论文标题
连续和不连续的盖尔金方法的统一框架，用于求解不可压缩的Navier-Stokes方程
A unified framework of continuous and discontinuous Galerkin methods for solving the incompressible Navier--Stokes equation
论文作者
论文摘要
在本文中，我们为时间相关的不可压缩的Navier提出了一个统一的数值框架 - stokes方程，该方程产生了$ h^1 $ - ，$ h（\ text {div}）$ - 符合不连续的galerkin方法，并使用不同的粘性压力张力和损坏的压力量和压力良好。在对Galerkin空间的最低假设下，当使用隐式runge（kutta方法）进行时间离散时，半差异的稳定性就会证明。此外，我们提出了有关罚款期限的统一讨论。提出了数值实验，以将我们的方案与文献中的经典方案进行比较，既不稳定又稳定的情况。事实证明，当应用于众所周知的基准问题时，我们的方案具有竞争力，例如泰勒 - 绿色涡流，kovasznay流动，电势流，盖子驱动的腔流量以及围绕圆柱体的流动。
In this paper, we propose a unified numerical framework for the time-dependent incompressible Navier--Stokes equation which yields the $H^1$-, $H(\text{div})$-conforming, and discontinuous Galerkin methods with the use of different viscous stress tensors and penalty terms for pressure robustness. Under minimum assumption on Galerkin spaces, the semi- and fully-discrete stability is proved when a family of implicit Runge--Kutta methods are used for time discretization. Furthermore, we present a unified discussion on the penalty term. Numerical experiments are presented to compare our schemes with classical schemes in the literature in both unsteady and steady situations. It turns out that our scheme is competitive when applied to well-known benchmark problems such as Taylor--Green vortex, Kovasznay flow, potential flow, lid driven cavity flow, and the flow around a cylinder.
