Possibilité et limite de la dégénérescence en système différentiel du modèle mathématique des intumescences

The possibility and limit of degeneration of a mathematical surge wave model into a differential system

¹ Professeur s.c. à la Faculté des Sciences de Toulouse.
² Maître-Assistant à la Faculté des Sciences de Toulouse.

Résumé

A mathematical model of transient conditions in rivers and canals stems from modified Saint Venant equations and is a hyperbolic partial differential system for which the theory of characteristics provides an accurate solution which agrees closely with physical reality. It can also be studied by other methods, among which especially translation of the mathematical model into a finite difference and its digital processing, which have been the subject of much investigation during the last few years. The authors have considered transformation of the partial differential system into a differential one solely by discretization with respect to the space variable. A differentiation operator Dfx enables the value of the partial derivatives ∂fx/∂x to be found if f is either function Q or function H. There are various approaches to the differential system this yields, especially if there are not too many equations, in which case an analogy approach is likely to be profitable. Numerical solution of the differential equations by explicit or implicit integration schemes provides an adequate solution to the problem, provided the stability condition (cΔt/Δx) ≤ = 1 is satisfied and a sufficiently fine subdivision is taken along the space variable for the operation to eliminate any influence of the frequency and amplitude of the system's eigenvalues.