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

TL;DR

This paper investigates the numerical approximation of the water hammer problem caused by sudden valve closure using a Lax-Wendroff finite difference scheme, establishing its theoretical properties and demonstrating its effectiveness through simulations.

Contribution

The paper provides a rigorous analysis of the Lax-Wendroff scheme's consistency, stability, and convergence for the water hammer problem, along with numerical validation.

Findings

The scheme is consistent, stable, and weakly convergent under certain conditions.

Numerical simulations illustrate the scheme's capability to accurately model water hammer phenomena.

Abstract

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.