We consider a stabilization method for divergence-conforming B-spline discretizations of the incompressible Navier--Stokes problem wherein jumps in high-order normal derivatives of the velocity field are penalized across interior mesh facets. We prove that this method is pressure robust, consistent, and energy stable, and we show how to select the stabilization parameter appearing in the method so that excessive numerical dissipation is avoided in both the cross-wind direction and in the diffusion-dominated regime. We examine the efficacy of the method using a suite of numerical experiments, and we find the method yields optimal $\textbf{L}^2$ and $\textbf{H}^1$ convergence rates for the velocity field, eliminates spurious small-scale structures that pollute Galerkin approximations, and is effective as an Implicit Large Eddy Simulation (ILES) methodology.
翻译:我们考虑的是无法压缩的导航-Stokes问题分解成异形的B-喷射分解的稳定方法,即速度场高阶正常衍生物的跳跃在内部网格方面受到约束。我们证明这种方法是压力强、一贯和能源稳定的,我们展示了如何选择方法中出现的稳定参数,以避免在横风方向和扩散占主导地位的制度中出现过量的消散。我们使用一组数字实验来审查该方法的功效,我们发现该方法产生速度场的最佳汇合率$\textbf{L ⁇ 2$和$\textbf{H ⁇ 1$,消除了污染加列金近似的虚假小型结构,并作为一种不透明的大型模拟(ILES)方法有效。