论文标题
骨骼稳定的差异 - 抗逆转的B型链接离散因素，用于高度对流不可压缩的流动问题
Skeleton-stabilized divergence-conforming B-spline discretizations for highly advective incompressible flow problems
论文作者
论文摘要
我们考虑了一种稳定方法，用于不可压缩的Navier的差异构成B-Spline离散 - Stokes问题，其中速度场的高阶正常衍生物的跳跃在整个内部网格方面受到惩罚。我们证明该方法是压力稳定，一致和能量稳定的，我们展示了如何选择该方法中出现的稳定参数，以便在交叉方向和扩散为主导的方向上避免过多的数值耗散。 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.
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.
