Approximation of the non-linear water hammer problem by a Lax-Wendroff finite difference scheme
Numerical Analysis
2023-03-31 v3 Numerical Analysis
Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.2212.00112,
title = {Approximation of the non-linear water hammer problem by a Lax-Wendroff finite difference scheme},
author = {Hugo Carrillo-Lincopi and Alden Waters and Teke Xu},
journal= {arXiv preprint arXiv:2212.00112},
year = {2023}
}
Comments
30 pages, 4 figures