A kinetic scheme for unsteady pressurised flows in closed water pipes

TL;DR

This paper introduces a kinetic numerical scheme for simulating unsteady pressurized flows in closed water pipes, providing a new approach that aligns well with existing industrial solutions for water hammer problems.

Contribution

The paper develops a kinetic scheme for pressurized pipe flows, ensuring accurate upwinding of source terms and validation against industry-standard methods.

Findings

The kinetic scheme accurately models transient pressurized flows.

Results agree closely with the Allievi equation-based industrial code.

The method effectively captures water hammer phenomena.

Abstract

The aim of this paper is to present a kinetic numerical scheme for the computations of transient pressurised flows in closed water pipes. Firstly, we detail the mathematical model written as a conservative hyperbolic partial differentiel system of equations, and the we recall how to obtain the corresponding kinetic formulation. Then we build the kinetic scheme ensuring an upwinding of the source term due to the topography performed in a close manner described by Perthame et al. using an energetic balance at microscopic level for the Shallow Water equations. The validation is lastly performed in the case of a water hammer in a uniform pipe: we compare the numerical results provided by an industrial code used at EDF-CIH (France), which solves the Allievi equation (the commonly used equation for pressurised flows in pipes) by the method of characteristics, with those of the kinetic scheme. It appears that they are in a very good agreement.