论文标题
使用涡度方程中的稳定化对Oseen方程的压力稳定离散化
A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation
论文作者
论文摘要
对于高雷诺数制度，考虑使用压力射击有限元方法对Navier-Stokes方程的离散化。为了应对对流的主导振荡，我们以批量术语的形式添加了稳定，以基于剩余的最小二乘正方形的稳定形式稳定涡度方程，并补充了梯度跳过（某些组成部分）上元素面孔（某些组件）的惩罚项。由于稳定化基于涡度方程，因此它与压力梯度无关，这使其成为压力量。因此，我们证明了在线性化情况下，被称为OSEEN的问题中无关依赖性误差估计。实际上，我们证明了$ o（h^{k+\ frac12}）$错误估计$ l^2 $ - norm中，这是可以预期的，这是这种类型的问题。还提供了数值示例，除了确认理论结果外，还表明，本方法与经典的基于残余的SUPG稳定相比。
Discretization of Navier-Stokes' equations using pressure-robust finite element methods is considered for the high Reynolds number regime. To counter oscillations due to dominating convection we add a stabilization based on a bulk term in the form of a residual-based least squares stabilization of the vorticity equation supplemented by a penalty term on (certain components of) the gradient jump over the elements faces. Since the stabilization is based on the vorticity equation, it is independent of the pressure gradients, which makes it pressure-robust. Thus, we prove pressure-independent error estimates in the linearized case, known as Oseen's problem. In fact, we prove an $O(h^{k+\frac12})$ error estimate in the $L^2$-norm that is known to be the best that can be expected for this type of problem. Numerical examples are provided that, in addition to confirming the theoretical results, show that the present method compares favorably to the classical residual-based SUPG stabilization.
