A kinetic scheme for pressurized flows in non uniform pipes
This work addresses the need for accurate numerical methods in hydraulic engineering for non-uniform pipe systems, but it is an incremental application of existing kinetic schemes to a specific domain.
The paper develops a kinetic numerical scheme for simulating transient pressurized flows in water pipes with variable cross-sections, deriving the mathematical model in curvilinear coordinates and validating it through asymptotic analysis.
The aim of this paper is to present a kinetic numerical scheme for the computations of transient pressurised flows in closed water pipes with variable sections. Firstly, we detail the derivation of the mathematical model in curvilinear coordinates under some hypothesis and we performe a formal asymptotic analysis. Then the obtained system is written as a conservative hyperbolic partial differential system of equations, and we recall how to obtain the corresponding kinetic formulation based on an upwinding of the source term due to the "pseudo topography" performed in a close manner described by Perthame and al.