论文标题
使用EMAC公式提高了Navier-Stokes方程的投影方法的长期准确性
Improved long time accuracy for projection methods for Navier-Stokes equations using EMAC formulation
论文作者
论文摘要
我们考虑了不可压缩的Navier-Stokes方程的压力校正时间离散。我们证明了混合有限元空间离散化情况的稳定性和误差估计，尤其是，与常用的偏压表格相比，Gronwall常数对雷诺数的指数级依赖性被删除（对于足够平滑的真实解决方案），或者至少显着降低。我们还显示了该方法可以保留动量和角动量，虽然它不能保留能量，但它确实承认了能量不平等。几个数值测试表明，EMAC比非线性的其他常用配方具有优势。此外，我们将结果扩展到通常的曲柄 - 尼科尔森时间离散化。
We consider a pressure correction temporal discretization for the incompressible Navier-Stokes equations in EMAC form. We prove stability and error estimates for the case of mixed finite element spatial discretization, and in particular that the Gronwall constant's exponential dependence on the Reynolds number is removed (for sufficiently smooth true solutions) or at least significantly reduced compared to the commonly used skew-symmetric formulation. We also show the method preserves momentum and angular momentum, and while it does not preserve energy it does admit an energy inequality. Several numerical tests show the advantages EMAC can have over other commonly used formulations of the nonlinearity. Additionally, we discuss extensions of the results to the usual Crank-Nicolson temporal discretization.
