| Abstract: | Based on Saint-Venant (shallow water) equations, in this paper the mathematical model of wreck events produced by dam collapse is constructed. A two-layer difference scheme with non-linear regularisation is used for the numerical solution of the aforementioned model. The convergence of this difference scheme in Eulerian variables with non-linear regularisation to the smooth solutions of one-dimensional Saint-Venant equations are considered for a Cauchy problem with periodic (in spatial variables) solutions. The proof of difference scheme convergence is conducted using the energetic method. The existence and uniqueness of the difference scheme solution is proved. That the difference scheme converges in mesh norm $L_2$ with speed $O\lpar h^2\rpar$ in the class of sufficiently smooth solutions of the difference scheme is also proved. |
