  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.
