在涡量方程中使用稳定化的Oseen方程的压力鲁棒离散
A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation
摘要：
本文考虑了高雷诺数区用压力鲁棒有限元法离散Navier-Stokes方程的问题。为了对抗由于主导对流的振荡，我们添加了一个稳定的基础上，在一个基于残差的最小二乘稳定的涡量方程的形式补充的惩罚项（某些组件）的梯度跳跃的元素面的基础上的散装项。由于稳定是基于涡量方程，它是独立的压力梯度，这使得它的压力鲁棒。因此，我们证明了压力无关的误差估计的线性化的情况下，被称为Oseen的问题。事实上，我们证明了一个$O(h^{k+\frac12})$误差估计的$L^2$规范，这是已知的最好的，可以预期这种类型的问题。数值算例表明，除了证实理论结果外，该方法与经典的基于残差的SUPG镇定方法相比具有良好的性能。
英文摘要：
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.
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