  We study the water hammer problem in the case of a sudden closing of a valve
upstream, and we consider a Lax-Wendroff finite difference scheme in order to
obtain a numerical solution of this problem. In order to establish the
approximation of this scheme to the original case, we rigorously show some
properties such as consistency, stability and weak convergence of the scheme
under reasonable conditions. In addition, we present some numerical simulations
in order to show some features of the numerical method.
