روش جديد حل معادلات امواج سينماتيك براي جريانهاي همگرا

A new method for solving kinematic wave equations of converging flows.

In this paper, a new analytical method for solving kinematic wave equations on converging planes, in which convergence of flow lines complicates the continuity equation, is presented. Veal (1966) derived the continuity and momentum equations in unsteady state for converging planes and numerical solutions for some special cases. Numerical solution of Vealʹs equations have been reported by Woolhiser (1967, 1969} and Singh (1996) as well. This research is based on Agiralioglu method (1984) for determining the equilibrium (concentration) time on converging planes, by nondimensionalizing of Veals equations and determining the ratio of converging palne time to equilibrium to that of a rectangular plane. In the new method presented in this paper, location of wave front and the corresponding equilibrium discharge (Qe) at each time step are calculated. For translation of the calculated discharge at wave front location to the outlet, a reduction factor based on the varying degree of convergence in each time step is proposed. Multiplication of this factor by the Qe yields discharge at the outlet. This procedure must be iterated until the wave front reaches the outlet. Results of applying the new method and Woolhiser numerical technique to a representative problem are compared. The outcome indicates that the two methods present similar results, where the proposed in this paper is analytically-based and has no stability condition.