论文标题
关于双曲线初始边界值问题的完全上风方案的稳定性
On the stability of totally upwind schemes for the hyperbolic initial boundary value problem
论文作者
论文摘要
在本文中，我们提出了一种数值策略，以检查具有数值边界条件的一维完全上风方案的一步明确方向的强稳定性（或GKS稳定性）。潜在的近似连续问题是一维对流方程。使用Kreiss-lopatinskii理论研究了强稳定性。我们引入了一种新工具，即固有的Kreiss-lopatinskii决定因素，具有显着的规律性。通过采用复杂分析的标准结果，我们能够使数值方案的强稳定性在绕组数字的计算上，该数字稳健且便宜。该研究用横梁温度方案以及边界处的简化逆宽带 - 温德罗夫程序进行了说明。
In this paper, we present a numerical strategy to check the strong stability (or GKS-stability) of one-step explicit totally upwind schemes in 1D with numerical boundary conditions. The underlying approximated continuous problem is the one-dimensional advection equation. The strong stability is studied using the Kreiss-Lopatinskii theory. We introduce a new tool, the intrinsic Kreiss-Lopatinskii determinant, which possesses remarkable regularity properties. By applying standard results of complex analysis, we are able to elate the strong stability of numerical schemes to the computation of a winding number, which is robust and cheap. The study is illustrated with the Beam-Warming scheme together with the simplified inverse Lax-Wendroff procedure at the boundary.
