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.

翻译：在本文中,我们提出了一个数字战略,以检查1D的单步直线完全上风的稳妥性(或GKS稳定性),带有数字边界条件。潜在的持续问题是单维对流方程。使用Kreiss-Lopatinskii理论研究强大的稳定性。我们引入了一个新的工具,即具有显著规律特性的内在Kreiss-Lopatinskii决定因素。通过应用复杂分析的标准结果,我们可以将数字法的稳妥性与一个稳健和廉价的通风数字的计算相提并论。该研究与Baam-Warming计划以及边界的简化的Lax-Wendroff程序一起进行。