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We study the water hammer problem in the case of a sudden closing of a valveupstream, and we consider a Lax-Wendroff finite difference scheme in order toobtain a numerical solution of this problem. In order to establish theapproximation of this scheme to the original case, we rigorously show someproperties such as consistency, stability and weak convergence of the schemeunder reasonable conditions. In addition, we present some numerical simulationsin order to show some features of the numerical method.

Approximation of the non-linear water hammer problem by a Lax-Wendroff finite difference scheme