Stable Numerical Calculation of Critical Flow
Jovan Stefanovski
Abstract
In the neighborhood of the points in the flow field in open canal whe-
re critical flow occurs, stability of each numerical scheme becomes proble-
matic. 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 the
numerical algorithm is verified only by numerous numerical examples and not
exactly, becouse critical flow is inherently nonlinear process as it is mo-
delled by the pair of Saint - Venan partial differential equations but the
methods for obtaining the stability limits of numerical schemes in the li-
terature (Furier's method,for example) may be applied to linear or lineari-
zed mathematical models only.