A Novel Adaptive Refinement Technique for Least-Squares-Based Numerical Solution of the Water–Hammer Problem

The manuscript presents the results of the application of a numerical method to solve one-dimensional hyperbolic equations. These equations simulate the dynamics of 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 (1) getting rid of the time-marching approach and (2) applying a new adaptive refinement. 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.