A numerical solution of the water-hammer problem based on the least-squares method with a new adaptive refinement technique

M. Lashkarbolok

Department of Civil Engineering, Faculty of Engineering, Golestan University, Aliabad Katoul, Iran

Abstract: The manuscript presents the results of an application of a numerical method to solve one-dimensional hyperbolic equations. These equations simulate the dynamics of a liquid in a pipe with varying cross-sections. The equations are written in terms of pressure-head and discharge. Radial-basis functions and least-squares optimization are used for the numerical simulation. This numerical method is specialized for working with arbitrary nodal distribution in the problem domain. The basics of the application of the numerical method were introduced in our previous work. In the current work, we updated previously applied methods by means of getting rid of the time-marching approach and applying another adaptive refinement technique. Three cases of the simulations of the reservoir-pipe-valve system are described, indicating that the sharp time-gradient phenomenon is reproduced by the model.

Key words: space-time formulation, radial basis functions, adaptive refinement, node-movement strategy, least squares technique.

MSC: 58D30

Received: 28.10.2023
Revised: 22.05.2024
Accepted: 26.08.2024

DOI: 10.15372/SJNM20240404

 English version: Numerical Analysis and Applications, 2024, 17:4, 339–357