论文标题
不可压缩的Navier-Stokes模拟使用EMAC配方的较长时间准确性
Longer time accuracy for incompressible Navier-Stokes simulations with the EMAC formulation
论文作者
论文摘要
在本文中，我们考虑了不可压缩的Navier-Stokes（NS）方程的最近引入的EMAC公式，这是唯一已知的NS公式，可以保留能量，动量和角度动量时，当差异约束仅被弱执行时。自引入以来，EMAC配方已成功用于各种流体动力学问题。我们证明，使用EMAC配方的离散化可能比基于常用的偏度对称配方的构建的分散率更好，这是通过得出EMAC的更好的更长的时间误差估计：而对于使用偏压配方的方案的经典结果，则依赖于$ \ exp（c \ cdot for cdot rep re re the $ cdot the $ cdot the $ cdot the $ cdot the $）估计不受此明确指数依赖性对雷诺数的依赖性。此外，由于{不正确的处理线性动量，角动量和能量诱导} $ l^2 $速度误差的下限，因此EMAC如何在其速度误差上接受较小的下限，并且更准确地处理这些量。还给出了通道流的数值测试的结果，这也给出了圆柱体和2D开尔文 - 螺旋的不稳定性，这两者都表明，随着雷诺数数量变大，并且在较长的仿真时间中，EMAC比偏度对称配方的优势增加了。
In this paper, we consider the recently introduced EMAC formulation for the incompressible Navier-Stokes (NS) equations, which is the only known NS formulation that conserves energy, momentum and angular momentum when the divergence constraint is only weakly enforced. Since its introduction, the EMAC formulation has been successfully used for a wide variety of fluid dynamics problems. We prove that discretizations using the EMAC formulation are potentially better than those built on the commonly used skew-symmetric formulation, by deriving a better longer time error estimate for EMAC: while the classical results for schemes using the skew-symmetric formulation have Gronwall constants dependent on $\exp(C\cdot Re\cdot T)$ with $Re$ the Reynolds number, it turns out that the EMAC error estimate is free from this explicit exponential dependence on the Reynolds number. Additionally, it is demonstrated how EMAC admits smaller lower bounds on its velocity error, since {incorrect treatment of linear momentum, angular momentum and energy induces} lower bounds for $L^2$ velocity error, and EMAC treats these quantities more accurately. Results of numerical tests for channel flow past a cylinder and 2D Kelvin-Helmholtz instability are also given, both of which show that the advantages of EMAC over the skew-symmetric formulation increase as the Reynolds number gets larger and for longer simulation times.
