粗微网格模型。