Stable numerical calculation of critical flow (Q2751296)

In the neighborhood of the points in the flow field in an open canal where critical flow occurs, stability of each numerical scheme becomes problematic. The goal of this paper is to give a stable numerical algorithm for stationary and nonstationary one-dimensional flow which successfully solves subcritical, supercritical as well as critical flow. The stability of theNEWLINEnumerical algorithm is verified only by numerous numerical examples and notNEWLINEexactly, because critical flow is inherently nonlinear process as it is modelled by the pair of Saint-Venant partial differential equations, but the methods for obtaining the stability limits of numerical schemes in the literature (Furier's method,for example) may be applied to linear or linearized mathematical models only.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00049].